CN112612211A - Servo system residual vibration suppression method based on parametric feedforward - Google Patents
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Abstract
The invention discloses a servo system residual vibration suppression method based on parametric feedforward, and belongs to the technical field of mechanical equipment control. The invention discloses a servo system residual vibration suppression method based on parameterized feedforward, which comprises the following steps: calculating a feedforward force by using a basis function parameterized feedforward controller through an input track and the parameterized feedforward controller; according to the optimal control theory, a performance objective function of a parameterized feedforward control algorithm is introduced to identify parameters of an input shaping filter and a feedforward controller; analyzing the error of the parameterized feedforward control and the convergence of the identification parameters; solving the optimal value of each parameter; through continuous exploration and test, the invention adopts a parameterized feedforward control algorithm, can effectively reduce the control difficulty of a servo system, reduces the calculated amount of a processor, has strong flexibility, high operation speed, good robustness and good control effect, and can meet the control requirement of the servo system.
Description
Technical Field
The invention relates to a servo system residual vibration suppression method based on parameterized feedforward, and belongs to the technical field of mechanical equipment control.
Background
In a servo system, a system is usually required to track a given track, so that errors are minimized, but the flexible characteristic existing in the motion process always generates a residual vibration phenomenon during high-speed positioning, and therefore, the positioning accuracy and requirements of the system are greatly influenced. In the servo system control method, the traditional feedback controller can only ensure the stability of the system, but has lag in time, and cannot meet the requirements of high positioning accuracy, high response speed and good robustness of the system; the feedforward controller can give a control quantity in advance according to the input track of the system, and has predictability. Therefore, a high-speed high-precision servo system generally adopts a two-degree-of-freedom control strategy of a feedforward controller and a feedback controller to meet the requirements of high positioning precision and stability.
The feedback controller of the servo system usually adopts PID control, and the high-precision track tracking performance and residual vibration suppression of the feedback controller are mainly realized by designing a feedforward controller. Most of the existing design methods for feedforward controllers adopt feedforward force injection or a method based on model inversion, wherein the method of feedforward force injection can realize the residual vibration suppression of fixed repeated tracks, and when the tracks change, the performance of the tracks is deteriorated; the feedforward control method based on the model inversion relies on a parametric model, the performance of the system deteriorates when the system is a non-minimum phase system, and the parametric model is difficult to identify for a complex system. Aiming at the defects in the prior art, research and development are needed to solve the defects in the prior art.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide the method for inhibiting the residual vibration of the servo system based on the parametric feedforward, which adopts the parametric feedforward control algorithm, can effectively reduce the control difficulty of the servo system, reduces the calculated amount of a processor, has strong flexibility, high operation speed, good robustness and good control effect, and can meet the control requirement of the servo system.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a servo system residual vibration suppression method based on parametric feedforward comprises the following steps:
the method comprises the following steps: connecting a servo control system, setting parameters of a relevant controller, and downloading the parameters to a chip on a motion control card;
step two: downloading controller parameters according to the time-invariant discrete state space requirement of the servo control system, enabling the servo system and enabling the motor to be closed-loop;
step three: inputting ideal track signal r (t) at signal input end of servo control system, and generating shaped input track signal r by parametric input shaping filtery(T) defining a sampling period TsCollecting output track signal y (t) and control signal u (f), collecting sampling point, shaping input signal ry(t) subtracting the output signal y (t) to form an error signal ey(t) and using the output signal y (t) and the control signal u (t) to remove the dependence on the model, parameterizing the feedforward controller with basis functions, calculating the feedforward force u through the input trajectory and the parameterized feedforward controllerff(t) specifying a response adjustment time of the servo system;
step four: according to the optimal control theory, a performance objective function of a parameterized feedforward control algorithm is introduced to identify a parameter theta input into a shaping filter and a feedforward controller, and a proper constraint parameter rho and lambda is selected to realize the suppression of residual vibration of a servo system;
step five: analyzing the error of the parameterized feedforward control and the convergence of the identification parameter theta;
step six: obtaining the optimal value of each parameter, utilizing an iterative optimization method to carry out iterative identification on the parameter theta according to the selected initial parameter and the measured error, the control signal and the output track data, utilizing the parameters of iterative identification to calculate the driving force and resend the driving force to the motion control card, and repeating the iteration to realize the residual vibration suppression of the system;
through continuous exploration and test, the invention adopts a parameterized feedforward control algorithm, can effectively reduce the control difficulty of a servo system, reduces the calculated amount of a processor, has strong flexibility, high operation speed, good robustness and good control effect, can meet the control requirement of the servo system, and can realize the suppression of the residual vibration of the track-changing task.
Further, the invention is particularly suitable for the identification of the parameter model of the non-minimum phase system and the complex system.
As a measure for improving the technical features of the present invention,
step two, the time-invariant discrete state space expression of the motion controller system of the unknown model is as follows:
wherein u isj＝[u(0)，…，u(N-1)]TFor finite discrete control input of commands, yj＝[y(0)，…，y(N-1)]TOutputting a signal for a finite discrete system, wherein j represents the iteration number, and N is the number of sampling points; the ideal trajectory is r (T), and the time span of iteration is T epsilon [0, T]。
As a measure for improving the technical features of the present invention,
step three, the parameterized feedforward control algorithm is as follows:
then the basis function is selected for the parameterized input shaping filter
And a feedforward controller
Basis functions
Is composed of
Wherein theta is an identification parameter of the parameterized input shaping filter and the feedforward controller, and na，nbTo form TyAnd TffNumber of basis functions, basis functions
Representing the i-th derivative of the input signal.
Parameterized input shaping filter
And a feedforward controller
Comprises the following steps:
the j iteration knows
Sr and SPr are related to a parametric model, and in order to eliminate the dependence on the model, the model is converted into a data-driven-based form
Sr＝T-1uj
SPr＝T-1yj
Wherein, S ═ 1+ PCfb)-1，
As a measure for improving the technical features of the present invention,
step four, the performance objective function of the parameterized feedforward control algorithm introduced by the optimal control theory is as follows:
because the reference track is in the stable period ryWhen r is equal to ey＝ryY-e, so the objective function can be written as
Then
Namely, it is
uj+1＝uj+ψLθΔ
Δu＝ψLθΔ
Wherein
As a measure for improving the technical features of the present invention,
based on the performance objective function, design of a parameterized input shaping filter and a feedforward controller is performed, since thetaΔAs a function Jj+1Variable of (2), order
The derivation can identify that:
therefore, the identification parameter update formula is:
as a measure for improving the technical features of the present invention,
and optimally designing a control signal constraint parameter rho, wherein the control signal constraint parameter rho limits the magnitude of control signal energy and influences an error convergence value, rho is any real number greater than or equal to 0, and the control signal energy is not limited when rho is 0.
As a measure for improving the technical features of the present invention,
and optimally designing a control variable quantity constraint parameter lambda, wherein the control variable quantity constraint parameter lambda limits the change step length of the control signal and influences the convergence speed, the lambda is any real number which is greater than or equal to 0, and the change step length of the control signal is not limited when the lambda is 0.
Step five, inputting a shaping filter in the parameterized feedforward algorithm
And a feedforward controller
Are all finite impulse response filters, and error eyError e is known in linear relation to the finite impulse response filter parametersyIs globally convergent, so:
according to
As known from the knowledge of the non-singularities and norms,
therefore, the recognition parameter θ is converged.
As a measure for improving the technical features of the present invention,
step six: identifying parameters of the parameterized input shaping filter and the feedforward controller by using upper computer simulation software MATLAB, and calculating feedforward force and input track signals; the motion control system is a direct current brushless motor, and the upper computer is a computer or an industrial personal computer. Preferably, the upper computer is a computer, the computer is widely applied, the computer is directly used as the upper computer, extra investment is not needed to be added, and the production cost is reduced.
Compared with the prior art, the invention has the following beneficial effects:
the invention adopts a parameterized feedforward control algorithm, can effectively reduce the control difficulty of a servo system, reduce the calculated amount of a processor and inhibit the residual vibration of the track-changing task.
The control method is detailed, the scheme is feasible, the process is simple and practical, the flexibility is strong, the operation speed is high, the control precision is high, the control effect is good, and the control requirement of a servo system can be met.
Drawings
FIG. 1 is a block diagram of a parameterized input shaping filter and feedforward controller control system according to the present invention;
FIG. 2 is a schematic diagram of a reference trajectory according to the present invention;
FIG. 3 is a graph of the error before and after iteration of the stabilization segment according to the present invention;
FIG. 4 is a graph of the variation of the trajectory error of the stable section in two norms according to the present invention;
FIG. 5 is a graph illustrating a variation of an identification parameter θ according to the present invention;
FIG. 6 is a graph of different reference trajectories for a variable trajectory test of the present invention;
FIG. 7 is a graph of the variation of the error of the stable section of the apodization test according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
As shown in fig. 1-7, a parametric feedforward-based servo system residual vibration suppression method includes the following steps:
the method comprises the following steps: connecting the brushless DC motor and the motion control card, opening the upper computer software, setting relevant parameters such as a controller and a sensor, and downloading the parameters to an ARM chip on the motion control card.
Step two: and after the parameters of the controller are downloaded, enabling the servo system to enable the motor to be closed-loop.
The time-invariant discrete state space expression of the motion controller system of the unknown model is as follows:
wherein u isj＝[u(0)，…，u(N-1)]TFor finite discrete control input of commands, yj＝[y(0)，…，y(N-1)]TOutputting a signal for a finite discrete system, wherein j represents the iteration number, and N is the number of sampling points; the ideal trajectory is r (T), and the time span of iteration is T epsilon [0, T]。
Step three: inputting a planned reference track r (t) at the signal input end of the motion control system, and generating a shaped input reference track r through a parameterized input shaping filtery(t) identifying the initial value of the parameter as theta0＝[0，0，0，0，0.1，0，0]TCalculating an initial feedforward force uff(T) defining a sampling period TsCollecting output trace signal y (t) and control signal u (t) for 0.0005s, collecting time 1.0235s, total 2048 sampling points, and shaping input signal ry(t) subtracting the output signal y (t) to form an error signal ey(t)；
The parameterized feedforward control algorithm shown in fig. 1 is used as follows:
uff＝Tffr
ry＝Tyr
input shaping filter TyAnd a feedforward controller TffThe parameterized polynomial is selected as
Wherein
Wherein theta is an identification parameter of the parameterized input shaping filter and the feedforward controller, and na，nbTo form TyAnd TffNumber of basis functions, basis functions
Representing the i-th derivative of the input signal.
Parameterized input shaping filter
And a feedforward controller
Comprises the following steps:
j th iteration measurement data
uj，yjIt can be known that
Sr and SPr are related to a parametric model, and in order to eliminate dependence on the model, the measured data is converted into a data-driven-based form
Sr＝T-1uj
SPr＝T-1yj
Wherein, S ═ 1+ PCfb)-1，
Step four: aiming at a control system block diagram of a parameterized input shaping filter and a feedforward controller shown in FIG. 1, parameters of the input shaping filter and the feedforward controller are identified according to a performance objective function of a parameterized feedforward control algorithm introduced by an optimal control theory, and proper constraint parameters rho and lambda are selected to realize tracking of a track or an apodization test.
The performance objective function of the parameterized feedforward control algorithm is as follows:
as can be seen from the figure 2 of the drawings,reference trajectory r during the stationary periodyWhen r is equal to ey＝ryY-e, so the objective function can be written as
Then
Namely, it is
uj+1＝uj+ψLθΔ
Δu＝ψLθΔ
Wherein
Based on performance objective function, design of parameterized input shaping filter and feedforward controller is carried out, because of thetaΔAs a function Jj+1Variable of (2), order
The derivation can identify that:
therefore, the identification parameter update formula is:
the control signal constraint parameter rho limits the magnitude of control signal energy and influences an error convergence value, rho is any real number greater than or equal to 0, and the control signal energy is not limited when rho is 0; and controlling a variable quantity constraint parameter lambda to limit the change step length of the control signal and influence the convergence speed, wherein lambda is any real number which is greater than or equal to 0, and the change step length of the control signal is not limited when lambda is 0.
Step five, the closed loop control object is shown in figure 1, and an input shaping filter in the parameterized feedforward algorithm
And a feedforward controller
Are all finite impulse response filters, and error eyError e is known in linear relation to the finite impulse response filter parametersyIs globally convergent, so:
according to
As known from the knowledge of the non-singularities and norms,
therefore, the recognition parameter θ is converged.
Step six: iterative optimization is carried out by acquiring errors, control signals and output track signals by utilizing host computer simulation software (such as MATLAB), parameters of an input shaping filter and a feedforward controller are identified by using a data driving method, a fourth-order S-shaped reference track shown in figure 2 or different reference tracks shown in figure 6 are adopted for a variable track test (the reference track 1 is run in the first 10 times of iteration, the reference track 2 is run in the 11 th time of iteration), the identified parameters are used for updating the input shaping filter and the feedforward controller, and then feedforward force is calculated
And issuing the data to the motion control card again, and repeating the iteration to realize the residual vibration suppression and the convergence of the identification parameters of the track or the track-changing tracking task. As shown in fig. 4 and 7, the present invention can achieve residual vibration suppression of the trajectory and has certain robustness to the apodization.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A servo system residual vibration suppression method based on parametric feedforward is characterized in that,
the method comprises the following steps:
the method comprises the following steps: connecting a servo control system, setting parameters of a relevant controller, and downloading the parameters to a chip on a motion control card;
step two: downloading controller parameters according to the time-invariant discrete state space requirement of the servo control system, enabling the servo system and enabling the motor to be closed-loop;
step three: inputting ideal track signal r (t) at signal input end of servo control system, and generating shaped input track signal r by parametric input shaping filtery(T) defining a sampling period TsCollecting output track signal y (t) and control signal u (t), collecting sampling point, shaping input signal ry(t) subtracting the output signal y (t) to form an error signal ey(t) and using the output signal y (t) and the control signal u (t) to remove the dependence on the model, parameterizing the feedforward controller with basis functions, calculating the feedforward force u through the input trajectory and the parameterized feedforward controllerff(t) specifying a response adjustment time of the servo system;
step four: according to the optimal control theory, a performance objective function of a parameterized feedforward control algorithm is introduced to identify a parameter theta input into a shaping filter and a feedforward controller, and a proper constraint parameter rho and lambda is selected to realize the suppression of residual vibration of a servo system;
step five: analyzing the error of the parameterized feedforward control and the convergence of the identification parameter theta;
step six: and solving the optimal value of each parameter, carrying out iterative identification on the parameter theta by utilizing an iterative optimization method to measure the error and the control signal according to the selected initial parameter and outputting track data, calculating the driving force by utilizing the iterative identification parameter and issuing the driving force to the motion control card again, and repeating the iteration to realize the residual vibration suppression of the system.
2. The method for suppressing residual vibration of a servo system based on parametric feedforward as claimed in claim 1, wherein in step two, the time-invariant discrete state space expression of the motion controller system of unknown model is:
wherein u isj＝[u(0)，…，u(N-1)]TFor finite discrete control input of commands, yj＝[y(0)，…，y(N-1)]TOutputting a signal for a finite discrete system, wherein j represents the iteration number, and N is the number of sampling points; the ideal trajectory is r (T), and the time span of iteration is T epsilon [0, T]。
3. The method for suppressing the residual vibration of the servo system based on the parametric feedforward as claimed in claim 1, wherein in step three, the parametric feedforward control algorithm is as follows:
then the basis function is selected for the parameterized input shaping filter
And a feedforward controller
Basis functions
Is composed of
Wherein theta is an identification parameter of the parameterized input shaping filter and the feedforward controller, and na，nbTo form TyAnd TffNumber of basis functions, basis functions
Represents the i-th derivative of the input signal;
parameterized input shaping filter
And a feedforward controller
Comprises the following steps:
the j iteration knows
Sr and SPr are related to a parametric model, and in order to eliminate the dependence on the model, the model is converted into a data-driven-based form
Sr＝T-1uj
SPr＝T-1yj
Wherein S ═ S(1+PCfb)-1，
4. The parametric feedforward-based servo system residual vibration suppression method as claimed in claim 1, wherein in step four, the performance objective function of the parameterized feedforward control algorithm introduced by the optimal control theory is as follows:
because the reference track is in the stable period ryWhen r is equal to ey＝ryY-e, so the objective function can be written as
Then
Namely, it is
uj+1＝uj+ψLθΔ
Δu＝ψLθΔ
Wherein
5. A parametric feedforward-based servo system residual vibration suppression method as in claim 4,
based on performance objective function, design of parameterized input shaping filter and feedforward controller is carried out, because of thetaΔAs a function Jj +1Variable of (2), order
The derivation can identify that:
therefore, the identification parameter update formula is:
6. a parametric feedforward-based servo system residual vibration suppression method as in claim 5,
and optimally designing a control signal constraint parameter rho, wherein the control signal constraint parameter rho limits the magnitude of control signal energy and influences an error convergence value, rho is any real number greater than or equal to 0, and the control signal energy is not limited when rho is 0.
7. A parametric feedforward-based servo system residual vibration suppression method as in claim 6,
and optimally designing a control variable quantity constraint parameter lambda, wherein the control variable quantity constraint parameter lambda limits the change step length of the control signal and influences the convergence speed, the lambda is any real number which is greater than or equal to 0, and the change step length of the control signal is not limited when the lambda is 0.
8. A parametric feedforward-based servo system residual vibration suppression method as in claim 1,
step five, inputting a shaping filter in the parameterized feedforward algorithm
And a feedforward controller
Are all finite impulse response filters, and error eyError e is known in linear relation to the finite impulse response filter parametersyIs globally convergent, so:
according to
As known from the knowledge of the non-singularities and norms,
therefore, the recognition parameter θ is converged.
9. A parametric feedforward-based servo system residual vibration suppression method as in claim 1,
step six: identifying parameters of the parameterized input shaping filter and the feedforward controller by using upper computer simulation software MATLAB, and calculating feedforward force and input track signals; the motion control system is a direct current brushless motor, and the upper computer is a computer or an industrial personal computer.
10. A parametric feedforward-based servo system residual vibration suppression method as in claim 9,
the upper computer is a computer, the computer application is common, the computer is directly used as the upper computer, additional investment is not required to be added, and the production cost is reduced.
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