CN115291516B - Vibration isolation pointing platform modal decoupling control method - Google Patents
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Abstract
The invention relates to a vibration isolation pointing platform modal decoupling control method, which comprises the following steps: determining the design requirement of the vibration isolation pointing platform, performing design optimization on the configuration, and selecting the type of a hinge and the type of a supporting leg actuator; determining configuration parameters and design parameters; deriving a dynamic model of the vibration isolation pointing platform; calculating a modal conversion matrix, and performing modal decoupling; the multi-degree-of-freedom system is subjected to modal decoupling and converted into a single-degree-of-freedom system, the directional control rate and the vibration isolation control rate are respectively designed in a modal space to achieve vibration isolation and precise directional characteristics, the received disturbance is divided into a low-frequency disturbance zone, a medium-frequency disturbance zone and a high-frequency disturbance zone, the low-frequency disturbance is counteracted by utilizing the directional, the medium-frequency disturbance is counteracted by utilizing the active vibration isolation, and the high-frequency disturbance is counteracted by utilizing the passive vibration isolation characteristic; and obtaining final control force output, and performing directional stable control on the vibration isolation directional platform. The vibration isolation directional platform solves the problem that the control precision and the system robustness of the vibration isolation directional platform cannot be met at the same time, and improves the directional precision and the vibration isolation bandwidth.
Description
Technical Field
The invention relates to a vibration isolation pointing platform modal decoupling control method.
Background
Future aerospace tasks (such as space science observation, deep space laser communication and the like) require that the spacecraft have extremely high control precision and stability performance indexes; while various disturbance sources on the support module, such as a flywheel, a control moment gyro, a directional driving device of a large antenna and a solar sailboard, a Stirling refrigerator and the like, can generate unavoidable low-frequency vibration and high-frequency vibration during normal operation, thereby seriously affecting the control precision and stability performance index of the high-precision spacecraft and obviously reducing the working performance of effective load.
To solve the problem of high precision pointing to optical payloads, two main approaches are currently adopted: vibration isolation and directional control of the spatial optical load. The purpose of vibration isolation is to prevent a vibration source on a spacecraft from transmitting micro-vibrations to a spatial optical load; the aim of the pointing control is to control the optical axis pointing through a driver, thereby improving the imaging quality, and the pointing control is mainly used for high-precision pointing of space optical load. At present, the two are generally designed by adopting a separate control strategy, but with the increasing requirement of loads such as telescope and the like on the limitation of volume and mass in the future, the adoption of a control strategy pointing to vibration isolation integration is an important development direction in the future.
In the application process, the Stewart configuration has the characteristics of high precision, high rigidity and good fault tolerance, and is an important configuration mode for manufacturing the vibration isolation directional platform. However, if and only if the geometric centers of the payload centroid and the upper platform hinge point completely coincide, a spatially complete structure can be ensured, and in practical design, the Stewart configuration platform considering vibration isolation performance cannot realize the design of a cube configuration, and thus cannot realize complete decoupling in terms of configuration design.
For the multi-degree-of-freedom Stewart system, the vibration control and pointing problems relate to the multiple-input multiple-output (MIMO) problem, and the mode decoupling control method can be used for changing the multiple-input multiple-output (MIMO) system into a plurality of single-input single-output (SISO) systems, so that the problem is simplified. Mode decoupling is realized by taking the natural vibration mode under the physical space of the system as a vector base according to the vibration mode theory, and converting the system model under the physical space to obtain the system model under the mode space, and the decoupling is realized by utilizing the property that all modes under the mode space are mutually orthogonal, so that the design difficulty of a system controller can be reduced, and the method has a good effect on solving the control problem of a Stewart system.
Currently, control for the Stewart platform is roughly divided into two types, namely hinge space control and task space control.
The hinge space control is simple, stable and easy to realize, but the control precision is not high in practical application, mainly, each supporting leg is regarded as a single-input single-output system to solve, the influence between the branched chains is simplified into external interference to be processed, and then each single supporting leg is controlled by PID, so that the control precision is high, but the control precision is not high in the precision required by the directional vibration isolation integrated platform.
The Stewart platform control for task space control is also one of important control methods, and the adopted calculation moment control utilizes a nonlinear system feedback linearization control method, so that the influence of system nonlinearity is weakened, but the robustness is poor in the actual application process, the system disturbance caused by the uncertainty of system parameters and modeling errors is difficult to accurately cancel, and the instability of a control system is easy to cause. Aiming at the improved control method for calculating the moment control, a robust item is added on the basis of calculating the moment control, and robust PI control is carried out, so that the robustness of the system is greatly improved, but in the practical application process, the jitter caused by the robustness has stronger influence on the precise pointing, and the pointing precision is reduced.
Disclosure of Invention
In view of the foregoing, it is necessary to provide a vibration isolation pointing platform modal decoupling control method to solve the technical problem that the vibration isolation pointing platform control precision and the system robustness cannot be satisfied at the same time.
The invention provides a vibration isolation pointing platform modal decoupling control method, which comprises the following steps: a. determining the design requirement of the vibration isolation pointing platform, carrying out design optimization on the configuration according to the design requirement, and selecting the type of a hinge and the type of a supporting leg actuator; b. determining configuration parameters and design parameters of the vibration isolation pointing platform according to the selected hinge type and the selected landing leg actuator type; c. according to the determined configuration parameters and design parameters, deducing a dynamic model of the vibration isolation directional platform, thereby determining a generalized mass matrix M (q), a generalized stiffness matrix K (q), a coriolis force matrix and a centrifugal force matrixTranspose J of jacobian matrix from dynamic to fixed coordinate system T The output force f of each leg a The method comprises the steps of carrying out a first treatment on the surface of the d. According to the obtained dynamic model of the vibration isolation directional platform, calculating a modal conversion matrix ψ through a damping-free vibration equation, and carrying out modal decoupling on a generalized mass matrix, a generalized damping matrix and a generalized stiffness matrix by utilizing the modal conversion matrix; e. the mode space control rate is designed, a mode conversion matrix is utilized to carry out mode decoupling and conversion on a complex multi-degree-of-freedom system which is coupled with each other into a single-degree-of-freedom system, vibration isolation and precise pointing characteristics are respectively achieved for the mode space design pointing control rate and the vibration isolation control rate, and the disturbance is divided into a low-frequency disturbance interval F a Intermediate frequency disturbance interval F b And a high-frequency disturbance section F c The low-frequency disturbance is counteracted by utilizing the direction, the medium-frequency disturbance is counteracted by utilizing the active vibration isolation, and the high-frequency disturbance is counteracted by utilizing the passive vibration isolation characteristic; f. and comprehensively designing the directional stable control, combining the directional control and the vibration isolation control to obtain final control force output, and performing the directional stable control on the vibration isolation directional platform.
Preferably, in the step a:
the hinge types selected are: the hinge of the upper platform and the supporting rod is an arc-shaped flexible spherical hinge, and the hinge of the lower platform and the supporting rod is a notch-shaped flexible hook hinge; the leg actuator types are: and a voice coil motor.
Preferably, the configuration parameters and design parameters include: radius R of upper hinge circle p Radius R of lower hinge circle b Central angle of upper platformCentral angle of lower platform, pose vector q of upper platform, height H of dynamic coordinate system in fixed coordinate system, distance r from upper hinge point to upper supporting leg centroid rci Distance r from lower hinge point to center of mass of lower leg tci Load centroid height z cm Damping coefficient c spring piece rigidity k, upper platform mass m, upper platform coiling coordinate system X-axis moment of inertia I xx Y-axis moment of inertia I of upper platform coiling coordinate system yy The Z-axis rotational inertia of the upper platform coiling coordinate system is I zz Mass m of upper leg rci Mass m of lower leg tci The upper landing leg is arranged on a landing leg coordinate systemLower moment of inertia I rci Moment of inertia I of lower leg in leg coordinate system rci 。
Preferably, the step c includes:
the dynamics model of the Stewart platform is deduced, and the deduced dynamics model is simplified into:
wherein: m (q) is a generalized mass array; k (q) is a generalized stiffness matrix;is a matrix of coriolis force and centrifugal force; j (J) T Transpose of jacobian matrix from dynamic to fixed coordinate system, f a The output force for each leg.
Preferably, the step d specifically includes:
the free vibration equation is, without considering the system damping:
the charge conditions for the presence of a non-zero solution are:
|K(q)-δ 2 M(q)|＝0
delta is the natural frequency of the system, and the vibration equation of the system is converted into a characteristic equation:
(K(q)-δ 2 M(q))χ＝0.
χ is a feature vector of the feature equation;
the natural frequencies of the ith and jth orders are calculated:
when i is not equal to j, it can be seen that the mass matrix M (q) and the stiffness matrix K (q) are orthogonal to the different eigenvectors of the vibration mode;
when i=j, the number of times, wherein lambda is i And eta i The modal mass and modal stiffness of the ith order vibration mode are respectively;
expansion to full-order mode condition, ψ T M(q)Ψ＝M(p)；Ψ T K(q)Ψ＝K(p)；
Wherein, ψ is a modal decoupling matrix, ψ= [ χ ] 1 ，...，χ 6 ]；
M (p) is a mass matrix in the modal space, M (p) =diag (λ) 1 ，…，λ 6 )；
K (p) is the stiffness matrix in the modal space, K (p) =diag (η) 1 ，…，η 6 )；
Decoupling by adopting a proportional damping mode:
preferably, the step e includes:
filtering the intermediate frequency disturbance interval F by a Kalman filter b Designing a vibration isolation control law:
5.1.1 measuring the Displacement x and the velocity in physical space
5.1.2, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ,
The control equation of the system under the modal coordinates is:
extracting modal coordinates and derivatives thereof;
5.1.3, determining the modal control displacement gain g and the velocity gain h of each order, giving an expected pole, comparing with the characteristic value of the feedback system, and obtaining a control coefficient
5.1.4, converting the modal control force to a control force in the actual physical space:
preferably, the step e further comprises:
filtering the low-frequency disturbance interval F by a Kalman filter a Is designed to point to the control law:
5.2.1 measuring the Displacement x and the velocity in physical space
5.2.2, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ：
The control equation of the system under the modal coordinates is:
extracting modal coordinates and derivatives thereof;
5.2.3 inputting the displacement x and velocity in the ideal physical space
5.2.4, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ,
Preferably, the step e further comprises:
carrying out error solving on the ideal pose error and the actual measured pose error in the independent modal space design;
the controller in the modal space is designed to:
u p is a control signal in the modal space;
the control force of the load in the modal space is expressed as:
the load control force in the joint space is expressed as:
obtaining:
set a systematic error e p ＝p d -p，
The system closed loop modal error equation is
Preferably, the step f includes:
combining the pointing and vibration isolation control to obtain final control force output, and performing pointing stable control on the Stewart platform: the influence of different frequencies is analyzed, control signals under different frequencies are output to the voice coil motor actuator, low-frequency precise pointing control is realized, medium-frequency active vibration isolation control and high-frequency passive vibration isolation control are realized, and therefore vibration isolation pointing performance of the platform is improved.
The beneficial effects of the application include;
firstly, the problem of difficult control caused by strong physical coupling of the vibration isolation pointing platform in the motion process is solved, the driving and control problems of the vibration isolation pointing platform with six degrees of freedom in space are effectively reduced, the pointing precision of a single degree of freedom is improved, and the frequency width of degrees of freedom except the mode approach degree of freedom is improved.
Secondly, by adopting a hierarchical control strategy, the pointing precision and vibration isolation bandwidth of the vibration isolation pointing integrated platform are improved, the frequency coincidence between a control system and a mechanical system is weakened by the design of a modal space controller, and the control performance of the Stewart platform is improved.
Thirdly, the integrated platform control method of the vibration isolation pointing platform reduces complicated steps of separate design of the traditional vibration isolation pointing platform and mutual coupling characteristics of mutual control systems, and a mode space decoupling control mode realizes mode decoupling control among various degrees of freedom, so that control robustness of the system is improved by utilizing pole allocation, single-degree-of-freedom optimal quadratic form, optimal quadratic Gaussian and other design schemes.
Drawings
FIG. 1 is a flow chart of a vibration isolation pointing platform modal decoupling control method of the present invention;
fig. 2 is a configuration diagram of a vibration isolation pointing platform according to an embodiment of the present invention;
fig. 3 is a schematic control diagram of a vibration isolation pointing platform according to an embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
Referring to fig. 1, a flowchart of a method for controlling modal decoupling of a vibration isolation pointing platform according to a preferred embodiment of the present invention is shown.
Referring to fig. 2 and 3 together, step S1 determines a design requirement of the vibration isolation pointing platform, performs design optimization on the configuration according to the design requirement, and selects a hinge type and a leg actuator type.
Specifically:
in this embodiment, the main design requirements of the Stewart platform are determined, the configuration is designed and optimized according to the design requirements, and the hinge type and the leg actuator type are selected. The hinge types selected in this embodiment are: the hinge of the upper platform and the supporting rod is an arc-shaped flexible spherical hinge, and the hinge of the lower platform and the supporting rod is a notch-shaped flexible hook hinge; the leg actuator types are: and a voice coil motor.
And S2, determining configuration parameters and design parameters of the vibration isolation pointing platform according to the selected hinge type and the selected support leg actuator type. Specifically:
this example determines the configuration parameters and design parameters of the Stewart platform. Wherein the configuration parameters and design parameters include: radius R of upper hinge circle p Radius R of lower hinge circle b Central angle of upper platformThe central angle theta of the lower platform, the pose vector q of the upper platform, the height H of the movable coordinate system in the fixed coordinate system and the distance r between the upper hinge point and the mass center of the upper supporting leg rci Distance r from lower hinge point to center of mass of lower leg tci Load centroid height z cm Damping coefficient c spring piece rigidity k, upper platform mass m, upper platform coiling coordinate system X-axis moment of inertia I xx Y-axis moment of inertia I of upper platform coiling coordinate system yy The Z-axis rotational inertia of the upper platform coiling coordinate system is I zz Mass m of upper leg rci Mass m of lower leg tci Moment of inertia I of upper leg in leg coordinate system rci Moment of inertia I of lower leg in leg coordinate system rci 。
S3, deducing a dynamic model of the vibration isolation directional platform according to the determined configuration parameters and design parameters, determining a generalized mass matrix M (q), a generalized stiffness matrix K (q), and a coriolis force and centrifugal force matrixTranspose J of jacobian matrix from dynamic to fixed coordinate system T The output force f of each leg a . Specifically:
the dynamic model of the Stewart platform is deduced in the embodiment, and the deduced dynamic model is simplified into:
wherein: m (q) is a generalized mass array; k (q) is a broad senseA stiffness matrix;is a matrix of coriolis force and centrifugal force; j (J) T Transpose of jacobian matrix from dynamic to fixed coordinate system, f a The output force for each leg.
And S4, calculating a modal transformation matrix psi through a undamped free vibration equation according to the obtained dynamic model of the vibration isolation directional platform, and performing modal decoupling on the generalized mass matrix, the generalized damping matrix and the generalized stiffness matrix by utilizing the modal transformation matrix. Specifically:
in this embodiment, the free vibration equation can be written as:
the charge conditions for the presence of a non-zero solution are:
|K(q)-δ 2 M(q)|＝0
delta is the natural frequency of the system, and the vibration equation of the system is converted into a characteristic equation:
(K(q)-δ 2 M(q))χ＝0
and x is the eigenvector of the eigenvector equation.
The natural frequencies of the ith and jth orders are calculated:
when i is not equal to j, it can be seen that the mass matrix M (q) and the stiffness matrix K (q) are orthogonal to the different eigenvectors of the vibration mode.
When i=j, the number of times, wherein lambda is i And eta i The modal mass and modal stiffness in the i-th order vibration mode are respectively.
Expansion to full-order mode condition, ψ T M(q)Ψ＝M(p)；Ψ T K(q)Ψ＝K(p)
Wherein, ψ is a modal decoupling matrix, ψ= [ χ ] 1 ，...，χ 6 ]；
M (p) is a mass matrix in the modal space, M (p) =diag (λ) 1 ，…，λ 6 )；
K (p) is the stiffness matrix in the modal space, K (p) =diag (η) 1 ，…，η 6 )；
The damping matrix is generally not completely decoupled, and therefore is decoupled in a proportional damping form:
step S5, designing a modal space control rate, performing modal decoupling on a complex multi-degree-of-freedom system which is coupled with each other by using a modal conversion matrix, converting the complex multi-degree-of-freedom system into a single-degree-of-freedom system, and dividing the disturbance into a low-frequency disturbance section F for respectively designing a directional control rate and a vibration isolation control rate in the modal space to achieve vibration isolation and precise directional characteristics a Intermediate frequency disturbance interval F b And a high-frequency disturbance section F c The low-frequency disturbance is counteracted by utilizing the direction, the medium-frequency disturbance is counteracted by utilizing the active vibration isolation, and the passive vibration isolation is utilizedThe characteristics counteract the high frequency disturbances. Specifically:
vibration isolation control design: filtering the intermediate frequency disturbance interval F by a Kalman filter b Designing a vibration isolation control law:
5.1.1 measuring the Displacement x and the velocity in physical space
5.1.2 introducing Modal coordinate transformations
Multiplying phi at both ends of the modal equation T ,
The control equation of the system under the modal coordinates is:
the modal coordinates and their derivatives are extracted.
And 5.1.3, determining the modal control displacement gain g and the velocity gain h of each order. Giving an expected pole, comparing the expected pole with a characteristic value of a feedback system to obtain a control coefficient
5.1.4, converting the modal control force to a control force in the actual physical space:
pointing control design: filtering the low-frequency disturbance interval F by a Kalman filter a Is designed to point to controlLaw:
5.2.1 measuring the Displacement x and the velocity in physical space
5.2.2 introducing Modal coordinate transformations
Multiplying phi at both ends of the modal equation T ,
The control equation of the system under the modal coordinates is:
the modal coordinates and their derivatives are extracted.
5.2.3 inputting the displacement x and velocity in the ideal physical space
5.2.4 introducing Modal coordinate transformations
Multiplying phi at both ends of the modal equation T ,
5.3, carrying out error solving on the ideal pose error and the actual measured pose error in the independent modal space design;
the controller in the modal space is designed to:
is a control signal in the modal space.
The control force of the load in the modal space is expressed as:
the load control force in the joint space is expressed as:
obtaining:
set a systematic error e p ＝p d -p，
The system closed loop modal error equation is
And S6, comprehensively designing the directional stable control, combining the directional control and the vibration isolation control to obtain final control force output, and performing the directional stable control on the vibration isolation directional platform. Specifically:
combining the pointing and vibration isolation control to obtain final control force output, and performing pointing stable control on the Stewart platform: the influence of different frequencies is analyzed, control signals under different frequencies are output to the voice coil motor actuator, low-frequency precise pointing control is realized, medium-frequency active vibration isolation control and high-frequency passive vibration isolation control are realized, and therefore vibration isolation pointing performance of the platform is improved.
According to the vibration isolation pointing platform control precision and system robustness can not be met at the same time, a mode decoupling mode is adopted to decouple the multi-degree-of-freedom vibration isolation pointing system, a mutually orthogonal system model is obtained in a mode space, at the moment, the system takes an inherent vibration mode as a new basis vector, a system transfer function of the system in the mode space is solved, the system transfer function is taken as a controlled object, a controller is designed in the mode space, a MIMO problem is converted into a SISO problem, and then a calculation result in the mode space is reversely decoupled into a physical space to obtain an external force required to be provided at a system centroid.
While the invention has been described with reference to the presently preferred embodiments, it will be understood by those skilled in the art that the foregoing is by way of illustration and not of limitation, and that any modifications, equivalents, variations and the like which fall within the spirit and scope of the principles of the invention are intended to be included within the scope of the appended claims.
Claims (7)
1. The vibration isolation pointing platform modal decoupling control method is characterized by comprising the following steps of:
a. determining the design requirement of the vibration isolation pointing platform, carrying out design optimization on the configuration according to the design requirement, and selecting the type of a hinge and the type of a supporting leg actuator;
b. determining configuration parameters and design parameters of the vibration isolation pointing platform according to the selected hinge type and the selected landing leg actuator type;
c. according to the determined configuration parameters and design parameters, deducing a dynamic model of the vibration isolation directional platform, thereby determining a generalized mass matrix M (q), a generalized stiffness matrix K (q), a coriolis force matrix and a centrifugal force matrixTranspose J of jacobian matrix from dynamic to fixed coordinate system T The output force f of each leg a ；
d. According to the obtained dynamic model of the vibration isolation directional platform, calculating a modal conversion matrix ψ through a damping-free vibration equation, and carrying out modal decoupling on a generalized mass matrix, a generalized damping matrix and a generalized stiffness matrix by utilizing the modal conversion matrix;
e. the mode space control rate is designed, a mode conversion matrix is utilized to carry out mode decoupling and conversion on a complex multi-degree-of-freedom system which is coupled with each other into a single-degree-of-freedom system, vibration isolation and precise pointing characteristics are respectively achieved for the mode space design pointing control rate and the vibration isolation control rate, and the disturbance is divided into a low-frequency disturbance interval F a Intermediate frequency disturbance interval F b And a high-frequency disturbance section F c The low-frequency disturbance is counteracted by utilizing the direction, the medium-frequency disturbance is counteracted by utilizing the active vibration isolation, and the high-frequency disturbance is counteracted by utilizing the passive vibration isolation characteristic;
f. the directional stable control is comprehensively designed, the directional and vibration isolation control are combined to obtain final control force output, and the directional stable control is carried out on the vibration isolation directional platform;
wherein: the step d specifically comprises the following steps:
the free vibration equation is, without considering the system damping:
the charge conditions for the presence of a non-zero solution are:
|K(q)-δ 2 M(q)|＝0；
converting the vibration equation of the system into a characteristic equation for the natural frequency of the system:
(K(q)-δ 2 M(q))χ＝0；
χ is a feature vector of the feature equation;
the natural frequencies of the ith and jth orders are calculated:
when i is not equal to j,it can be seen that the mass matrix M (q) and the stiffness matrix K(q) is orthogonal to the different eigenvectors of the vibration mode;
when i=j, the number of times,wherein lambda is i And eta i The modal mass and modal stiffness of the ith order vibration mode are respectively;
expansion to full-order mode condition, ψ T M(q)Ψ＝M(p)；Ψ T K(q)Ψ＝K(p)；
Wherein, ψ is a modal decoupling matrix, ψ= [ χ ] 1 ，...，χ 6 ]
M (q) is a mass matrix in the modal space, M (p) =diag (λ) 1 ，…，λ 6 )
K (q) is a stiffness matrix in modal space, K (p) =diag (η) 1 ，…，η 6 )
Decoupling by adopting a proportional damping mode:
the step e comprises the following steps:
filtering the intermediate frequency disturbance interval F by a Kalman filter b Designing a vibration isolation control law:
5.1.1 measuring the Displacement x and the velocity in physical space
5.1.2, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ,
The control equation of the system under the modal coordinates is:
extracting modal coordinates and derivatives thereof;
5.1.3, determining the modal control displacement gain g and the velocity gain h of each order, giving an expected pole, comparing with the characteristic value of the feedback system, and obtaining a control coefficient
5.1.4, converting the modal control force to a control force in the actual physical space:
2. the method as claimed in claim 1, wherein in the step a:
the hinge types selected are: the hinge of the upper platform and the supporting rod is an arc-shaped flexible spherical hinge, and the hinge of the lower platform and the supporting rod is a notch-shaped flexible hook hinge; the leg actuator types are: and a voice coil motor.
3. The method of claim 2, wherein the configuration parameters and design parameters include: radius R of upper hinge circle p Radius R of lower hinge circle b Central angle of upper platformThe central angle theta of the lower platform, the pose vector q of the upper platform, the height H of the movable coordinate system in the fixed coordinate system and the distance r between the upper hinge point and the mass center of the upper supporting leg rci Distance r from lower hinge point to center of mass of lower leg tci Load centroid height z cm Damping coefficient c spring piece rigidity k, upper platform mass m, upper platform coiling coordinate system X-axis moment of inertia I xx Y-axis moment of inertia I of upper platform coiling coordinate system yy The Z-axis rotational inertia of the upper platform coiling coordinate system is I zz Mass m of upper leg rci Mass m of lower leg tci Moment of inertia I of upper leg in leg coordinate system rci Moment of inertia I of lower leg in leg coordinate system rci 。
4. A method according to claim 3, wherein said step c comprises:
the dynamics model of the Stewart platform is deduced, and the deduced dynamics model is simplified into:
wherein: m (q) is a generalized mass array; k (q) is a generalized stiffness matrix;is a matrix of coriolis force and centrifugal force; j (J) T Transpose of jacobian matrix from dynamic to fixed coordinate system, f a The output force for each leg.
5. The method of claim 4, wherein said step e further comprises:
filtering the low-frequency disturbance interval F by a Kalman filter a Is designed to point to the control law:
5.2.1 measuring the Displacement x and the velocity in physical space
5.2.2, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ：
The control equation of the system under the modal coordinates is:
extracting modal coordinates and derivatives thereof;
5.2.3 inputting the displacement x and velocity in the ideal physical space
5.2.4, introducing modal coordinate transformation:
multiplying phi at both ends of the modal equation T ,
6. The method of claim 5, wherein said step e further comprises:
carrying out error solving on the ideal pose error and the actual measured pose error in the independent modal space design;
the controller in the modal space is designed to:
u p is a control signal in the modal space;
the control force of the load in the modal space is expressed as:
the load control force in the joint space is expressed as:
obtaining:
set a systematic error e p ＝p d -p，
The system closed loop modal error equation is
7. The method of claim 6, wherein said step f comprises:
combining the pointing and vibration isolation control to obtain final control force output, and performing pointing stable control on the Stewart platform: the influence of different frequencies is analyzed, control signals under different frequencies are output to the voice coil motor actuator, low-frequency precise pointing control is realized, medium-frequency active vibration isolation control and high-frequency passive vibration isolation control are realized, and therefore vibration isolation pointing performance of the platform is improved.
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