CN113703310A - Decoupling method and device for vibration isolation platform, computer equipment and storage medium - Google Patents

Decoupling method and device for vibration isolation platform, computer equipment and storage medium Download PDF

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CN113703310A
CN113703310A CN202110859678.5A CN202110859678A CN113703310A CN 113703310 A CN113703310 A CN 113703310A CN 202110859678 A CN202110859678 A CN 202110859678A CN 113703310 A CN113703310 A CN 113703310A
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rotation
equation
initial
vibration isolation
isolation platform
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CN113703310B (en
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伍康
李振兴
储迅潮
王力军
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Tsinghua University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The application relates to a decoupling method and device for a vibration isolation platform, computer equipment and a storage medium. The method comprises the following steps: acquiring previous output data and determining a deviation value between the previous output data and expected data; when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable; performing feedback linearization processing based on the auxiliary control variable to obtain a plurality of leg forces; transmitting the plurality of leg forces to the vibration isolation platform to obtain current output data; and entering next cycle iteration, taking the current output data as the previous output data corresponding to the next iteration, returning to the step of determining the deviation value, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a complete decoupling state, and further improve the decoupling effect.

Description

Decoupling method and device for vibration isolation platform, computer equipment and storage medium
Technical Field
The present application relates to the field of decoupling technology for vibration isolation platforms, and in particular, to a decoupling method and apparatus for a vibration isolation platform, a computer device, and a storage medium.
Background
With the development of the decoupling technology of the vibration isolation platform, when a Stewart (Stewart platform) parallel robot is used as the vibration isolation platform, decoupling control is usually realized based on the simplified mathematical relationship between the angular acceleration and the second derivative of the euler angle, wherein the simplified mathematical relationship between the angular acceleration and the second derivative of the euler angle is obtained by neglecting the first derivative of the euler angle.
However, there is a non-diagonal matrix relationship between the first derivative of the euler angle and the angular velocity, i.e. the first derivative of the euler angle cannot be equal to the angular velocity, and therefore, neglecting the first derivative of the euler angle in the angular acceleration formula may result in poor decoupling effect of each degree of freedom in the vibration isolation platform.
Disclosure of Invention
In view of the above, it is necessary to provide a decoupling method and apparatus for a vibration isolation platform, a computer device, and a storage medium.
A method of decoupling a vibration isolation platform, the method comprising:
acquiring previous output data obtained through previous measurement of the vibration isolation platform, and determining a deviation value between the previous output data and expected data; the previous output data comprises the freedom degree information of an upper disc in the vibration isolation platform; when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable; performing feedback linearization processing on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform; transmitting the plurality of leg forces to the vibration isolation platform so that the vibration isolation platform performs current measurement based on the plurality of leg forces to obtain current output data; and entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state.
A decoupling assembly for a vibration isolation platform, the assembly comprising:
the determining module is used for acquiring previous output data obtained through previous measurement of the vibration isolation platform and determining a deviation value between the previous output data and expected data; the previous output data comprises the freedom degree information of an upper disc in the vibration isolation platform;
the first obtaining module is used for processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable when the deviation value is larger than a deviation threshold value;
the second obtaining module is used for carrying out feedback linearization processing on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform;
the transmission module is used for transmitting the plurality of supporting leg forces to the vibration isolation platform so that the vibration isolation platform can carry out current measurement based on the plurality of supporting leg forces to obtain current output data;
and the iteration module is used for entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state.
A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the decoupling method of the vibration isolation platform as described in any one of the above when executing the computer program.
A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, implements the decoupling method of a vibration isolation platform as in any one of the above.
The decoupling method, the decoupling device, the computer equipment and the storage medium of the vibration isolation platform acquire previous output data which is obtained through previous measurement of the vibration isolation platform and comprises the freedom degree information of an upper disc in the vibration isolation platform, and determine a deviation value between the previous output data and expected data; and when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable. Because the translational control law and the rotational control law in the control matrix respectively correspond to the translational degree of freedom and the rotational degree of freedom, auxiliary control variables containing error information of the translational degree of freedom and the rotational degree of freedom can be obtained, and feedback linearization processing is carried out on the basis of the auxiliary control variables to obtain a plurality of leg forces corresponding to the vibration isolation platform; transmitting the plurality of leg forces to the vibration isolation platform so that the vibration isolation platform performs current measurement based on the plurality of leg forces to obtain current output data; and entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state. Therefore, complete decoupling between the translational degrees of freedom and complete decoupling between the rotational degrees of freedom can be ensured, and the decoupling effect of each degree of freedom in the vibration isolation platform is further improved.
Drawings
FIG. 1 is a diagram of an exemplary decoupling method for vibration isolation platforms;
FIG. 2 is a schematic flow diagram of a decoupling method for a vibration isolation platform according to an embodiment;
FIG. 3 is a schematic diagram of a three-dimensional rotation process in one embodiment;
FIG. 4 is a flow chart of a control scheme for the vibration isolation platform according to one embodiment;
FIG. 5 is a flow chart illustrating steps of constructing a control matrix according to an embodiment;
FIG. 6 is a graphical illustration of the relationship between the angular velocity of the inertial system and the derivative of the Euler angle in one embodiment;
FIG. 7 is a flowchart illustrating the step of determining a pan control law in one embodiment;
FIG. 8 is a flowchart illustrating the steps of determining a rotation control law in one embodiment;
FIG. 9 is a flowchart illustrating the steps of determining a rotation control law in another embodiment;
FIG. 10 is a block diagram of the decoupling assembly of the vibration isolation platform according to one embodiment;
FIG. 11 is a diagram illustrating an internal structure of a computer device in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The decoupling method of the vibration isolation platform can be applied to the application environment shown in fig. 1. Wherein the vibration isolation platform 102 communicates with the computer device 104 via a network. The vibration isolation platform 102 sends the previous output data obtained by the previous measurement to the computer device 104, and the computer device 104 obtains the previous output data and determines a deviation value between the previous output data and the expected data; the previous output data includes the degree of freedom information of the upper puck in the isolation platform 102; when the deviation value is greater than the deviation threshold value, the computer device 104 processes the deviation value based on a control matrix composed of a translation control law and a rotation control law to obtain an auxiliary control variable; the computer device 104 performs feedback linearization processing on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform; the computer device 104 transmits the leg forces to the vibration isolation platform 102, so that the vibration isolation platform performs current measurement based on the leg forces to obtain current output data; the computer device 104 enters the next iteration, and takes the current output data as the previous output data corresponding to the next iteration, and returns to the step of determining the deviation value between the previous output data and the expected data to continue to be executed until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disk in the vibration isolation platform 102 are in the decoupling state. The computer device 104 may be implemented as a stand-alone server or a server cluster composed of a plurality of servers.
In one embodiment, as shown in fig. 2, a decoupling method for vibration isolation platform is provided, which is illustrated by applying the method to the computer device 104 in fig. 1, and includes the following steps:
step S202, obtaining previous output data obtained through previous measurement of the vibration isolation platform, and determining a deviation value between the previous output data and expected data; the previous output data includes information on the degree of freedom of the upper disk in the vibration isolation platform.
As shown in fig. 1, the isolation Platform 102 is a six-axis isolator, which generally comprises an upper disc (Platform)1021, a lower disc (Base)1022, and six legs 1023. Each leg is in UPS configuration, i.e. the leg is a Prismatic linear drive (prism Joint), the upper end of the leg is connected to the upper disc 1021 by a Spherical hinge 1024(Spherical Joint), and the lower end of the leg is connected to the lower disc 1022 by a hooke Joint 1025(Universal Joint). Wherein, O-XOYOZOThe system being an inertial coordinate system, OP-XPYPZPSystem and OB-XBYBZBThe system is a loading system fixedly connected with the upper disc and the lower disc respectively. When the environment has vibration interference, both carrier systems move relative to the inertial system. The reasonable driving of six legs can lead the O of the upper discP-XPYPZPThe system is kept stationary relative to the inertial system, thereby achieving vibration isolation. The vibration isolation platform has six linearly independent space drives, namely six degrees of freedom (three translational motions and 3 rotational motions). The rotation in space is generally described by Euler angles, and when an internal rotation, X-Y-Z combined Tait-Btyan angle, such as the three-dimensional rotation process shown in FIG. 3, is used, step 1 is to rotate the phi angle about the OZ axis, so that OX rotates to O1X1OY rotated to O1Y1. Step 2 is to wind O1Y1The shaft being rotated by an angle theta such that O1X1Is rotated to O2X2，O1Z1Is rotated to O2Z2. Step 3 is to wind O2X2Rotation of the shaft
Figure BDA0003185260630000031
Angle of so that O2Y2Is rotated to O3Y3，O2Z2Is rotated to O3Z3. Therefore, the output data of the vibration isolation platform comprises six-degree-of-freedom information of the upper disc, 3 translation degrees of freedom corresponding to the x, y and z translation directions respectively, and rotation
Figure BDA0003185260630000032
The angles theta and psi correspond to 3 rotational degrees of freedom. And the output matrix of the vibration isolation platform is represented by translation and Euler angles, so the output matrix of the vibration isolation platform is as follows:
Figure BDA0003185260630000033
i.e. the output of the disc on the vibration isolation platform in the translation direction is
Figure BDA0003185260630000034
The output of the disk on the vibration isolation platform in the rotating direction is
Figure BDA0003185260630000035
Figure BDA0003185260630000036
Because, in the calculation process, the output value of the vibration isolation platform is an expression of a second derivative, namely
Figure BDA0003185260630000037
The second derivative is integrated to obtain an output matrix, and the integration step is generally completed by a combined navigation algorithm of the sensor, so that the following output data based on the vibration isolation platform are the second derivatives of the displacement and the rotation of the vibration isolation platform.
Specifically, the computer device sets desired data including desired displacement data of the upper puck and desired rotation data of the upper puck in the vibration isolation platform. The computer equipment acquires previous output data obtained by previous measurement of the vibration isolation platform, wherein the previous output data comprises previous output displacement data of an upper disc in the vibration isolation platform and previous output rotation data of the upper disc; the computer device subtracts the expected displacement data from the previous output displacement data to obtain a displacement deviation value and subtracts the expected rotation data from the previous output rotation data to obtain a rotation deviation value based on the previous output data and the expected data, and the computer device determines the deviation value based on the translation deviation value and the rotation deviation value. Wherein, the initial output data is obtained by the first measurement of the vibration isolation platform.
And step S204, when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable.
And the deviation threshold is a condition for judging whether the vibration isolation platform reaches a full decoupling state. The deviation threshold is a constant value, which is ideally zero. The translational control law is used for decoupling the translational direction, the rotational control law is used for decoupling the rotational direction, and the control matrix can be written as a diagonal matrix of 2X2, i.e. the control matrix ko(s) can be expressed as:
Figure BDA0003185260630000041
wherein, Ktra0(s) is the law of translational control, Krot0(s) is a rotation control law, and the formula relates to Laplace transformation, namely, a time domain function is transformed into a complex domain function, namely, the time domain function with an independent variable of time t is transformed into the complex domain function with the independent variable of complex frequency s after the Laplace transformation.
Specifically, the computer device sets a numerical value of a deviation threshold value, compares the determined deviation value with the deviation threshold value, and when the deviation value is greater than the deviation threshold value, the computer device acquires a control matrix formed by a translation control law and a rotation control law, processes the deviation value based on the control matrix, and acquires an auxiliary control variable; wherein the computer device determines the control matrix based on an angular acceleration relation composed of a first derivative of the euler angle and a second derivative of the euler angle.
For example, the computer device sets the value of a deviation threshold, which may be 0.1, based on the previous output data y1And expected data ydObtaining the deviation e1＝(yd-y1) (ii) a The computer equipment compares the deviation value with a deviation threshold value, and when the deviation value is larger than the deviation threshold value, the computer equipment acquires a control matrix formed by a translation control law and a rotation control law, wherein the control matrix is determined according to an angular acceleration relational expression formed by a first derivative of an Euler angle and a second derivative of the Euler angle; and acquiring the second derivative of the upper disc expected state variable
Figure BDA0003185260630000046
Determining an auxiliary control variable u based on a control matrix and an upper disk expected state variable second derivative1。
Step S206, a feedback linearization process is performed on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform.
The feedback linearization process is determined based on the generalized centrifugal force parameter, the state variable first derivative, the interference item parameter, the upper disc gravity parameter in the vibration isolation platform, the chassis interference acceleration, the upper disc generalized mass coefficient matrix parameter and the Jacobian moment matrix parameter. The supporting leg force is a vector corresponding to the six supporting leg forces in the vibration isolation platform respectively.
Specifically, the computer equipment obtains an auxiliary control variable, and performs feedback linearization processing on the auxiliary control variable based on a generalized centrifugal force parameter, a state variable first-order derivative, an interference item parameter, an upper disc gravity parameter, a chassis interference acceleration, an upper disc generalized mass coefficient matrix parameter and a Jack moment matrix parameter to obtain a plurality of leg forces corresponding to the vibration isolation platform.
For example, the computer device obtains the auxiliary control variable u1And based on a generalized centrifugal force parameter CpFirst derivative of state variable
Figure BDA0003185260630000042
Interference term parameter MbGravity parameter of upper disc in vibration isolation platformGpChassis disturbance acceleration daObtaining an intermediate parameter, i.e. the parameter is
Figure BDA0003185260630000043
Figure BDA0003185260630000044
The computer equipment is based on the intermediate parameter, the auxiliary control variable u and the generalized quality coefficient matrix parameter M of the upper discpJack moment array parameter JpThe leg force vector f can be determineda1I.e. by
Figure BDA0003185260630000045
The leg force vector fa1＝[f1，f2，f3，f4，f5，f6]TWherein f is1，f2，f3，f4，f5，f6Corresponding to the six leg forces in the isolation platform 102 of figure 1.
Step S208, the leg forces are transmitted to the vibration isolation platform, so that the vibration isolation platform performs the current measurement based on the leg forces to obtain the current output data.
Specifically, the computer device transmits the plurality of leg forces to the vibration isolation platform, so that the plurality of leg forces act on the vibration isolation platform, current measurement is performed based on the plurality of leg forces, and the computer device obtains the current output data obtained by the current measurement of the vibration isolation platform.
And step S210, entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state.
Specifically, the computer device enters the next loop iteration based on the obtained current output data, and takes the current output data as the previous output data corresponding to the next iteration; and the computer equipment returns to the step of determining the deviation value between the previous output data and the expected data to be continuously executed, determines whether the deviation value is larger than a deviation threshold value or not through the obtained deviation value, if the deviation value is smaller than or equal to the deviation threshold value, the feedback is stopped, the fact that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state is determined, the deviation value is processed based on a control matrix and feedback linearization, a plurality of supporting leg forces corresponding to the decoupling are obtained, the plurality of supporting leg forces are only related to gravity, namely approximate to a normal number, the plurality of supporting leg forces corresponding to the decoupling are applied to the vibration isolation platform, a converged output value is obtained through measurement, and the computer equipment continuously obtains the converged output value. If the deviation value is greater than the deviation threshold value, feedback continues until the deviation value is less than or equal to the deviation threshold value, so that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state, namely the vibration isolation platform is in a complete decoupling state, wherein when the deviation value is greater than the deviation threshold value, a plurality of leg forces obtained correspondingly are variables, and an output value after the leg forces act on the vibration isolation platform is not converged.
In the decoupling method of the vibration isolation platform, previous output data which is obtained through previous measurement of the vibration isolation platform and comprises the freedom degree information of an upper disc in the vibration isolation platform is obtained, and a deviation value between the previous output data and expected data is determined; and when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable. Because the translational control law and the rotational control law in the control matrix respectively correspond to the translational degree of freedom and the rotational degree of freedom, auxiliary control variables containing error information of the translational degree of freedom and the rotational degree of freedom can be obtained, and feedback linearization processing is carried out on the basis of the auxiliary control variables to obtain a plurality of leg forces corresponding to the vibration isolation platform; transmitting the plurality of leg forces to the vibration isolation platform so that the vibration isolation platform performs current measurement based on the plurality of leg forces to obtain current output data; and entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state. Therefore, complete decoupling between the translational degrees of freedom and complete decoupling between the rotational degrees of freedom can be ensured, and the decoupling effect of each degree of freedom in the vibration isolation platform is further improved.
In one embodiment, as shown in fig. 4, which is a flowchart of a control scheme of a vibration isolation platform, wherein the vibration isolation platform is a Stewart six-axis vibration isolator, first, initial output data measured by the vibration isolation platform is based on the initial output data measured by the vibration isolation platform, and the initial output data measured by the vibration isolation platform is input into a computer device, and the computer device is based on the obtained output data y1And the set desired output data ydObtaining a deviation value e1＝(yd-y1) The deviation value is compared with a deviation threshold e0Comparing the deviation values e1Greater than a deviation threshold e0Inputting the deviation value into a control matrix, wherein the control matrix is determined by an angular acceleration relational expression formed by a first derivative of an Euler angle and a second derivative of the Euler angle; and obtaining the second derivative of the upper disc expected control variable
Figure BDA0003185260630000051
Based on a control matrix K0(s) determining the auxiliary control variable u from the second derivative of the upper disk desired state variable1That is, the expression of the auxiliary control variable is as follows:
Figure BDA0003185260630000052
based on generalized centrifugal force parameter CPFirst derivative of state variable
Figure BDA0003185260630000053
Interference term parameter MbMiddle and upper disc gravity parameter C in vibration isolation platformpChassis disturbance acceleration daObtaining an intermediate parameter, i.e. the parameter is
Figure BDA0003185260630000054
The computer equipment is based on the intermediate parameter, the auxiliary control variable u and the generalized quality coefficient matrix parameter M of the upper discpJack moment array parameter JpThe leg force vector f can be determineda1I.e. by
Figure BDA0003185260630000055
Figure BDA0003185260630000056
The leg force vector fa1＝[f1，f2，f3，f4，f5，f6]TWherein f is1，f2，f3，f4，f5，f6Corresponding to the six leg forces in the isolation platform 102 in fig. 1, respectively, the computer device transmits the leg force vectors to the isolation platform, so that the leg forces act on the isolation platform, current measurement is performed based on the leg forces, and the computer device obtains current output data obtained by the current measurement of the isolation platform; the computer equipment enters next cycle iteration based on the obtained current output data and takes the current output data as the previous output data corresponding to the next iteration; and the computer equipment returns to the step of determining the deviation value between the previous output data and the expected data to be continuously executed, determines whether the deviation value is larger than a deviation threshold value or not through the obtained deviation value, if the deviation value is smaller than or equal to the deviation threshold value, the feedback is stopped, the fact that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state is determined, the deviation value is processed based on a control matrix and feedback linearization, a plurality of supporting leg forces corresponding to the decoupling are obtained, the plurality of supporting leg forces are only related to gravity, namely approximate to a normal number, the plurality of supporting leg forces corresponding to the decoupling are applied to the vibration isolation platform, a converged output value is obtained through measurement, and the computer equipment continuously obtains the converged output value.If the deviation value is greater than the deviation threshold value, feedback continues until the deviation value is less than or equal to the deviation threshold value, so that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state, namely the vibration isolation platform is in a complete decoupling state, wherein when the deviation value is greater than the deviation threshold value, a plurality of leg forces obtained correspondingly are variables, and an output value after the leg forces act on the vibration isolation platform is not converged.
In the embodiment, previous output data which is obtained through previous measurement of the vibration isolation platform and comprises the freedom degree information of the upper disc in the vibration isolation platform is obtained, and a deviation value between the previous output data and expected data is determined; and when the deviation value is larger than the deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable. Because the translational control law and the rotational control law in the control matrix respectively correspond to the translational degree of freedom and the rotational degree of freedom, auxiliary control variables containing error information of the translational degree of freedom and the rotational degree of freedom can be obtained, and feedback linearization processing is carried out on the basis of the auxiliary control variables to obtain a plurality of leg forces corresponding to the vibration isolation platform; transmitting the plurality of leg forces to the vibration isolation platform so that the vibration isolation platform performs current measurement based on the plurality of leg forces to obtain current output data; and entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state. Therefore, complete decoupling between the translational degrees of freedom and complete decoupling between the rotational degrees of freedom can be ensured, and the decoupling effect of each degree of freedom in the vibration isolation platform is further improved.
In one embodiment, as shown in fig. 5, the step of constructing the control matrix includes:
step S502, obtaining initial output data corresponding to the vibration isolation platform, and determining an initial deviation value between the initial output data and the expected data.
Specifically, the computer equipment acquires initial output data measured by the vibration isolation platform and obtains an initial deviation value based on the initial output data and the expected data. For example, the initial primary data obtained by the computer equipment through measurement of the vibration isolation platform is y, and the y is based on the expected datadObtaining an initial deviation value e ═ yd-y)。
Step S504, an initial control matrix is constructed, and translation control and rotation control are carried out on the initial deviation value based on the initial control matrix to obtain an initial auxiliary control variable; the initial control matrix comprises an initial translation control law and an initial rotation control law.
Specifically, the computer device constructs an initial translation control law and an initial rotation control law, constructs a diagonal matrix of 2X2 based on the initial translation control law and the initial rotation control law, takes the diagonal matrix as an initial control matrix, and performs translation control and rotation control on the initial deviation value based on the initial control matrix to obtain an initial auxiliary control variable u. For example, the computer device constructs an initial control matrix k(s) whose expression is as follows:
Figure BDA0003185260630000061
wherein, Ktra(s) is the initial translation control law, Krot(s) is an initial rotation control law, and a second derivative of the upper disc expected state variable is obtained
Figure BDA0003185260630000062
The computer equipment controls the initial deviation value based on the initial control matrix to obtain an initial control result, and the initial control result and the derivative of the upper disc expected state variable are added to obtain an initial auxiliary control variable u, wherein the expression of the initial auxiliary control variable u is as follows:
Figure BDA0003185260630000063
wherein the second derivative of the desired state variable in the vibration isolation platform
Figure BDA0003185260630000064
Is defined as
Figure BDA0003185260630000065
Wherein
Figure BDA0003185260630000066
As a transpose of the second derivative of the desired displacement,
Figure BDA0003185260630000067
is a transpose of the desired angular acceleration. Second derivative of desired state variable
Figure BDA0003185260630000068
Output matrix y, desired output matrix ydSubstituting the definitional expression of (a) into an initial secondary control variable expression, the initial secondary control variable, as follows:
Figure BDA0003185260630000071
wherein the content of the first and second substances,
Figure BDA0003185260630000072
second derivative of desired displacement, alpha, for the upper discp_dAngular acceleration, r, desired for the upper discp_dFor the desired displacement of the upper disc, rpFor upper disc displacement, xip_dEuler angle, xi, is desired for the upper discpThe upper disc euler angle.
Step S506, performing feedback linearization on the initial auxiliary control variable to obtain a plurality of initial leg forces corresponding to the vibration isolation platform.
Specifically, the computer equipment is based on generalized centrifugal force parameters, first-order derivative of control variable, interference item parameters, upper disc gravity parameters, chassis interference acceleration and upper disc gravity parameters in the vibration isolation platformAnd the generalized mass coefficient matrix parameter and the Jack moment matrix parameter perform feedback linearization processing on the auxiliary control variable to obtain a plurality of initial leg forces corresponding to the vibration isolation platform. For example, the computer device is based on the generalized centrifugal force parameter CpFirst derivative of state variable
Figure BDA0003185260630000073
Interference term parameter MbMiddle and upper disc gravity parameter G in vibration isolation platformpChassis disturbance acceleration daObtaining an intermediate parameter, i.e. the parameter is
Figure BDA0003185260630000074
The computer equipment is further based on the intermediate parameters, the initial auxiliary control variable u and the generalized quality coefficient matrix parameters M of the upper diskpJack moment matrix JpAn initial leg force vector f may be determinedaI.e. by
Figure BDA0003185260630000075
The initial leg force vector includes a plurality of initial leg forces.
Step S508, a state equation of the vibration isolation platform is obtained, and the initial supporting leg forces are substituted into the state equation to obtain an initial state variable.
Specifically, the computer equipment obtains a state equation of the vibration isolation platform based on a complete dynamic equation of the vibration isolation system, and substitutes a plurality of initial leg forces in the initial leg force vector into the state equation to obtain an initial state variable. For example, the computer equipment obtains the complete kinetic equation of the vibration isolation system, namely:
Figure BDA0003185260630000076
wherein M ispThe generalized quality coefficient matrix parameters of the upper disk,
Figure BDA0003185260630000077
is the second derivative of the state variable, CpIs a generalized centrifugationThe force parameters,
Figure BDA0003185260630000078
Is the first derivative of the state variable,
Figure BDA0003185260630000079
Is the transposition of an acrylic matrix, faIs the initial leg force vector, MbAs interference term parameter, daFor disturbance of acceleration, G, of the chassispIs the gravity parameter of the upper disc in the vibration isolation platform. And then based on the dynamic equation, obtaining a state equation of the vibration isolation platform, wherein the expression is as follows:
Figure BDA00031852606300000710
y＝[rp T ζp T]T
the above equation of state includes state variables
Figure BDA00031852606300000711
And an expression of the output matrix y, wherein,
Figure BDA00031852606300000712
is a transposition of the displacement output of the upper disc,
Figure BDA00031852606300000713
The upper disc is transposed by the Euler angle; the computer device substitutes the initial leg force vector into the state variable
Figure BDA00031852606300000714
In the expression of (2), the initial state variables are obtained, i.e.
Figure BDA00031852606300000715
Step S510, acquiring an angular velocity relational expression containing a first derivative of an Euler angle, and deriving the time based on the angular velocity relational expression to obtain a complete angular acceleration relational expression containing a first derivative term and a second derivative term of the Euler angle; wherein, the Euler angle is the rotation angle of the upper disc when an external force acts on the vibration isolation platform.
In the kinematic and dynamic modeling, a mathematical model is generally established in an inertial coordinate system. The measurement output data of a sensor (e.g. a gyroscope) is typically referenced to an internally rotating carrier coordinate system. But the base vectors of the inertial frame are not parallel to the base vectors of the internal rotating carrier frame as shown in fig. 6, the order of rotation and the angular extent of which are consistent with fig. 3. Where XYZ is an inertial coordinate system, XYZ is a carrier coordinate system after three-dimensional rotation, N (x)1) And N (y)1) The dotted turning arrow represents the reciprocal of the euler angle for each rotation, and the basis vectors of the inertial coordinate system are the z-axis, y-axis, and x-axis, which are the auxiliary lines during the rotation. The base vector of the internal rotating carrier coordinate system is a z-axis and N (y)1) Axis, X-axis. Thus, the first derivative of the Euler angle is calculated based on the geometric relationship
Figure BDA0003185260630000081
Projected onto the x, y and z axes, wherein,
Figure BDA0003185260630000082
angle of rotation
Figure BDA0003185260630000083
Is N (y)1) Angle pointing to the Y-axis, angle psi being the Y-axis pointing to N (Y)1) Angle theta is N (x)1) An angle pointing towards the X-axis. When external force acts on the vibration isolation platform, the vibration isolation platform can translate and rotate, wherein the rotating angle comprises an angle
Figure BDA0003185260630000084
Angle ψ, angle θ, and therefore, the carrier relative inertial system angular velocity:
Figure BDA0003185260630000085
Figure BDA0003185260630000086
Figure BDA0003185260630000087
wherein, ω isxIs the angular velocity, omega, on the x-axisyIs the angular velocity, omega, on the y-axiszWriting the angular velocity of the carrier into a matrix form to obtain an angular velocity ω relation as follows:
Figure BDA0003185260630000088
wherein, U is a parameter matrix, namely the expression is as follows:
Figure BDA0003185260630000089
specifically, the computer device acquires an angular velocity relational expression containing a first derivative of the euler angle, performs first derivation on time based on the angular velocity relational expression, and arranges a result of the first derivation into a relational expression in which a first derivative term of the euler angle and a second derivative term of the euler angle are added. For example, the computer device obtains the angular velocity relationship as
Figure BDA00031852606300000810
Respectively carrying out time derivation on two ends of the expression to obtain an expression of complete angular acceleration comprising an Euler angle first-order derivative term and an Euler angle second-order derivative term:
Figure BDA00031852606300000811
wherein alpha is angular acceleration, alphax、αy、αzAngular accelerations on the x-axis, the y-axis and the z-axis respectively,and with respect to the parameter matrix
Figure BDA00031852606300000812
The expression of (a) is as follows:
Figure BDA00031852606300000813
the parameter matrix
Figure BDA0003185260630000091
And
Figure BDA0003185260630000092
the product of (a) is the first derivative term of the Euler angle, and U is taken as UωThe U isωAnd
Figure BDA0003185260630000093
the product of (d) is the euler angle second derivative term.
Step S512, determining the Euler angle second derivative relation based on the complete angular acceleration relation and the angular velocity relation.
Specifically, the computer device determines the euler angle second derivative relation by substituting the complete angular acceleration relation into the angular velocity relation based on the complete angular acceleration relation and the angular velocity relation. For example: the computer device obtains the complete angular acceleration alpha as:
Figure BDA0003185260630000094
Figure BDA0003185260630000095
and obtaining the angular velocity ω as:
Figure BDA0003185260630000096
the complete angular acceleration is substituted into the angular velocity relation, and U is equal to Uω，
Figure BDA0003185260630000097
Obtaining the expression of the second derivative of the Euler angleNamely:
Figure BDA0003185260630000098
step S514, acquiring an output expression, and acquiring an output relational expression of the vibration isolation platform based on the output expression and the Euler angle second derivative relational expression; wherein, the output expression defines the position information of the upper disc when the vibration isolation platform is subjected to external force.
When the vibration isolation platform is subjected to an external force, the upper disc of the vibration isolation platform changes in displacement and rotation, and the output expression is a displacement amount and a rotation amount in the upper disc, wherein the displacement amount is expressed based on coordinates on x, y and x axes, and the rotation amount can be expressed by Euler angles.
Specifically, the computer equipment obtains an output expression of the vibration isolation platform, and substitutes the Euler angle second derivative relational expression into the value output expression to obtain the output relational expression of the vibration isolation platform, wherein the output expression of the vibration isolation platform is the output second derivative expression of an upper disc in the vibration isolation platform. For example, the vibration isolation platform output expression obtained by the computer device is as follows:
Figure BDA0003185260630000099
and acquiring a Euler angle second derivative relation:
Figure BDA00031852606300000910
substituting the euler second derivative relation into the output expression to obtain the output relation:
Figure BDA00031852606300000911
step S516, substituting the initial state variable into the output relational expression to obtain an output equation, and performing matrix operation based on the output equation to obtain a translation equation and a rotation equation.
Specifically, the computer device substitutes the initial state variable into the output relational expression to obtain an output equation, and obtains a translation equation and a rotation method by performing matrix multiplication on a block matrix in the output equation. For example, after the computer device substitutes the obtained initial state variables into the above output relational expression, an output equation shown below is obtained:
Figure BDA00031852606300000912
by matrix multiplication, the following translation equation and rotation equation can be obtained:
Figure BDA00031852606300000913
and step S518, determining a translation control law based on the translation equation, and determining a rotation control law based on the complete angular acceleration relational expression and the rotation equation.
Specifically, the computer equipment determines a matrix structure of a translation control law based on a translation equation and determines the translation control law based on the matrix structure; the computer device determines a rotation control law based on the full angular acceleration relation and the rotation equation.
And step S520, determining a control law model based on the translation control law and the rotation control law.
Specifically, the computer device obtains an initial control law matrix of which the constructed matrix structure is a 2X2 diagonal matrix, and substitutes the determined translation control law and the determined rotation control law into the initial control matrix to determine a control law model.
In the embodiment, initial output data corresponding to the vibration isolation platform and including the degree of freedom information of an upper disc in the vibration isolation platform is obtained, and an initial deviation value between the initial output data and the expected data is determined; constructing an initial control matrix, and performing translation control and rotation control on the initial deviation value based on the initial control matrix to obtain an initial auxiliary control variable; performing feedback linearization processing on the initial auxiliary control variable to obtain a plurality of initial leg forces corresponding to the vibration isolation platform; acquiring a state equation of the vibration isolation platform, and substituting the initial supporting leg forces into the state equation to acquire an initial state variable; acquiring an angular velocity relational expression containing a first derivative of an Euler angle, and deriving the time based on the angular velocity relational expression to obtain a complete angular acceleration relational expression containing a first derivative term of the Euler angle and a second derivative term of the Euler angle; determining a Euler angle second derivative relation based on the complete angular acceleration relation and the angular velocity relation; acquiring an output expression, and acquiring an output relational expression of the vibration isolation platform based on the output expression and the Euler angle second derivative relational expression; substituting the initial state variable into the output relational expression to obtain an output equation, and performing matrix operation based on the output equation to obtain a translation equation and a rotation equation; determining a translation control law based on the translation equation, and determining a rotation control law based on the complete angular acceleration relational expression and the rotation equation; a control law model is determined based on the translational control law and the rotational control law. Therefore, based on the relation between the complete angular acceleration and the Euler angle, a control law model for realizing complete decoupling among all the degrees of freedom can be obtained, and the decoupling effect of all the degrees of freedom in the vibration isolation platform is further improved.
In one embodiment, as shown in FIG. 7, determining a translational control law based on the translational equation includes:
step S702, determining a displacement error relational expression based on the expected displacement of the upper disk of the vibration isolation platform and the displacement of the upper disk of the vibration isolation platform, and obtaining a displacement error second-order relational expression based on the displacement error relational expression.
Specifically, the computer device obtains the translation equation, obtains the upper disc expected displacement and the upper disc displacement of the vibration isolation platform based on the translation equation, subtracts the upper disc displacement from the upper disc expected displacement to obtain a displacement error relational expression, and performs second-order derivation on the displacement error relational expression to obtain a displacement error second-order relational expression. For example, computer equipment obtains the expected displacement of the upper disk of the vibration isolation platform and the upper disk of the vibration isolation platform, and the expected displacement r of the upper disk is obtainedp_dMinus the upper disc displacement rpObtaining a displacement error etraThe displacement error relation is formed, namely:
etra＝rp_d-rp
and then based on the displacement error relational expression, carrying out second-order derivation on the displacement error relational expression to obtain a displacement error second-order relational expression, namely:
Figure BDA0003185260630000101
wherein the content of the first and second substances,
Figure BDA0003185260630000102
for the second derivative of the displacement error,
Figure BDA0003185260630000103
for the second derivative of the desired displacement of the upper disc,
Figure BDA0003185260630000104
the second derivative of the upper disk displacement.
Step S704, the displacement error relational expression and the displacement error second order relational expression are substituted into a translation equation to obtain a translation error equation.
Specifically, the computer device obtains a translation equation, a displacement error relational expression and a displacement error second-order relational expression, and substitutes the displacement error relational expression and the displacement error second-order relational expression into the translation equation respectively to obtain the translation error equation. For example, the computer device obtains a translation equation, a displacement error relation, and a displacement error second order relation, as follows:
Figure BDA0003185260630000105
etra＝rp_d-rp
Figure BDA0003185260630000106
based on the expression of the displacement error in the displacement error relational expression and the expression of the second derivative of the displacement error in the displacement error second-order relational expression, a translation error equation is obtained as follows:
Figure BDA0003185260630000111
wherein, Ktra(s) is the initial translation control law.
Step S706, a plurality of initial sub-translation control laws are constructed, the initial translation control laws are determined based on the plurality of initial sub-translation control laws, and each initial sub-translation control law is composed of each initial sub-translation parameter.
Specifically, the computer equipment determines a target translation control operation mode from at least one preset control operation mode, and determines a plurality of corresponding initial sub-translation control laws based on the target translation control operation mode; adding the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine an initial translation control law; the initial sub-translation control laws are composed of initial sub-translation parameters. For example, there are control operation manners such as PID, PD, PI, and P, and when the computer device determines that the target translational control operation manner is PID control from at least one preset control operation manner, an initial sub-translational proportion control law, an initial sub-translational integral control law, and an initial sub-translational differential control law are determined based on the PID control selected by the computer device, where a parameter corresponding to the initial sub-translational proportion control law is a P parameter, a parameter corresponding to the initial sub-translational integral control law is an I parameter, and a parameter corresponding to the initial sub-translational differential control law is a D parameter.
Step S708, setting each initial sub-translational control law as a third-order diagonal matrix, substituting each initial sub-translational control law into the translational error equation, and adjusting each initial sub-translational parameter in each initial sub-translational control law until the solution of the translational error equation converges.
Specifically, the computer device sets each initial sub-translation control law as a three-order diagonal matrix and obtains a translation error equation, substitutes each initial sub-translation control into the translation error equation, and determines final sub-translation parameters by adjusting each initial sub-translation parameter corresponding to each initial sub-translation control law until the solution of the translation error equation converges, so that the translation error can converge to zero. For example, based on the PID control selected by the computer device, an initial sub-translational proportion control law, an initial sub-translational integral control law and an initial sub-translational differential control law are determined, the matrix structure of the initial sub-translational proportion control law, the initial sub-translational integral control law and the initial sub-translational differential control law is set as a three-order diagonal matrix, each initial sub-translational control is substituted into the translational error equation, the P parameter is adjusted to ensure that the vibration isolation platform starts oscillation, half of the current P parameter is taken as the determined P parameter, and the computer device determines the final P parameter, I parameter and D parameter by adjusting the I parameter and D parameter until the solution of the translational error equation converges, so that the translational error can converge to zero.
And each initial sub-translation control law is set as a third-order diagonal matrix, so that no coupling among three translation degrees of freedom can be ensured, and translation decoupling is realized.
Step S710, using each adjusted initial sub-translation parameter corresponding to the convergence of the solution of the translation error equation as each final sub-translation parameter, and determining a translation control law based on each final sub-translation parameter.
Specifically, the computer device takes each adjusted initial sub-translation parameter corresponding to the convergence of the solution of the translation error equation as each final sub-translation parameter, determines each final sub-translation control law based on each final sub-translation parameter, and determines the translation control law based on each final sub-translation control law.
Wherein the translation control law determined based on the final respective sub-translation control laws enables convergence of a solution to a translation error equation, the translation error etraMay converge to zero.
In this embodiment, a displacement error relational expression is determined based on the expected displacement of the upper disk of the vibration isolation platform and the displacement of the upper disk of the vibration isolation platform, and a displacement error second-order relational expression is obtained based on the displacement error relational expression; substituting the displacement error relational expression and the displacement error second-order relational expression into a translation equation to obtain a translation error equation; constructing a plurality of initial sub-translation control laws, and determining the initial translation control laws based on the plurality of initial sub-translation control laws; setting each initial sub-translation control law as a three-order diagonal matrix, substituting each initial sub-translation control law into the translation error equation, and adjusting each initial sub-translation parameter in each initial sub-translation control law until the solution of the translation error equation is converged so as to ensure that no coupling exists among the three translation degrees of freedom; and taking each adjusted initial sub-translation parameter corresponding to the convergence of the solution of the translation error equation as each final sub-translation parameter, and determining a translation control law based on each final sub-translation parameter, so that the obtained translation control law can realize translation decoupling, and the decoupling effect of each degree of freedom in the vibration isolation platform can be improved subsequently.
In one embodiment, as shown in FIG. 8, determining a rotation control law based on the full angular acceleration relationship and the rotation equation comprises:
step S802, based on the complete angular acceleration relational expression, respectively obtaining an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform.
Specifically, the computer device obtains a complete angular acceleration relational expression, and based on the complete angular acceleration relational expression, an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform are respectively obtained. For example, the computer device obtains the full angular acceleration relationship as shown below:
Figure BDA0003185260630000121
then, the computer device can obtain the upper disc desired angular acceleration relation and the upper disc angular acceleration relation as follows, respectively:
Figure BDA0003185260630000122
wherein alpha isp_dAnd alphapRespectively the expected angular acceleration of the upper disc and the angular acceleration of the upper disc;
Figure BDA0003185260630000123
and
Figure BDA0003185260630000124
respectively an upper disc expected parameter matrix first-order derivative and an upper disc parameter matrix first-order derivative;
Figure BDA0003185260630000125
and
Figure BDA0003185260630000126
respectively a first derivative of the Euler angle expected by the upper disc and a first derivative of the Euler angle of the upper disc; u shapep_dAnd UpRespectively an upper disc expected parameter matrix and an upper disc parameter matrix;
Figure BDA0003185260630000127
and
Figure BDA0003185260630000128
the second derivative of the desired euler angle of the upper disc, and the second derivative of the euler angle of the upper disc, respectively.
Step S804, substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotational equation, and substituting a rotational error relational expression determined by the upper disc expected euler angle of the vibration isolation platform and the upper disc euler angle of the vibration isolation platform into the rotational equation to obtain an updated rotational equation, wherein the updated rotational equation includes a rotational error first order deviation term and a rotational error second order deviation term.
Specifically, the computer equipment substitutes the obtained upper disc angular acceleration relational expression and the obtained upper disc expected angular acceleration relational expression into a rotation equation, obtains an upper disc expected euler angle of the vibration isolation platform and an upper disc euler angle of the vibration isolation platform, subtracts the upper disc expected euler angle from the upper disc expected euler angle to obtain a rotation error relational expression, performs first-order derivation on the rotation error relational expression to obtain a rotation error first-order relational expression, and performs second-order derivation on the rotation error relational expression to obtain a rotation error second-order relational expression; and the computer equipment substitutes the rotation error relational expression, the rotation error first-order relational expression and the rotation error second-order relational expression into the rotation equation to obtain an updated rotation equation.
For example, the computer device substitutes the upper disk angular acceleration relational expression and the upper disk expected angular acceleration relational expression into the rotation equation, and the upper disk expected euler angle ξp_dSubtracting the Euler angle xi of the upper discpObtaining a rotation error erotAnd constructing a rotation error relation, namely:
erot＝ξp_d-ξp
the computer equipment respectively carries out first-order derivation and second-order derivation on the rotation error relational expression to obtain a first-order derivative related to the rotation error
Figure BDA0003185260630000131
First order relation of rotation error, second order derivative of rotation error
Figure BDA0003185260630000132
Substituting the second order relational expression of the rotation error relational expression into the rotation equation to obtain an updated rotation equation, namely the equation shown as follows:
Figure BDA0003185260630000133
wherein, Krot(s) is the initial rotation control law.
Step S806 is to construct a plurality of initial sub-rotation control laws, and determine an initial rotation control law based on the plurality of initial sub-rotation control laws, each of which is composed of each of the initial sub-rotation parameters.
Specifically, the computer device constructs a plurality of initial sub-rotation control laws based on the initial sub-rotation parameter configurations, and determines the initial rotation control law based on the plurality of initial sub-rotation control laws.
And step S808, substituting the initial rotation control law into the updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation.
Specifically, the computer device substitutes the initial rotation control law into the updated rotation equation, takes a product term obtained by multiplying a first derivative of the rotation error by a first derivative of the parameter matrix as a first-order deviation term, and eliminates the first-order deviation term in the updated rotation equation to obtain the first rotation equation.
Step S810, setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until a solution of the first rotation equation converges.
Specifically, the computer device sets each initial sub-rotation control law as a third-order diagonal matrix, substitutes each initial sub-rotation control law into the first rotation equation, and determines each final sub-rotation parameter by adjusting each initial sub-rotation parameter in each initial sub-rotation control law until a solution of the first rotation equation converges, so that the rotation error can converge to zero.
The three initial sub-rotation control laws are set as three-order diagonal matrixes, so that the three rotational degrees of freedom are not coupled, and the rotational decoupling is realized.
Step S812, using each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the first rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
Specifically, the computer device determines final individual sub-rotation control laws based on the final individual sub-rotation parameters, using the adjusted individual initial sub-rotation parameters corresponding to the convergence of the solution of the first rotation equation as the final individual sub-rotation parameters, and determines the rotation control laws based on the final individual sub-rotation control laws.
Wherein the rotation control law determined based on the final respective sub-rotation control laws enables convergence of the solution of the first rotation equation, the rotation error erotMay converge to zero.
In this embodiment, based on the complete angular acceleration relational expression, an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform are obtained respectively; substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by the upper disc expected Euler angle of the vibration isolation platform and the upper disc Euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation, wherein the updated rotation equation comprises a rotation error first-order deviation term and a rotation error second-order deviation term; constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws; substituting the initial rotation control law into the updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation; setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges, so as to ensure that no coupling exists among the three rotational degrees of freedom; and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the first rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter, so that the obtained rotation control law can realize rotation decoupling, and the decoupling effect of each degree of freedom in the vibration isolation platform can be improved subsequently.
In one embodiment, constructing a plurality of initial sub-rotation control laws, the determining the initial rotation control law based on the plurality of initial sub-rotation control laws comprises:
determining a target control operation mode from at least one preset control operation mode, and constructing a plurality of corresponding initial sub-rotation control laws based on the target control operation mode; and adding the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine the initial rotation control laws.
Specifically, the computer device determines a target control operation mode from at least one preset control operation mode, determines corresponding initial sub-rotation parameters based on the target control operation mode, constructs a plurality of corresponding initial sub-rotation control laws based on the initial sub-rotation parameters, and adds the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine the initial rotation control laws.
In one embodiment, PID control is determined from at least one preset control mode as a target control operation mode, and an initial sub-rotation proportional control law K is constructed based on the target control operation moderot_P(s) initial sub-rotation integral control law Krot_I(s) initial sub-rotation differential control law Krot_D(s) adding the initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law, the initial sub-rotation integral control law and the initial sub-rotation differential control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000141
wherein, UpIs a parameter matrix of an upper disc,
Figure BDA0003185260630000142
the first derivative of the upper disc parameter matrix is obtained, and s is the complex frequency.
Substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation, wherein the first rotation equation is as follows:
Figure BDA0003185260630000143
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges.
In the embodiment, by adopting the PID control as a target control operation mode, based on the target control operation mode, an initial sub-rotation proportional control law, an initial sub-rotation integral control law, and an initial sub-rotation differential control law are constructed, and initial sub-rotation control items corresponding to the initial sub-rotation proportional control law, the initial sub-rotation integral control law, and the initial sub-rotation differential control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation; setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges, thereby determining the rotation error erotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, PD control is determined from at least one preset control mode as a target control operation mode, and an initial sub-rotation proportion control law K is constructed based on the target control operation moderot_P(s) initial sub-rotation differential control law Krot_D(s) adding the initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law and the initial sub-rotation differential control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000151
wherein, UpIs a parameter matrix of an upper disc,
Figure BDA0003185260630000152
the first derivative of the upper disc parameter matrix is obtained, and s is the complex frequency.
Substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation, wherein the first rotation equation is as follows:
Figure BDA0003185260630000153
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges.
In the embodiment, the PD control is adopted as a target control operation mode, an initial sub-rotation proportional control law and an initial sub-rotation differential control law are constructed based on the target control operation mode, and initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law and the initial sub-rotation differential control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation; setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges, thereby determining the rotation error erotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, PI control is determined from at least one preset control mode to serve as a target control operation mode, and an initial sub-rotation ratio control law K is constructed based on the target control operation moderot_P(s) initial sub-rotation integral control law Krot_I(s) and reacting withAdding initial sub-rotation control items corresponding to the initial sub-rotation proportional control law and the initial sub-rotation integral control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000154
wherein, UpIs a parameter matrix of an upper disc,
Figure BDA0003185260630000155
the first derivative of the upper disc parameter matrix is obtained, and s is the complex frequency.
Substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation, wherein the first rotation equation is as follows:
Figure BDA0003185260630000156
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges.
In the embodiment, an initial sub-rotation proportional control law and an initial sub-rotation integral control law are constructed by adopting PI control as a target control operation mode based on the target control operation mode, and initial sub-rotation control items corresponding to the initial sub-rotation proportional control law and the initial sub-rotation integral control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation; setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law to obtain the final rotation equationSo that the solution of the first rotation equation converges, thereby enabling the determination of the error e with respect to rotationrotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, P control is determined from at least one preset control mode to serve as a target control operation mode, and an initial sub-rotation proportion control law K is constructed based on the target control operation moderot_P(s) and determining an initial rotation control law based on the initial sub-rotation control term corresponding to the initial sub-rotation proportional control law, the initial rotation control law being:
Figure BDA0003185260630000161
wherein, UpIs a parameter matrix of an upper disc,
Figure BDA0003185260630000162
the first derivative of the upper disc parameter matrix is obtained, and s is the complex frequency.
Substituting the determined initial rotation control law into an updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation, wherein the first rotation equation is as follows:
Figure BDA0003185260630000163
and setting the initial sub-rotation proportion control law as a third-order diagonal matrix, substituting the initial sub-rotation proportion control law into the first rotation equation, and adjusting corresponding initial sub-rotation parameters in the initial sub-rotation proportion control law until the solution of the first rotation equation converges.
In the embodiment, an initial sub-rotation proportion control law is constructed by adopting P control as a target control operation mode based on the target control operation mode, and the initial sub-rotation control law is determined based on an initial sub-rotation control item corresponding to the initial sub-rotation proportion control law; the determined initial rotation control law is substituted and updatedThe first order deviation term in the updated rotation equation is eliminated to obtain a first rotation equation; setting the initial sub-rotation proportion control law as a third-order diagonal matrix, substituting the initial sub-rotation proportion control law into the first rotation equation, and adjusting corresponding initial sub-rotation parameters in the initial sub-rotation proportion control law until the solution of the first rotation equation converges, so that the rotation error e can be determinedrotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, the substituting the upper disc angular acceleration relation and the upper disc expected angular acceleration relation into the rotation equation and substituting a rotation error relation determined by the upper disc expected euler angle of the vibration isolation platform and the upper disc euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation includes:
substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation to obtain a first updated rotation equation; acquiring an upper disc expected matrix equation of the vibration isolation platform, and substituting the upper disc expected matrix equation into the rotation equation updated for the first time to obtain a rotation equation updated for the second time; and substituting the first derivative of the expected Euler angle set to be zero and the second derivative of the expected Euler angle set to be zero into the rotation equation updated for the second time, and substituting a rotation error relational expression determined by the expected Euler angle of the upper disk of the vibration isolation platform and the Euler angle of the upper disk of the vibration isolation platform into the rotation equation updated for the second time to obtain the updated rotation equation.
Specifically, the computer device substitutes the obtained upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into a rotation equation to obtain a first updated rotation equation; the computer device obtains an upper disc expected matrix equation of the vibration isolation platform, substitutes the upper disc expected matrix equation into the first updated rotation equation to obtain a second updated rotation equation, sets a first derivative of an expected Euler angle to zero and a second derivative of the expected Euler angle to zero, substitutes the first derivative of the expected Euler angle set to zero and the second derivative of the expected Euler angle set to zero into the second updated rotation equation to obtain a second updated intermediate rotation equation, obtains an upper disc expected Euler angle of the vibration isolation platform and an upper disc Euler angle of the vibration isolation platform, subtracts the upper disc Euler angle from the upper disc expected Euler angle to obtain a rotation error relation, and performs first derivation on the rotation error relation to obtain a rotation error first relation, and carrying out second-order derivation on the rotation error relational expression to obtain a rotation error second-order relational expression, and substituting the rotation error relational expression, the rotation error first-order relational expression and the rotation error second-order relational expression into a second updated intermediate rotation equation by the computer equipment to obtain an updated rotation equation.
For example, the computer device substitutes the upper disk angular acceleration relation and the upper disk expected angular acceleration relation into the rotation equation to obtain a first updated rotation equation, namely:
Figure BDA0003185260630000164
the computer equipment obtains an upper disc expected matrix equation of the vibration isolation platform, namely:
Up_d＝Up+Δ
and the computer equipment substitutes the upper disc expected matrix equation into the first updated rotation equation to obtain a second updated rotation equation, wherein delta is the difference value of the upper disc parameter matrix, and the second updated rotation equation is obtained, namely:
Figure BDA0003185260630000171
wherein the content of the first and second substances,
Figure BDA0003185260630000172
the first derivative of the difference value of the upper disc parameter matrix is obtained; the computer device expects the first derivative of Euler angle by using the upper disc
Figure BDA0003185260630000173
Set to zero and the second derivative of the desired euler angle of the upper disc
Figure BDA0003185260630000174
Set to zero, ensures that the upper disc remains stationary, i.e.:
Figure BDA0003185260630000175
the computer device obtains a second updated intermediate rotation equation by substituting the first derivative of the desired euler angle set to zero and the second derivative of the desired euler angle set to zero into the second updated rotation equation, i.e.:
Figure BDA0003185260630000176
computer equipment obtains the upper disc expected Euler angle of the vibration isolation platform and the upper disc Euler angle of the vibration isolation platform, and the upper disc expected Euler angle xip_dSubtracting the Euler angle xi of the upper discpObtaining a rotation error erotAnd performing first order derivation on the rotation error relational expression to obtain a rotation error first order relational expression, performing second order derivation on the rotation error relational expression to obtain a rotation error second order relational expression, and substituting the rotation error relational expression, the rotation error first order relational expression and the rotation error second order relational expression into a second updated intermediate rotation equation by the computer equipment to obtain an updated rotation equation, namely:
Figure BDA0003185260630000177
in this embodiment, the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression are substituted into the rotation equation to obtain a first updated rotation equation; acquiring an upper disc expected matrix equation of the vibration isolation platform, and substituting the upper disc expected matrix equation into the rotation equation updated for the first time to obtain a rotation equation updated for the second time; and substituting the first derivative of the expected Euler angle set to be zero and the second derivative of the expected Euler angle set to be zero into the rotation equation updated for the second time, and substituting a rotation error relational expression determined by the expected Euler angle of the upper disk of the vibration isolation platform and the Euler angle of the upper disk of the vibration isolation platform into the rotation equation updated for the second time to obtain the updated rotation equation. In this way, the rotation control law can be determined based on the updated rotation equation, and further rotation decoupling can be achieved.
In one embodiment, as shown in fig. 9, the method further comprises the steps of:
step S902, based on the complete angular acceleration relational expression, respectively obtaining an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform.
Specifically, the computer device obtains a complete angular acceleration relational expression, and based on the complete angular acceleration relational expression, an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform are respectively obtained. For example, the computer device obtains the full angular acceleration relationship as shown below:
Figure BDA0003185260630000181
then, the computer device can obtain the upper disc desired angular acceleration relation and the upper disc angular acceleration relation as follows, respectively:
Figure BDA0003185260630000182
wherein alpha isp_dAnd alphapRespectively the expected angular acceleration of the upper disc and the angular acceleration of the upper disc;
Figure BDA0003185260630000183
and
Figure BDA0003185260630000184
respectively an upper disc expected parameter matrix first-order derivative and an upper disc parameter matrix first-order derivative;
Figure BDA0003185260630000185
and
Figure BDA0003185260630000186
respectively a first derivative of the Euler angle expected by the upper disc and a first derivative of the Euler angle of the upper disc; u shapep_dAnd UpRespectively an upper disc expected parameter matrix and an upper disc parameter matrix;
Figure BDA0003185260630000187
and
Figure BDA0003185260630000188
the second derivative of the desired euler angle of the upper disc, and the second derivative of the euler angle of the upper disc, respectively.
And step S904, substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotational equation, and substituting a rotational error relational expression determined by the upper disc expected euler angle of the vibration isolation platform and the upper disc euler angle of the vibration isolation platform into the rotational equation to obtain an updated rotational equation, wherein the updated rotational equation comprises a rotational error first order deviation term and a rotational error second order deviation term.
Specifically, the computer equipment substitutes the obtained upper disc angular acceleration relational expression and the obtained upper disc expected angular acceleration relational expression into a rotation equation, obtains an upper disc expected euler angle of the vibration isolation platform and an upper disc euler angle of the vibration isolation platform, subtracts the upper disc expected euler angle from the upper disc expected euler angle to obtain a rotation error relational expression, performs first-order derivation on the rotation error relational expression to obtain a rotation error first-order relational expression, and performs second-order derivation on the rotation error relational expression to obtain a rotation error second-order relational expression; and the computer equipment substitutes the rotation error relational expression, the rotation error first-order relational expression and the rotation error second-order relational expression into the rotation equation to obtain an updated rotation equation.
For example, the computer device substitutes the upper disk angular acceleration relational expression and the upper disk expected angular acceleration relational expression into the rotation equation, and the upper disk expected euler angle ξp_dSubtracting the Euler angle xi of the upper discpObtaining a rotation error erotAnd constructing a rotation error relation, namely:
erot＝ξp_d-ξp
the computer equipment respectively carries out first-order derivation and second-order derivation on the rotation error relational expression to obtain a first-order derivative related to the rotation error
Figure BDA0003185260630000189
First order relation of rotation error, second order derivative of rotation error
Figure BDA00031852606300001810
Substituting the second order relational expression of the rotation error relational expression into the rotation equation to obtain an updated rotation equation, namely the equation shown as follows:
Figure BDA00031852606300001811
wherein, Krot(s) is the initial rotation control law.
Step S906, a plurality of initial sub-rotation control laws are constructed, and the initial sub-rotation control laws are determined based on the plurality of initial sub-rotation control laws, each of which is composed of each of the initial sub-rotation parameters.
Specifically, the computer device constructs a plurality of initial sub-rotation control laws based on the initial sub-rotation parameter configurations, and determines the initial rotation control law based on the plurality of initial sub-rotation control laws. For example, a target control operation mode is determined from at least one preset control operation mode, and a plurality of corresponding initial sub-rotation control laws are determined based on the target control operation mode; and adding the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine the initial rotation control laws.
Step S908, substituting the initial rotation control law into the updated rotation equation, and eliminating a second order deviation term in the updated rotation equation to obtain a second rotation equation.
Specifically, the computer device substitutes the initial rotation control law into the updated rotation equation, takes a product term obtained by multiplying the second derivative of the rotation error by the parameter matrix as a second-order deviation term, and eliminates the second-order deviation term in the updated rotation equation to obtain a second rotation equation.
Step S910, setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until a solution of the second rotation equation converges.
Specifically, the computer device sets each initial sub-rotation control law as a third-order diagonal matrix, substitutes each initial sub-rotation control law into the second rotation equation, and determines each final sub-rotation parameter by adjusting each initial sub-rotation parameter in each initial sub-rotation control law until a solution of the second rotation equation converges, so that the rotation error can converge to zero.
The three initial sub-rotation control laws are set as three-order diagonal matrixes, so that the three rotational degrees of freedom are not coupled, and the rotational decoupling is realized.
Step S912, using each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the second rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
Specifically, the computer device determines final individual sub-rotation control laws based on the final individual sub-rotation parameters, using the adjusted individual initial sub-rotation parameters corresponding to the convergence of the solution of the second rotation equation as the final individual sub-rotation parameters, and determines the rotation control laws based on the final individual sub-rotation control laws.
Wherein the rotation determined based on the final individual sub-rotation control lawsA rotation law capable of causing convergence of the solution of the second rotation equation, the rotation error erotMay converge to zero.
In this embodiment, based on the complete angular acceleration relational expression, an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform are obtained respectively; substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by the upper disc expected Euler angle of the vibration isolation platform and the upper disc Euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation; constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws; substituting the initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges; and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the second rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter, so that the obtained rotation control law can realize rotation decoupling, and the decoupling effect of each degree of freedom in the vibration isolation platform can be improved subsequently.
In one embodiment, PID control is determined from at least one preset control mode as a target control operation mode, and an initial sub-rotation proportional control law K is constructed based on the target control operation moderot_P(s) initial sub-rotation integral control law Krot_I(s) initial sub-rotation differential control law Krot_D(s) adding the initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law, the initial sub-rotation integral control law and the initial sub-rotation differential control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000191
substituting the determined initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation, wherein the second rotation equation is as follows:
Figure BDA0003185260630000201
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges.
In the embodiment, by adopting the PID control as a target control operation mode, based on the target control operation mode, an initial sub-rotation proportional control law, an initial sub-rotation integral control law, and an initial sub-rotation differential control law are constructed, and initial sub-rotation control items corresponding to the initial sub-rotation proportional control law, the initial sub-rotation integral control law, and the initial sub-rotation differential control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges, thereby determining the rotation error erotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, PD control is determined from at least one preset control mode as a target control operation mode, and an initial sub-rotation proportion control law K is constructed based on the target control operation moderot_P(s) initial sub-rotationLaw of differential control Krot_D(s) adding the initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law and the initial sub-rotation differential control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000202
substituting the determined initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation, wherein the second rotation equation is as follows:
Figure BDA0003185260630000203
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges.
In the embodiment, the PD control is adopted as a target control operation mode, an initial sub-rotation proportional control law and an initial sub-rotation differential control law are constructed based on the target control operation mode, and initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law and the initial sub-rotation differential control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges, thereby determining the rotation error erotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one of the embodiments, the first and second electrodes are,determining PI control as a target control operation mode from at least one preset control mode, and constructing an initial sub-rotation proportional control law K based on the target control operation moderot_P(s) initial sub-rotation integral control law Krot_I(s), adding the initial sub-rotation control terms corresponding to the initial sub-rotation proportional control law and the initial sub-rotation integral control law to determine an initial rotation control law, wherein the initial rotation control law is as follows:
Figure BDA0003185260630000211
substituting the determined initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation, wherein the second rotation equation is as follows:
Figure BDA0003185260630000212
and setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges.
In the embodiment, an initial sub-rotation proportional control law and an initial sub-rotation integral control law are constructed by adopting PI control as a target control operation mode based on the target control operation mode, and initial sub-rotation control items corresponding to the initial sub-rotation proportional control law and the initial sub-rotation integral control law are added to determine the initial rotation control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting each initial sub-rotation control law as a third-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the second rotation equation is enabledSo that the solution with respect to the rotation error e can be determinedrotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
In one embodiment, P control is determined from at least one preset control mode to serve as a target control operation mode, and an initial sub-rotation proportion control law K is constructed based on the target control operation moderot_P(s) and determining an initial rotation control law based on the initial sub-rotation control term corresponding to the initial sub-rotation proportional control law, the initial rotation control law being:
Figure BDA0003185260630000213
substituting the determined initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation, wherein the second rotation equation is as follows:
Figure BDA0003185260630000214
and setting the initial sub-rotation proportion control law as a third-order diagonal matrix, substituting the initial sub-rotation proportion control law into the second rotation equation, and adjusting corresponding initial sub-rotation parameters in the initial sub-rotation proportion control law until the solution of the second rotation equation converges.
In the embodiment, an initial sub-rotation proportion control law is constructed by adopting P control as a target control operation mode based on the target control operation mode, and the initial sub-rotation control law is determined based on an initial sub-rotation control item corresponding to the initial sub-rotation proportion control law; substituting the determined initial rotation control law into an updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting the initial sub-rotation proportional control law as a third-order diagonal matrix, substituting the initial sub-rotation proportional control law into the second rotation equation, and adjusting the corresponding initial sub-rotation parameter in the initial sub-rotation proportional control lawUntil the solution of the second rotation equation is made to converge, so that the error e can be determined with respect to the rotationrotThe solution of the differential equation of (a) converges, i.e. the rotation error may converge to zero.
It should be understood that although the various steps in the flowcharts of fig. 2, 5, 7-9 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least some of the steps in fig. 2, 5, 7-9 may include multiple steps or multiple stages, which are not necessarily performed at the same time, but may be performed at different times, which are not necessarily performed in sequence, but may be performed alternately or alternately with other steps or at least some of the other steps.
In one embodiment, as shown in fig. 10, there is provided a decoupling assembly of a vibration isolation platform, comprising: a determining module 1002, a first obtaining module 1004, a second obtaining module 1006, a transmitting module 1008, and an iterating module 1010, wherein:
a determining module 1002, configured to obtain previous output data obtained through previous measurement of the vibration isolation platform, and determine a deviation value between the previous output data and expected data; the previous output data comprises the freedom degree information of an upper disc in the vibration isolation platform;
a first obtaining module 1004, configured to, when the deviation value is greater than a deviation threshold, process the deviation value based on a control matrix formed by a translational control law and a rotational control law to obtain an auxiliary control variable;
a second obtaining module 1006, configured to perform feedback linearization on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform;
a transmission module 1008, configured to transmit the leg forces to the vibration isolation platform, so that the vibration isolation platform performs current measurement based on the leg forces to obtain current output data;
and the iteration module 1010 is configured to enter a next iteration, use the current output data as previous output data corresponding to the next iteration, and return to the step of determining the deviation value between the previous output data and the expected data to continue to be executed until the deviation value is less than or equal to the deviation threshold value, so as to achieve that all the degrees of freedom of the upper disk in the vibration isolation platform are in a decoupling state.
In one embodiment, the first obtaining module 1004 is configured to obtain initial output data corresponding to the vibration isolation platform, and determine an initial deviation value between the initial output data and the expected data; constructing an initial control matrix, and performing translation control and rotation control on the initial deviation value based on the initial control matrix to obtain an initial auxiliary control variable; wherein, the initial control matrix comprises an initial translation control law and an initial rotation control law; performing feedback linearization processing on the initial auxiliary control variable to obtain a plurality of initial leg forces corresponding to the vibration isolation platform; acquiring a state equation of the vibration isolation platform, and substituting the initial supporting leg forces into the state equation to acquire an initial state variable; acquiring an angular velocity relational expression containing a first derivative of an Euler angle, and deriving the time based on the angular velocity relational expression to obtain a complete angular acceleration relational expression containing a first derivative term of the Euler angle and a second derivative term of the Euler angle; wherein, the Euler angle is the rotation angle of the upper disc when an external force acts on the vibration isolation platform; determining a Euler angle second derivative relation based on the complete angular acceleration relation and the angular velocity relation; acquiring an output expression, and acquiring an output relational expression of the vibration isolation platform based on the output expression and the Euler angle second derivative relational expression; the output expression defines the position information of the upper disc when the vibration isolation platform is subjected to external force; substituting the initial state variable into the output relational expression to obtain an output equation, and performing matrix operation based on the output equation to obtain a translation equation and a rotation equation; determining a translation control law based on the translation equation, and determining a rotation control law based on the complete angular acceleration relational expression and the rotation equation; a control law model is determined based on the translational control law and the rotational control law.
In one embodiment, the first obtaining module 1004 is configured to determine a displacement error relation based on the expected displacement of the upper disk of the vibration isolation platform and the displacement of the upper disk of the vibration isolation platform, and obtain a displacement error second order relation based on the displacement error relation; substituting the displacement error relational expression and the displacement error second-order relational expression into a translation equation to obtain a translation error equation; constructing a plurality of initial sub-translation control laws, and determining the initial translation control laws based on the plurality of initial sub-translation control laws, wherein each initial sub-translation control law is composed of each initial sub-translation parameter; setting each initial sub-translation control law as a three-order diagonal matrix, substituting each initial sub-translation control law into the translation error equation, and adjusting each initial sub-translation parameter in each initial sub-translation control law until the solution of the translation error equation is converged; and taking each adjusted initial sub-translation parameter corresponding to the convergence of the solution of the translation error equation as each final sub-translation parameter, and determining a translation control law based on each final sub-translation parameter.
In one embodiment, the first obtaining module 1004 is configured to obtain an upper disc angular acceleration relation of the vibration isolation platform and an upper disc expected angular acceleration relation of the vibration isolation platform, respectively, based on the complete angular acceleration relation; substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by the upper disc expected Euler angle of the vibration isolation platform and the upper disc Euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation, wherein the updated rotation equation comprises a rotation error first-order deviation term and a rotation error second-order deviation term; constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws, wherein each initial sub-rotation control law is composed of each initial sub-rotation parameter; substituting the initial rotation control law into the updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation; setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges; and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the first rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
In an embodiment, the first obtaining module 1004 is configured to determine a target control operation manner from at least one preset control operation manner, and construct a plurality of corresponding initial sub-rotation control laws based on the target control operation manner; and adding the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine the initial rotation control laws.
In one embodiment, the first obtaining module 1004 is configured to substitute the upper disk angular acceleration relation and the upper disk expected angular acceleration relation into the rotation equation to obtain a first updated rotation equation; acquiring an upper disc expected matrix equation of the vibration isolation platform, and substituting the upper disc expected matrix equation into the rotation equation updated for the first time to obtain a rotation equation updated for the second time; and substituting the first derivative of the expected Euler angle set to be zero and the second parameter of the expected Euler angle set to be zero into the rotation equation updated for the second time, and substituting a rotation error relational expression determined by the expected Euler angle of the upper disk of the vibration isolation platform and the Euler angle of the upper disk of the vibration isolation platform into the rotation equation updated for the second time to obtain the updated rotation equation.
In one embodiment, the first obtaining module 1004 is further configured to obtain an upper disc angular acceleration relation of the vibration isolation platform and an upper disc expected angular acceleration relation of the vibration isolation platform, respectively, based on the complete angular acceleration relation; substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by the upper disc expected Euler angle of the vibration isolation platform and the upper disc Euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation, wherein the updated rotation equation comprises a rotation error first-order deviation term and a rotation error second-order deviation term; constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws, wherein each initial sub-rotation control law is composed of each initial sub-rotation parameter; substituting the initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation; setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges; and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the second rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
For specific definition of the decoupling device of the vibration isolation platform, reference may be made to the above definition of the decoupling method of the vibration isolation platform, and details are not described here. The modules in the decoupling device of the vibration isolation platform can be wholly or partially realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a computer device, the internal structure of which may be as shown in fig. 11. The computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the computer device is used for storing decoupling data of the vibration isolation platform. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method of decoupling a vibration isolation platform.
Those skilled in the art will appreciate that the architecture shown in fig. 11 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is provided, comprising a memory and a processor, the memory having stored therein a computer program, the processor implementing the steps of the above-described method embodiments when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored which, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database or other medium used in the embodiments provided herein can include at least one of non-volatile and volatile memory. Non-volatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical storage, or the like. Volatile Memory can include Random Access Memory (RAM) or external cache Memory. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM), among others.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method of decoupling a vibration isolation platform, the method comprising:
acquiring previous output data obtained through previous measurement of a vibration isolation platform, and determining a deviation value between the previous output data and expected data; the previous output data comprises the freedom degree information of an upper disc in the vibration isolation platform;
when the deviation value is larger than a deviation threshold value, processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable;
performing feedback linearization processing on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform;
transmitting the plurality of leg forces to the vibration isolation platform, so that the vibration isolation platform performs current measurement based on the plurality of leg forces to obtain current output data;
and entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so as to realize that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state.
2. The method of claim 1, wherein the step of constructing the control matrix comprises:
acquiring initial output data corresponding to the vibration isolation platform, and determining an initial deviation value between the initial output data and the expected data;
constructing an initial control matrix, and performing translation control and rotation control on the initial deviation value based on the initial control matrix to obtain an initial auxiliary control variable; the initial control matrix comprises an initial translation control law and an initial rotation control law;
performing feedback linearization processing on the initial auxiliary control variable to obtain a plurality of initial leg forces corresponding to the vibration isolation platform;
acquiring a state equation of the vibration isolation platform, and substituting the initial supporting leg forces into the state equation to acquire an initial state variable;
acquiring an angular velocity relational expression containing a first derivative of an Euler angle, and deriving the time based on the angular velocity relational expression to obtain a complete angular acceleration relational expression containing a first derivative term of the Euler angle and a second derivative term of the Euler angle; the Euler angle is the rotating angle of the upper disc when an external force acts on the vibration isolation platform;
determining a Euler angle second derivative relation based on the integral angular acceleration relation and the angular velocity relation;
acquiring an output expression, and acquiring an output relational expression of the vibration isolation platform based on the output expression and the Euler angle second derivative relational expression; the output expression defines the position information of the upper disc when the vibration isolation platform is subjected to external force;
substituting the initial state variable into the output relational expression to obtain an output equation, and performing matrix operation based on the output equation to obtain a translation equation and a rotation equation;
determining a translation control law based on the translation equation, and determining a rotation control law based on the complete angular acceleration relational expression and the rotation equation;
determining a control law model based on the translational control law and the rotational control law.
3. The method of claim 2, wherein determining a translational control law based on the translational equation comprises:
determining a displacement error relational expression based on the expected displacement of the upper disc of the vibration isolation platform and the displacement of the upper disc of the vibration isolation platform, and obtaining a displacement error second-order relational expression based on the displacement error relational expression;
substituting the displacement error relational expression and the displacement error second-order relational expression into a translation equation to obtain a translation error equation;
constructing a plurality of initial sub-translation control laws, and determining the initial translation control laws based on the plurality of initial sub-translation control laws, wherein each initial sub-translation control law is composed of each initial sub-translation parameter;
setting each initial sub-translation control law as a three-order diagonal matrix, substituting each initial sub-translation control law into the translation error equation, and adjusting each initial sub-translation parameter in each initial sub-translation control law until the solution of the translation error equation is converged;
and taking each adjusted initial sub-translation parameter corresponding to the convergence of the solution of the translation error equation as each final sub-translation parameter, and determining a translation control law based on each final sub-translation parameter.
4. The method of claim 2, wherein determining a rotation control law based on the full angular acceleration relation and the rotation equation comprises:
based on the complete angular acceleration relational expression, respectively obtaining an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform;
substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by an upper disc expected euler angle of the vibration isolation platform and an upper disc euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation, wherein the updated rotation equation comprises a rotation error first-order deviation term and a rotation error second-order deviation term;
constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws, wherein each initial sub-rotation control law is composed of each initial sub-rotation parameter;
substituting the initial rotation control law into the updated rotation equation, and eliminating a first-order deviation term in the updated rotation equation to obtain a first rotation equation;
setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the first rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the first rotation equation converges;
and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the first rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
5. The method according to claim 4, wherein the constructing a plurality of initial sub-rotation control laws and the determining an initial rotation control law based on the plurality of initial sub-rotation control laws comprises:
determining a target control operation mode from at least one preset control operation mode, and constructing a plurality of corresponding initial sub-rotation control laws based on the target control operation mode;
and adding the initial sub-rotation control items corresponding to the initial sub-rotation control laws to determine the initial rotation control laws.
6. The method of claim 4, wherein said substituting said upper disc angular acceleration relationship and said upper disc desired angular acceleration relationship into said rotation equation and substituting a rotation error relationship determined by an upper disc desired euler angle of said vibration isolation platform and an upper disc euler angle of said vibration isolation platform into said rotation equation results in an updated rotation equation comprising:
substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation to obtain a first updated rotation equation;
acquiring an upper disc expected matrix equation of the vibration isolation platform, and substituting the upper disc expected matrix equation into the first updated rotation equation to obtain a second updated rotation equation;
and substituting the first derivative of the expected Euler angle set to be zero and the second parameter of the expected Euler angle set to be zero into the rotation equation updated for the second time, and substituting a rotation error relational expression determined by the expected Euler angle of the upper disk of the vibration isolation platform and the Euler angle of the upper disk of the vibration isolation platform into the rotation equation updated for the second time to obtain the updated rotation equation.
7. The method of claim 2, further comprising:
based on the complete angular acceleration relational expression, respectively obtaining an upper disc angular acceleration relational expression of the vibration isolation platform and an upper disc expected angular acceleration relational expression of the vibration isolation platform;
substituting the upper disc angular acceleration relational expression and the upper disc expected angular acceleration relational expression into the rotation equation, and substituting a rotation error relational expression determined by an upper disc expected euler angle of the vibration isolation platform and an upper disc euler angle of the vibration isolation platform into the rotation equation to obtain an updated rotation equation, wherein the updated rotation equation comprises a rotation error first-order deviation term and a rotation error second-order deviation term;
constructing a plurality of initial sub-rotation control laws, and determining the initial rotation control laws based on the plurality of initial sub-rotation control laws, wherein each initial sub-rotation control law is composed of each initial sub-rotation parameter;
substituting the initial rotation control law into the updated rotation equation, and eliminating a second-order deviation term in the updated rotation equation to obtain a second rotation equation;
setting each initial sub-rotation control law as a three-order diagonal matrix, substituting each initial sub-rotation control law into the second rotation equation, and adjusting each initial sub-rotation parameter in each initial sub-rotation control law until the solution of the second rotation equation converges;
and taking each adjusted initial sub-rotation parameter corresponding to the convergence of the solution of the second rotation equation as each final sub-rotation parameter, and determining a rotation control law based on each final sub-rotation parameter.
8. A decoupling assembly for a vibration isolation platform, said assembly comprising:
the determining module is used for acquiring previous output data obtained through previous measurement of the vibration isolation platform and determining a deviation value between the previous output data and expected data; the previous output data comprises the freedom degree information of an upper disc in the vibration isolation platform;
the first obtaining module is used for processing the deviation value based on a control matrix formed by a translation control law and a rotation control law to obtain an auxiliary control variable when the deviation value is larger than a deviation threshold value;
the second obtaining module is used for performing feedback linearization processing on the auxiliary control variable to obtain a plurality of leg forces corresponding to the vibration isolation platform;
the transmission module is used for transmitting the plurality of leg forces to the vibration isolation platform so that the vibration isolation platform can perform current measurement based on the plurality of leg forces to obtain current output data;
and the iteration module is used for entering next cycle iteration, taking the current output data as previous output data corresponding to the next iteration, returning to the step of determining the deviation value between the previous output data and the expected data, and continuing to execute until the deviation value is less than or equal to the deviation threshold value, so that all the degrees of freedom of the upper disc in the vibration isolation platform are in a decoupling state.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of any of claims 1 to 7.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
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