CN113359454A - Method for improving control precision of multi-degree-of-freedom motion system - Google Patents

Method for improving control precision of multi-degree-of-freedom motion system Download PDF

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CN113359454A
CN113359454A CN202110659583.9A CN202110659583A CN113359454A CN 113359454 A CN113359454 A CN 113359454A CN 202110659583 A CN202110659583 A CN 202110659583A CN 113359454 A CN113359454 A CN 113359454A
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周烽
王辉
金春水
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Abstract

The invention relates to a method for improving the control precision of a multi-degree-of-freedom motion system, which comprises the following steps: converting the multi-degree-of-freedom motion system into a plurality of single-degree-of-freedom systems through a static decoupling matrix; carrying out system identification on the converted single-degree-of-freedom system to obtain a nominal model of the system; designing a disturbance observer matrix aiming at the plurality of single-degree-of-freedom systems; designing an adaptive filter matrix, and defining an error signal; and setting an evaluation function and a parameter iterative updating algorithm. The invention can solve the problem of static and dynamic coupling of the multi-degree-of-freedom motion system, and simultaneously improve the anti-interference capability, thereby improving the control precision of the multi-degree-of-freedom motion system.

Description

Method for improving control precision of multi-degree-of-freedom motion system
Technical Field
The invention relates to a method for improving the control precision of a multi-degree-of-freedom motion system.
Background
The motion precision is an important performance index of an electromechanical motion system, and has extremely high requirements particularly in the fields of optical instruments, precision detection equipment, semiconductor manufacturing and the like. On one hand, the extremely high precision has very high requirements on the mechanical design, manufacture and assembly of the equipment; on the other hand, the effective control method has important significance for improving the motion precision of the electromechanical equipment.
The complex electromechanical motion system generally has multiple degrees of freedom and the characteristic of multiple input and multiple output, and the design of the control method is more complex compared with a single-degree-of-freedom system with single input and single output. In order to improve the motion precision of the electromechanical motion system, on one hand, an anti-disturbance control method is adopted for external disturbance of the system; on the other hand, the decoupling control is carried out on the electromechanical motion system by considering the internal coupling of the multi-input multi-output system. In practical application, a common method is to convert the multivariable control problem into a single-input single-output univariate control problem through a decoupling proportion matrix and then design the controller for the motion of single degree of freedom one by one. However, the decoupling ratio can only solve the problem of static coupling, and a certain dynamic coupling still exists in an actual system, so that the motion precision of the electromechanical motion system cannot achieve the optimal effect.
At present, no method can solve the problems that a multi-degree-of-freedom motion system is statically and dynamically coupled and is easy to suffer from external disturbance to cause the precision of the motion system to be reduced.
Disclosure of Invention
In view of the above, there is a need to provide a method for improving the control accuracy of a multi-degree-of-freedom motion system, which can solve the problem of static and dynamic coupling of the multi-degree-of-freedom motion system, and improve the anti-interference capability of the system, thereby improving the control accuracy of the multi-degree-of-freedom motion system.
The invention provides a method for improving the control precision of a multi-degree-of-freedom motion system, which comprises the following steps: a. converting the multi-degree-of-freedom motion system into a plurality of single-degree-of-freedom systems through a static decoupling matrix; carrying out system identification on the converted single-degree-of-freedom system to obtain a nominal model of the system; b. designing a disturbance observer matrix based on a nominal model of the system; c. designing an adaptive filter matrix, and defining an error signal; d. and setting an evaluation function and a parameter iterative updating algorithm according to the defined error signal and the designed adaptive filter matrix.
Specifically, the method further comprises: and e, initializing the matrix parameters of the adaptive filter according to the evaluation function and the parameter iterative update algorithm, and carrying out adaptive adjustment in a closed-loop state until the adjustment is finished.
Specifically, the step a specifically includes:
obtaining a static decoupling matrix K of the multi-degree-of-freedom motion system P by adopting a traditional dynamics or test method for the multi-degree-of-freedom motion system P0Is connected in series with K in front of a multi-degree-of-freedom motion system P0And converting the data into superposition of a plurality of single-degree-of-freedom systems and the residual coupling part.
Further applying multi-degree-of-freedom input excitation to the multi-degree-of-freedom motion system, testing a multi-degree-of-freedom output response curve to obtain a frequency domain response curve matrix, respectively carrying out system identification on curves on diagonal lines to obtain Pn1, Pn2 and Pn3 …, and combining the curves into a diagonal matrix to obtain Pn ═ diag (Pn1, Pn2, Pn3 and …);
the controllers C1, C2, and C3 … …, which are designed separately, are combined into a diagonal matrix to obtain an overall closed-loop controller matrix C ═ diag (C1, C2, …), that is, a diagonal matrix.
Specifically, the step b specifically includes:
respectively designing a self-adjusting interference observer for the single-degree-of-freedom system by using a nominal model Pn of the system to obtain a low-pass filter matrix Q and a matrix QPn-1Wherein the Q diagonal matrix form is:
Q＝diag(Q1(z),Q2(z),Q3(z),Q4(z),Q5(z),Q6(z))
the element in Q is a low pass filter to ensure QPn-1And (5) stabilizing and regularizing.
Specifically, the step c comprises:
the adaptive filter matrix is represented by the following formula:
Figure BDA0003114607070000031
Figure BDA0003114607070000032
Figure BDA0003114607070000033
wherein, WijFor digital filters, i and j are matrix indices, θ iN jRepresenting the digital filter coefficients and N the order of the digital filter.
Specifically, the step c further comprises:
the error of the disturbance estimate is expressed as the difference between the system output and the ideal nominal model output, i.e.:
eT(n)＝Y(n)-Pn·UT(n)
Figure BDA0003114607070000034
wherein U (n) represents input voltage vector, e (n) represents output Y vector of whole system and output Pn.U of ideal nominal modelTThe difference of (n), also a vector,
Figure BDA0003114607070000035
and the disturbance observation value of the input end of the self-adaptive filter matrix W and the disturbance estimation value of the output end of the self-adaptive filter matrix W are respectively represented, and the forms are vectors. n represents the number of iterations.
Specifically, the step d includes:
the adaptive filter evaluation function j (n) is:
J(n)＝e(n)γe(n)T
Figure BDA0003114607070000041
where j (n) represents an evaluation function or target value, γ represents a weight matrix, in diagonal form, with the elements in γ being the weight of each degree of freedom, where each element corresponds to each degree of freedom.
Specifically, the step d further includes:
the weight coefficient of the adaptive filter matrix W is iterated by a steepest descent method, and the formula is as follows:
Figure BDA0003114607070000042
specifically, the step e includes:
initializing parameters of the self-adaptive filter matrix W to be zero, opening and closing the loop state, enabling closed-loop input to be a fixed value and operating a self-adaptive adjustment program, and when the value error of the system output Y closed-loop input meets the requirement, closing the self-adaptive adjustment and keeping the final parameters.
The beneficial effect of this application is as follows: firstly, the self-adjusting interference observer is suitable for a multi-degree-of-freedom system, and can simultaneously realize dynamic decoupling and interference suppression of the multi-degree-of-freedom system; secondly, the method for improving the control precision of the multi-degree-of-freedom motion system, namely the parameters of the self-adjusting disturbance observer can be automatically adjusted according to input and output data, so that the precision of the multi-degree-of-freedom motion system achieves the target effect; finally, the self-adjusting disturbance observer can be designed independently of the closed-loop controller, and the self-adjusting process of the parameters can be performed under the closed-loop condition of the system.
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FIG. 1 is a flow chart of a method of improving control accuracy of a multiple degree of freedom motion system in accordance with the present invention;
FIG. 2 is a schematic diagram of an embodiment of the method for improving the control accuracy of a multi-degree-of-freedom motion system according to the present invention;
FIG. 3 is a diagram illustrating a multiple degree of freedom motion system P according to an embodiment of the present invention;
fig. 4 is a schematic diagram illustrating an implementation of dynamic decoupling, showing an original model of a multi-degree-of-freedom motion system and a compensated model to which the present invention is applied according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, it is a flowchart illustrating a preferred embodiment of the method for improving the control accuracy of a multi-degree-of-freedom motion system according to the present invention.
It should be noted that, referring to fig. 2, an implementation environment of the method for improving the control accuracy of the multi-degree-of-freedom motion system according to the present invention is shown: where R is the system input, C is the closed-loop controller, U is the closed-loop controller output, K0The method is characterized in that the method is a static decoupling matrix, P is a multi-degree-of-freedom motion system, Y represents the output of the multi-degree-of-freedom motion system, and d is the external disturbance of the multi-degree-of-freedom motion system. And a self-adjusting interference observer is arranged in the scope of the Sob dotted line, and comprises a low-pass filter matrix Q, a system nominal model Pn, an adaptive filter matrix W and an Update rule Update.
And step S1, converting the multi-degree-of-freedom motion system into a plurality of single-degree-of-freedom systems through the static decoupling matrix. Specifically, the method comprises the following steps:
in this embodiment, a dynamic analysis or a test analysis is performed on the multiple degree of freedom motion system P shown in fig. 3 to obtain a static decoupling matrix K of the multiple degree of freedom motion system P0Is connected in series with K in front of a multi-degree-of-freedom motion system P0(i.e., P.times.K)0) To be converted into a single-degree-of-freedom system with a plurality of single inputs and single outputs.
The static decoupling matrix is obtained through dynamic analysis or experiments, and the purpose and principle are as follows: in order to enable the multi-degree-of-freedom motion system to move along a certain degree of freedom, the force output by each motor needs to keep a certain relative relation, so that the direction of resultant force is the same as the motion direction. The relation that the moving direction of different degrees of freedom needs to keep is different, and the matrix form is formed by combining. When only the proportional relationship between the motors is considered, the matrix is a constant matrix, called a static decoupling matrix.
And step S2, performing system identification on the converted single-degree-of-freedom system to obtain a nominal model of the system, and primarily performing closed-loop controller design. Specifically, the method comprises the following steps:
in this embodiment, the decoupled single-degree-of-freedom systems are subjected to system identification to obtain a nominal model Pn of the single-degree-of-freedom systems, and a multi-degree-of-freedom closed-loop controller C is designed by using the nominal model Pn, so that the system can realize preliminary closed-loop control.
In this embodiment, after decoupling, system identification is performed on a plurality of single-degree-of-freedom systems to obtain Pn1, Pn2, Pn3 …, and the like, and these are combined into a diagonal matrix to obtain Pn (Pn1, Pn2, Pn3, …), so Pn is a matrix, belongs to a multiple-degree-of-freedom model, and is a nominal model of a multiple-degree-of-freedom motion system P.
The closed-loop controller is a conversion controller designed for a single-degree-of-freedom system, and may select common PID control, internal model control, and the like, and combine the controllers C1, C2, and C3 … …, which are designed separately, into a diagonal matrix, thereby obtaining an overall closed-loop controller matrix C — diag (C1, C2, …), that is, the diagonal matrix.
And step S3, designing a disturbance observer matrix for the multiple single-degree-of-freedom systems. Specifically, the method comprises the following steps:
respectively designing a self-adjusting interference observer for the single-degree-of-freedom system by using a nominal model Pn of the system to obtain a low-pass filter matrix Q and a matrix QPn-1Wherein the Q diagonal matrix form is:
Q＝diag(Q1(z),Q2(z),Q3(z),Q4(z),Q5(z),Q6(z))
the element in Q is a low-pass filter, either a classical polynomial filter or a zero-pole filter to ensure QPn-1And (5) stabilizing and regularizing.
Step S4, an adaptive filter matrix is designed to define an error signal. Specifically, the method comprises the following steps:
the adaptive filter matrix designed in this embodiment is expressed as the following formula:
Figure BDA0003114607070000071
Figure BDA0003114607070000072
Figure BDA0003114607070000073
wherein, WijFor a digital filter, i and j are matrix indices,
Figure BDA0003114607070000074
representing the digital filter coefficients and N the order of the digital filter.
Taking the nominal model of the system as a reference model, the difference between the reference model response and the system output response is called an error signal, denoted by e (n), and since the disturbance observer brings the system closer to the nominal model Pn after active compensation, the error of the disturbance estimate can be expressed as the difference between the system output and the ideal nominal model output, i.e.:
eT(n)＝Y(n)-Pn·UT(n)
Figure BDA0003114607070000075
wherein U (n) represents input voltage vector, e (n) represents output Y vector of whole system and output Pn.U of ideal nominal modelTThe difference of (n), is also a vector.
Figure BDA0003114607070000076
Representing the disturbance observed value at the input end of the adaptive filter matrix W and the disturbance estimated value at the output end of the adaptive filter matrix W, respectively, and deriving the above formulas according to fig. 2, both of which are in the form of vectors. n represents the number of iterations.
Step S5: and setting an evaluation function and a parameter iterative updating algorithm according to the defined error signal and the designed adaptive filter matrix. The method specifically comprises the following steps:
in this embodiment, the adaptive filter evaluation function j (n) is set as:
J(n)＝e(n)γe(n)T
Figure BDA0003114607070000081
where j (n) represents an evaluation function or target value, γ represents a weight matrix, in diagonal form, with the elements in γ being the weight for each degree of freedom, and e (n) is the same as described above, with each element corresponding to each degree of freedom.
The weight coefficient of the adaptive filter matrix W in this embodiment is iterated by a steepest descent method, and the formula is:
Figure BDA0003114607070000082
step S6: and initializing the matrix parameters of the adaptive filter according to the evaluation function and the parameter iterative update algorithm, and performing adaptive adjustment in a closed loop state until the adjustment is finished. The method specifically comprises the following steps:
initializing parameters of the self-adaptive filter matrix W to be zero, opening and closing the loop state, enabling closed-loop input to be a fixed value and operating a self-adaptive adjustment program, and when the value error of the system output Y closed-loop input meets the requirement, closing the self-adaptive adjustment and keeping the final parameters. If it is desired that the error between the value of the system output Y and the closed-loop input value is as small as possible, the adaptive adjustment can also be ended and the final parameters can be retained when the error has changed very slowly. And after the self-adaptive adjustment, fixing the filter matrix parameters as a part of the overall control parameters, so that the self-adaptive adjustment is completed. Referring to fig. 4, the implementation of dynamic decoupling is shown in detail by referring to the original model of the multi-degree-of-freedom platform and the compensated model of the method for improving the control accuracy of the multi-degree-of-freedom motion system.
Although the present invention has been described with reference to the presently preferred embodiments, it will be understood by those skilled in the art that the foregoing description is illustrative only and is not intended to limit the scope of the invention, as claimed.

Claims (9)

1. A method for improving the control accuracy of a multi-degree-of-freedom motion system is characterized by comprising the following steps:
a. converting the multi-degree-of-freedom motion system into a plurality of single-degree-of-freedom systems through a static decoupling matrix; carrying out system identification on the converted single-degree-of-freedom system to obtain a nominal model of the system;
b. designing a disturbance observer matrix based on a nominal model of the system;
c. designing an adaptive filter matrix, and defining an error signal;
d. and setting an evaluation function and a parameter iterative updating algorithm according to the defined error signal and the designed adaptive filter matrix.
2. The method of claim 1, wherein the method further comprises:
and e, initializing the matrix parameters of the adaptive filter according to the evaluation function and the parameter iterative update algorithm, and carrying out adaptive adjustment in a closed-loop state until the adjustment is finished.
3. The method according to claim 2, wherein the step a specifically comprises the steps of:
applying multi-degree-of-freedom input excitation to the multi-degree-of-freedom motion system decoupled by a static decoupling method, testing a multi-degree-of-freedom output response curve to obtain a frequency domain response curve matrix, respectively carrying out system identification on curves on diagonal lines to respectively obtain Pn1, Pn2 and Pn3 …, and combining the Pn1, Pn2 and Pn3 … into a diagonal matrix to obtain Pn ═ diag (Pn1, Pn2, Pn3 and …);
the controllers C1, C2, and C3 … …, which are designed separately, are combined into a diagonal matrix to obtain an overall closed-loop controller matrix C ═ diag (C1, C2, …), that is, a diagonal matrix.
4. The method according to claim 3, wherein said step b comprises in particular:
respectively designing a self-adjusting interference observer for the single-degree-of-freedom system by using a nominal model Pn of the system to obtain a low-pass filter matrix Q and a matrix QPn-1Wherein the Q diagonal matrix form is:
Q＝diag(Q1(z),Q2(z),Q3(z),Q4(z),Q5(z),Q6(z))
the element in Q is a low pass filter to ensure QPn-1And (5) stabilizing and regularizing.
5. The method of claim 4, wherein said step c comprises:
the adaptive filter matrix is represented by the following formula:
Figure FDA0003114607060000021
Figure FDA0003114607060000022
Figure FDA0003114607060000023
wherein, WijFor a digital filter, i and j are matrix indices,
Figure FDA0003114607060000024
representing the digital filter coefficients and N the order of the digital filter.
6. The method of claim 5, wherein said step c further comprises:
the error of the disturbance estimate is expressed as the difference between the system output and the ideal nominal model output, i.e.:
eT(n)＝Y(n)-Pn·UT(n)
Figure FDA0003114607060000025
wherein U (n) represents the input voltageQuantity, e (n) represents the overall system output Y vector and the ideal nominal model output Pn.UTThe difference of (n), also a vector,
Figure FDA0003114607060000026
and the disturbance observation value of the input end of the self-adaptive filter matrix W and the disturbance estimation value of the output end of the self-adaptive filter matrix W are respectively represented, the forms are vectors, and n represents the iteration times.
7. The method of claim 6, wherein said step d comprises:
the adaptive filter evaluation function j (n) is:
J(n)＝e(n)γe(n)T
Figure FDA0003114607060000031
where j (n) represents an evaluation function or target value, γ represents a weight matrix, in diagonal form, with the elements in γ being the weight of each degree of freedom, where each element corresponds to each degree of freedom.
8. The method of claim 7, wherein step d further comprises:
the weight coefficient of the adaptive filter matrix W is iterated by a steepest descent method, and the formula is as follows:
Figure FDA0003114607060000032
9. the method of claim 8, wherein step e comprises:
initializing parameters of the self-adaptive filter matrix W to be zero, opening and closing the loop state, enabling closed-loop input to be a fixed value and operating a self-adaptive adjustment program, and when the value error of the system output Y closed-loop input meets the requirement, closing the self-adaptive adjustment and keeping the final parameters.
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