CN110879553B - Control method and system of micro gyroscope available based on output state - Google Patents
Control method and system of micro gyroscope available based on output state Download PDFInfo
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Abstract
The invention discloses a control method and a system of a micro-gyroscope available based on an output state, wherein a dynamic model of the micro-gyroscope is established according to an internal operation mechanism of the micro-gyroscope; establishing an observer of the micro gyroscope available based on output signals; carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer; designing a controller with a gain coefficient; the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer; designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient; the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized. The invention effectively scales the related quantity in the design process by methods such as matrix property, Yang inequality and the like.
Description
Technical Field
The invention belongs to the technical field of control, and particularly relates to a control method and a control system of a micro gyroscope available based on an output state.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The development of electronics and micromachining technology has led to the birth of micro-gyroscopes at the beginning of the 20 th century. Micro gyroscopes have gradually gained wide use in civilian products since the 90 s of the 20 th century and in some low precision inertial navigation products. The research of the micro gyroscope technology in China begins in 1989, and an electrostatic motor with the size of hundreds of micrometers and a piezoelectric motor with the size of 3mm are developed. Through the micro-mechanical and optical waveguide gyroscope technology, a micro gyroscope prototype has been made, and some research data are obtained; and the requirements of the military and civil dual-purpose market are met through continuous development and research on key components, a micro gyroscope, a novel inertial device and a GPS combined navigation system. With the development of scientific technology, compared with the high cost of the traditional electrostatic gyroscope, the precision of the micro gyroscope with lower cost is higher and higher, which is the general development trend of future mechanical technology.
The control problem of the micro gyroscope is always concerned, and the previous research results show that the control method mostly passes through the strategies of backstepping design, neural network or sliding mode control and the like, but the iteration of the backstepping method is too complicated, the result obtained by the neural network is locally stable, and the control of the sliding mode technology has the shake phenomenon. In general, the micro gyroscope can be measured only when the output signal of the system is available, and other signals are not measurable, so that the design of a new control strategy for the micro gyroscope under the condition that only the output signal is available is of great research significance.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a control method of a micro-gyroscope based on available output state, and a controller is designed for the micro-gyroscope by means of a static gain strategy on the premise that an output signal is available so as to achieve the goal of gradually stabilizing a system signal of the micro-gyroscope.
In order to achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
a method for controlling a micro-gyroscope available based on output states, comprising:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized.
According to the further technical scheme, a dynamic model of the micro gyroscope is established according to the internal operation mechanism of the micro gyroscope:
wherein: x and y respectively represent the displacement of the micro-gyroscope in the direction of the X, Y axis and are the outputs of the system, exx、eyyRespectively representing the elastic coefficient of the micro-gyroscope in the direction of the X, Y axis, dxx、dyyRespectively representing the damping coefficient of the micro-gyroscope in the direction of the X, Y axis, exy、dxyRepresenting the coupling parameters due to machining errors, m representing the mass of the micro-gyroscope, a being the angular speed of rotation of the mass, ux、uyRespectively representing the input control force in the direction of axis X, Y,
x (y) first and second derivatives with respect to time, respectively.
According to a further technical scheme, a dynamic model of the micro gyroscope is written in a matrix form as follows:
wherein:
x1＝x、
y1＝y、
x is due to1＝x、y1The micro-gyroscopes denoted y are often measured as engineering displacements in the X, Y axis direction, and are defined as the output signals of the gyroscope.
In a further technical solution, an observer of the micro-gyroscope is available based on the output signal:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2Observation of (2); a is1、a2Is a set of hervatz coefficients.
The further technical scheme is that the coordinate transformation is carried out on an error system:
order: e.g. of the type1＝x1-z1、
e3＝y1-z3、
Obtaining the following components:
wherein: e ═ e (e)1 e2 e3 e4)T、F＝(0 f1 0 f2)T。
In a further technical scheme, a controller with a gain coefficient is designed:
wherein: b1、b2Is a set of hervatz coefficients.
In the present application, since the signals of the system are not all available, provided that only the output signal (the micro gyroscope is displaced in the direction of the X, Y axis) is available, an observer is designed for the whole system, and the output information is used to estimate the information unavailable to the system: rate of change of displacement of the micro-gyroscope in the direction of the X, Y axis.
However, there must be an error between the information estimated by the observer and the original information, so the error system needs to be asymptotically stable as well, which is used to prove that the observer design is effective.
The further technical scheme is that the observer is subjected to coordinate transformation:
the designed controller is brought into an observer system, and then coordinate transformation is introduced:
can be obtained
The system comprises the following steps:
wherein:
the above one or more technical solutions have the following beneficial effects:
(1) compared with the prior control method, the control method designed by the scheme is simpler.
(2) The invention firstly applies a static gain method to design a controller for the micro gyroscope.
(3) The invention only applies the output state to design the observer and the controller for the micro gyroscope. The controller is designed by using the knowledge of linear system theory, and the effect is that the signals of the system all tend to zero gradually.
(4) Compared with the controller designed in the past, the controller designed by the scheme is simpler and more effective in form.
(5) The invention effectively scales the related quantity in the design process by methods such as matrix property, Yang inequality and the like.
(6) Used information only has two in this application, is the displacement of micro gyroscope in X axle and Y axle direction respectively, and the information that this special use utilized is less.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a schematic block diagram of an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a controller according to an exemplary embodiment of the present disclosure;
FIG. 3 is a schematic diagram illustrating control of the X-axis state and the observation state of the system according to an exemplary embodiment of the present disclosure;
FIG. 4 is a control diagram of the system in the Y-axis direction and the observation state according to the embodiment of the disclosure;
fig. 5 is a control flow chart of an embodiment of the disclosure.
Detailed Description
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
Example one
As shown in fig. 5, the present embodiment discloses a method for controlling a micro-gyroscope available based on an output state, which includes first establishing a mathematical model of the micro-gyroscope according to an internal operation mechanism of the micro-gyroscope; designing an observer with a gain coefficient form, carrying out coordinate transformation on an error system, and carrying out coordinate transformation on the observation system after designing a controller with a gain coefficient in a form; constructing a Lyapunov function, and performing primary scaling treatment on the derivative of the Lyapunov function by using methods such as a matrix inequality and a Yang inequality; and finally, after the magnitude of the static gain coefficient is determined, final arrangement is carried out on the derivative of the Lyapunov function, and finally, the scheme is proved to realize the asymptotic and stable control target of the micro gyroscope. The invention has simple control strategy, simple controller and easy operation and realization.
In a specific embodiment, a dynamic model is first established.
Referring to fig. 1, according to the internal operation mechanism of the micro-gyroscope, taking the occurrence of the internal coupling phenomenon into full consideration, a kinematic equation set is written as:
wherein: x, y respectively represent the displacement of the micro-gyroscope in the direction of the X, Y axis, which can be measured directly, so that only these two states are available for the output of the system, i.e. the controller is designed, exx、eyyRespectively, the Elastic coefficients (Elastic coefficients), d, of the micro-gyroscope in the direction of the X, Y axisxx、dyyRespectively, the Damping coefficients (damper coefficient), e, of the micro-gyroscope in the direction of the X, Y axisxy、dxyRepresenting the coupling parameters due to machining errors, m representing the mass of the micro-gyroscope, a being the angular velocity of the mass's rotation (Angula)r velocity)，ux、uyRespectively representing the input control force in the direction of axis X, Y,
x (y) first and second derivatives with respect to time, respectively.
Carrying out dimensionless processing on the dynamic equation set of the micro gyroscope to obtain a dimensionless equation set:
wherein:
as shown in fig. 2 and 3, it can be rewritten as:
wherein: x is the number of1＝x、
y1＝y、
Displacement and acceleration of the micro-gyroscope in the direction of the axis X, Y, respectively, defined here as the signal of the system; x is the number of1、y1For micro-gyroscopes to be displaced in the direction of the X, Y axis, often measurable at engineering time, they are defined as the output signal of the gyroscope.
Rewriting the dimensionless equation set to matrix form:
wherein:
when modeling a system, firstly, the internal relevant information (elastic coefficient, damping coefficient, coupling parameter, angular velocity, etc. of the micro gyroscope) of the system is quantized, so in the actual engineering, when designing an observer and controlling force for the micro gyroscope, the information is quantized first, and then the scheme is used for the purpose of quantizing the information
The design of (2) is used for realizing the goal of asymptotic stabilization of the micro gyroscope signal.
In the specific implementation example, an observer is designed for the micro-gyroscope.
Since only the displacement of the micro-gyroscope X, Y in the axial direction is a measurable signal, i.e. state x1、y1If available, the observer can only be designed to use both pieces of information. The observation was of the form:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2For ease of comparative observation, state z in the simulation1、z2、z3、z4Are used separately
Replacing; a is1、a2Is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
it will be applied belowThe popularization form is as follows:
then there are:
a1、a2has strong selectivity as long as the Herviz coefficient is a group, so that a can be properly changed for different micro-gyroscopes1、a2And searching a group of Helverz coefficients corresponding to the condition with better observation effect according to the size, and applying the group of Helverz coefficients to the setting of the observer.
In a specific embodiment, the coordinate transformation is performed on the error system.
Error system is composed of1-z1、x2-z2、y1-z3、y2-z4The error system is subjected to a reversible transformation (i.e. static gain transformation), such that: e.g. of the type1＝x1-z1、
e3＝y1-z3、
Obtaining the following components:
wherein: e ═ e (e)1 e2 e3 e4)T、F＝(0 f1 0 f2)T。
Namely:
in the specific embodiment, as shown in fig. 4, a controller with a gain factor is designed.
Wherein: b1、b2Is a set of hervaz coefficients and has the following properties: there is a positive definite matrix Q satisfying BTQ + QB is less than or equal to-I, wherein:
we will apply this generalized form below:
then there are:
in practical engineering, x in the state of micro-gyroscope1、y1The displacement in the direction of the X, Y axis can be accurately measured, so the controller is designed in engineering
Then x can be directly applied1、y1The information of (1). b1、b2Has strong selectivity as long as the selectivity is satisfied as a group of Helverz coefficients, so that b can be changed for different micro-gyroscopes1、b2The size of the controller is used for searching a controller which can make the control force moderate and change the state appropriately.
In a specific embodiment, the observer is subjected to coordinate transformation.
To be designed
Taking into an observer system, and introducing coordinate transformation:
to obtain the new
The system comprises the following steps:
wherein:
namely:
in the specific embodiment, the lyapunov function is designed.
Wherein:
the corresponding positive definite matrix mentioned earlier. The matrix can be obtained by directly solving the lyap function in the matlab toolbox
Sum matrix
When the size of the gain coefficient r is solved, matlab is needed to obtain a matrix
Norm of (d).
In the specific implementation example, the lyapunov function is derived and subjected to preliminary scaling.
Wherein the non-linear terms are processed:
the first item:
wherein:
p is the norm of the matrix P.
The second term is:
wherein:
is a matrix
And there must be such a set a1、a2、b1、b2So that
From the above work it can be derived:
in a specific embodiment, the magnitude of the gain factor is determined.
Selecting:
where a is a small constant. In practice, this is not necessary
Because the non-linear terms are more scaled, it is only stated that there must be one such constant r that meets our design requirements. However, the larger the setting of the parameter r is, the better the parameter r is, if the control force is too large, the transient response of the system is too large; on the other hand, when r is set to be small, the control force is too small, and the control force on the micro gyroscope signal cannot achieve the corresponding effect, so that an appropriate r can be found in engineering application in a parameter adjusting mode, and the phenomenon of overlarge transient response of the system signal can be avoided on the premise of realizing a control target.
In one embodiment, the derivative of the Lyapunov function is properly arranged
From the value of r
Where δ is a constant. The derivative of the lyapunov function satisfies:
the method is obtained according to the theoretical knowledge related to the control science field, and therefore the designed controller is proved to ensure that the signal of the micro gyroscope is asymptotically stable, namely the displacement and the acceleration of the micro gyroscope in the direction of the X, Y axis are gradually zero, and the control target of asymptotically stable system signals is realized.
The control objects are the displacements of the micro-gyroscope in the X-axis and Y-axis directions, respectively, and the derivatives of the displacements in the X-axis and Y-axis directions, i.e., the accelerations.
The output signals are: displacement of the micro-gyroscope in the X-axis and Y-axis directions. Is used for acting on other devices, and the micro gyroscope plays the role of the micro gyroscope by acting on other devices. If the micro gyroscope output signal is expected to be a specific target signal rather than a zero signal, the target signal of the system after coordinate transformation can be changed into the zero signal by a coordinate transformation method.
The scheme gives the displacement (x) in the direction of the axis of the micro gyroscope X, Y only applied in practical engineering1、y1) Selecting two sets of appropriate Hulvier coefficients (a)1、a2；b1、b2) And a gain factor of suitable magnituderA control force in the form of a controller is designed in accordance with the method of the present disclosure to achieve the goal of asymptotically stabilizing the signal of the micro-gyroscope. Wherein a group of Herviz coefficients a1、a2An observer used for setting the system can search a group of corresponding coefficients under the condition of better observation effect by a proper parameter adjusting mode and apply the coefficients to the setting of the observer; another set of Herviz coefficients b1、b2And the gain coefficient r is used for directly designing the controller, and a group of parameters which can make the control force mild and the state change appropriate can be found in a controller design of practical engineering in a proper parameter adjusting mode.
The simulation legend is drawn by applying matlab, and gives simulation data: exx＝Eyy＝Exy＝Dxx＝Dyy＝Dxy＝a＝1、r＝2、a1＝a2＝b1＝b2＝2、x1(0)＝2、x2(0)＝1、y1(0)＝1、y2(0) One is 2. For easy comparative observation, state z in the diagram1、z2、z3、z4Are used separately
Instead.
Example two
The present embodiment aims to provide a computing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the following steps, including:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized.
EXAMPLE III
An object of the present embodiment is to provide a computer-readable storage medium.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, performs the steps of:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized.
Example four
An object of the present embodiment is to provide a control system of a micro-gyroscope available based on output states, comprising a server configured to:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized.
The steps involved in the apparatuses of the above second, third and fourth embodiments correspond to the first embodiment of the method, and the detailed description thereof can be found in the relevant description of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media containing one or more sets of instructions; it should also be understood to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any of the methods of the present invention.
Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using general purpose computer means, or alternatively, they can be implemented using program code that is executable by computing means, such that they are stored in memory means for execution by the computing means, or they are separately fabricated into individual integrated circuit modules, or multiple modules or steps of them are fabricated into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (7)
1. A control method of a micro gyroscope available based on an output state is characterized by comprising the following steps:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized;
carrying out coordinate transformation on the error system, designing a controller with a gain coefficient in a form, and then carrying out coordinate transformation on the observation system; constructing a Lyapunov function, and performing primary scaling treatment on the derivative of the Lyapunov function through a matrix inequality and Yang inequality method; after the magnitude of the static gain coefficient is determined, the derivative of the Lyapunov function is finally sorted; designing a controller for the micro gyroscope by means of a static gain strategy on the premise that an output signal is available so as to achieve the goal of asymptotic stabilization of a system signal of the micro gyroscope;
an observer of a micro-gyroscope available on the basis of output signals:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2Observation of (2); a is1、a2Is a set of Herviz coefficients, x1＝x、y1Y represents a displacement of the micro-gyroscope in the direction of the X, Y axis, ux、uyRespectively represent input control forces in the direction of the X, Y axes;
controller with gain factor:
wherein: b1、b2Is a set of Herviz coefficients;
and (3) carrying out coordinate transformation on the observer:
the designed controller is brought into an observer system, and then coordinate transformation is introduced:
can be obtained
The system comprises the following steps:
wherein:
a1、a2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
b1、b2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix Q satisfying BTQ + QB is less than or equal to-I, wherein:
2. the method for controlling a micro-gyroscope available based on output states as claimed in claim 1, characterized in that the dynamic model of the micro-gyroscope is established according to the internal operating mechanisms of the micro-gyroscope:
wherein: x and y respectively represent the displacement of the micro-gyroscope in the direction of the X, Y axis and are the outputs of the system, exx、eyyRespectively representing the elastic coefficient of the micro-gyroscope in the direction of the X, Y axis, dxx、dyyRespectively representing the damping coefficient of the micro-gyroscope in the direction of the X, Y axis, exy、dxyRepresenting the coupling parameters due to machining errors, m representing the mass of the micro-gyroscope, a being the angular speed of rotation of the mass, ux、uyRespectively representing the input control force in the direction of axis X, Y,
x (y) first and second derivatives with respect to time, respectively.
3. The method for controlling a micro-gyroscope usable based on an output state as claimed in claim 1, characterized in that the dynamic model of the micro-gyroscope is written in the form of a matrix:
wherein:
4. The method for controlling a micro-gyroscope usable based on an output state as claimed in claim 1, characterized in that the error system is subjected to a coordinate transformation:
order: e.g. of the type1＝x1-z1、
e3＝y1-z3、
Obtaining the following components:
wherein: e ═ e (e)1 e2 e3 e4)T、F＝(0 f1 0 f2)T；
a1、a2Is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
5. a computing device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to perform steps comprising:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized;
carrying out coordinate transformation on the error system, designing a controller with a gain coefficient in a form, and then carrying out coordinate transformation on the observation system; constructing a Lyapunov function, and performing primary scaling treatment on the derivative of the Lyapunov function through a matrix inequality and Yang inequality method; after the magnitude of the static gain coefficient is determined, the derivative of the Lyapunov function is finally sorted; designing a controller for the micro gyroscope by means of a static gain strategy on the premise that an output signal is available so as to achieve the goal of asymptotic stabilization of a system signal of the micro gyroscope;
an observer of a micro-gyroscope available on the basis of output signals:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2Observation of (2); a is1、a2Is a set of Herviz coefficients, x1＝x、y1Y represents a displacement of the micro-gyroscope in the direction of the X, Y axis, ux、uyRespectively represent input control forces in the direction of the X, Y axes;
controller with gain factor:
wherein: b1、b2Is a set of Herviz coefficients;
and (3) carrying out coordinate transformation on the observer:
the designed controller is brought into an observer system, and then coordinate transformation is introduced:
can be obtained
The system comprises the following steps:
wherein:
a1、a2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
b1、b2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix Q satisfying BTQ + QB is less than or equal to-I, wherein:
6. a computer-readable storage medium, having a computer program stored thereon, the program, when executed by a processor, performing the steps of:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized;
carrying out coordinate transformation on the error system, designing a controller with a gain coefficient in a form, and then carrying out coordinate transformation on the observation system; constructing a Lyapunov function, and performing primary scaling treatment on the derivative of the Lyapunov function through a matrix inequality and Yang inequality method; after the magnitude of the static gain coefficient is determined, the derivative of the Lyapunov function is finally sorted; designing a controller for the micro gyroscope by means of a static gain strategy on the premise that an output signal is available so as to achieve the goal of asymptotic stabilization of a system signal of the micro gyroscope;
an observer of a micro-gyroscope available on the basis of output signals:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2Observation of (2); a is1、a2Is a set of Herviz coefficients, x1＝x、y1Y represents a displacement of the micro-gyroscope in the direction of the X, Y axis, ux、uyRespectively represent input control forces in the direction of the X, Y axes;
controller with gain factor:
wherein: b1、b2Is a set of Herviz coefficients;
and (3) carrying out coordinate transformation on the observer:
the designed controller is brought into an observer system, and then coordinate transformation is introduced:
can be obtained
The system comprises the following steps:
wherein:
a1、a2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
b1、b2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix Q satisfying BTQ + QB is less than or equal to-I, wherein:
7. a micro-gyroscope control system usable based on output states, comprising a server, wherein the server is configured to:
establishing a dynamic model of the micro gyroscope according to an internal operation mechanism of the micro gyroscope;
establishing an observer of the micro gyroscope available based on output signals;
carrying out coordinate transformation on an error system formed by a dynamic model of the micro gyroscope and an observer;
designing a controller with a gain coefficient;
the controller is brought into an observer system, and then coordinate transformation is introduced to carry out coordinate transformation on the observer;
designing a Lyapunov function, deriving the Lyapunov function, performing primary scaling treatment, and determining the size of a gain coefficient;
the derivative of the Lyapunov function is sorted, and the controller is proved to ensure that the state of the micro gyroscope is asymptotically stable, so that the control target is realized;
carrying out coordinate transformation on the error system, designing a controller with a gain coefficient in a form, and then carrying out coordinate transformation on the observation system; constructing a Lyapunov function, and performing primary scaling treatment on the derivative of the Lyapunov function through a matrix inequality and Yang inequality method; after the magnitude of the static gain coefficient is determined, the derivative of the Lyapunov function is finally sorted; designing a controller for the micro gyroscope by means of a static gain strategy on the premise that an output signal is available so as to achieve the goal of asymptotic stabilization of a system signal of the micro gyroscope;
an observer of a micro-gyroscope available on the basis of output signals:
wherein: r is a constant greater than 1, the range of which is given in the following process; state z1、z2、z3、z4Are respectively x1、x2、y1、y2Observation of (2); a is1、a2Is a set of Herviz coefficients, x1＝x、y1Y represents a displacement of the micro-gyroscope in the direction of the X, Y axis, ux、uyRespectively in the direction of the X, Y axisInputting a control force;
controller with gain factor:
wherein: b1、b2Is a set of Herviz coefficients;
and (3) carrying out coordinate transformation on the observer:
the designed controller is brought into an observer system, and then coordinate transformation is introduced:
can be obtained
The system comprises the following steps:
wherein:
a1、a2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix P satisfying ATP + PA is less than or equal to-I, wherein:
b1、b2is a set of hervaz coefficients and has the following properties: there is a positive definite matrix Q satisfying BTQ + QB is less than or equal to-I, wherein:
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