CN115356932A - Servo control system and feedforward controller parameter setting method - Google Patents
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Abstract
The invention relates to a servo control system and a parameter setting method of a feedforward controller, which comprises the following steps: an addition and subtraction arithmetic unit, a feedback controller, a feedforward controller, an addition arithmetic unit and a controlled object; the input end of the addition and subtraction arithmetic unit is connected with the output ends of the reference track and the controlled object so as to determine the track tracking error and output the track tracking error to the feedback controller; the feedback controller generates a feedback control signal based on the trajectory tracking error; the feedforward controller generates a feedforward control signal based on the reference trajectory; the output end of the feedback controller and the output end of the feedforward controller are connected with the input end of the addition arithmetic unit; the output end of the addition arithmetic unit is connected with the input end of the controlled object; and (3) the parameters of the feedforward controller are iteratively optimized according to the reference track and the track tracking error, and the iteration is stopped when the iteration termination condition is met. The servo control system and the feedforward controller parameter setting method do not need to establish a mathematical model of the controlled object, and can avoid the restriction of modeling errors on the servo performance.
Description
Technical Field
The invention relates to the technical field of servo control, in particular to a servo control system and a parameter setting method of a feedforward controller.
Background
Servo control systems are of great importance in modern industrial applications. In servo control systems, the purpose of using a feedforward controller is to eliminate the tracking error introduced by the reference trajectory. Therefore, the reasonable design of the servo control system has important significance, and particularly, the parameterization method of the feedforward controller and the determination of the optimal parameters of the feedforward controller directly determine the trajectory tracking precision of the servo control system.
The existing design method of the feedforward controller generally adopts a model-based method, namely, the feedforward controller is designed according to an accurate model of a controlled object; although the feedforward controller is designed based on a model method, the feedforward controller is simple and practical, an accurate model of a controlled object needs to be obtained, and the requirement on modeling accuracy is high; particularly, for a controlled object with complex dynamic characteristics, it is expensive to obtain an accurate model, modeling errors are inevitable, implementation based on a model method is difficult, and effects are difficult to guarantee.
Disclosure of Invention
In view of the above, it is necessary to provide a servo control system and a method for tuning parameters of a feedforward controller.
A servo control system comprising: an addition and subtraction arithmetic unit, a feedback controller C, a feedforward controller F, an addition arithmetic unit and a controlled object P;
the input end of the addition and subtraction arithmetic unit is connected with the reference track r and the output end of the controlled object P; the output end of the addition and subtraction arithmetic unit is connected with the input end of the feedback controller C; the input end of the feedforward controller F is connected with a reference track r; the output end of the feedback controller C and the output end of the feedforward controller F are connected with the input end of the addition arithmetic unit; the output end of the addition arithmetic unit is connected with the input end of the controlled object P;
the addition and subtraction arithmetic unit obtains a reference track r and a position signal y output by a controlled object, determines a track tracking error e according to the difference value of the reference track r and the position signal y, and inputs the track tracking error e into the feedback controller C;
the feedback controller C generates a feedback control signal u based on the tracking error e c (ii) a The feedforward controller F generates a feedforward control based on the reference trajectory r and the feedforward controller parameter ρSignal u f (ii) a The parameter rho of the feedforward controller is iteratively optimized according to the reference track r and the track tracking error e, and when the iteration termination condition is met, the iteration is stopped, and the obtained parameter of the feedforward controller is an optimal parameter;
the addition operator acquires a feedback control signal u output by the feedback controller C c And a feedforward control signal u output by the feedforward controller F f Feedback control signal u c And a feedforward control signal u f Adding the signals to obtain a total control signal u, and outputting the total control signal u to a controlled object P;
and after receiving the master control signal u output by the addition arithmetic unit, the controlled object P outputs a position signal y and feeds the position signal y back to the addition and subtraction arithmetic unit.
A method of feedforward controller parameter tuning, the method comprising: a feedforward controller parameter optimization objective function J, a feedforward controller parameterization method, a feedforward controller parameter iteration optimization method and an iteration termination condition;
the feedforward controller parameter optimization objective function J is determined according to the actual control requirement of the servo control system, and the optimal parameter of the feedforward controller is determined by minimizing the feedforward controller parameter optimization objective function J;
the feedforward controller parameterization method expresses the feedforward controller F as a mathematical expression with respect to a finite number of parameters and basis functions;
according to the feedforward controller parameter iterative optimization method, updating a feedforward controller parameter rho by adopting an iterative optimization method according to a reference track r and a track tracking error e until an iteration termination condition is met;
the iteration termination condition is a basis for judging whether the parameter rho of the feedforward controller stops iteration, if the iteration termination condition is met, the iteration is stopped, the parameter optimization objective function J of the feedforward controller can be considered to reach the minimum value, and the obtained parameter of the feedforward controller is the optimal parameter; otherwise, continuing the iteration until the iteration termination condition is met.
The feedforward controller parameter optimization objective function J is the square sum of the track tracking error e, and the expression is as follows:
where N is the sample length.
The parameterization method of the feedforward controller comprises the following steps:
wherein z is a complex variable of the discrete transfer function; n and m are denominator polynomial order and numerator polynomial order respectively, and natural numbers are taken; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing denominator polynomial parameters a 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
If there is an output delay in the controlled object P, the method for parameterizing the feedforward controller may be:
wherein d is the known output delay number of the controlled object P; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing a parameter a of a denominator polynomial 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
If the controlled object P has a rigid body mode, the parameterization method of the feedforward controller can be as follows:
wherein, T s Sampling time of a servo control system; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing denominator polynomial parameters a 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
The parameter iterative optimization method of the feedforward controller comprises the following steps:
wherein j is the number of iterations; λ is learning rate, and is between 0 and 1;
optimizing the first derivative of the objective function J on the feedforward controller parameter p at p for the feedforward controller parameter j Taking the value of (A);
optimizing the Hessian matrix of the objective function J to the feedforward controller parameter rho at rho for the feedforward controller parameter j The value of (c) is as follows.
The method for setting the parameters of the feedforward controller comprises the following specific steps:
initializing, enabling the iteration times j =0, and setting an initial parameter rho of a feedforward controller F 0 ；
Step two, in the feed forward controller F = F (rho) j Z) performing the j-th track following task, and recording the track following error e j ；
Step three, estimating a first derivative of a feedforward controller parameter optimization objective function J to a feedforward controller parameter rho to be in rho j Value of (a)
Step four, estimating the Hessian matrix of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Inverse of the value of
Step five, according to the parameter iteration optimization method of the feedforward controllerUpdating feedforward controller parameters to obtain rho j+1 ；
Step six, in the feed forward controller F = F (rho) j+1 Z) performing the j +1 th track following task, and recording the track following error e j+1 ；
Step seven, judging whether the result of the J +1 th track tracking task meets the iteration termination condition, if so, stopping the iteration, considering that the parameter optimization objective function J of the feedforward controller reaches the minimum value, and obtaining the parameter rho of the feedforward controller j+1 Is an optimal parameter; otherwise, let j = j +1, jump to step three.
Initial parameter ρ of the feedforward controller F 0 May be set to zero.
If the controlled object P has rigid body mode and the nominal quality is known, adopting the parameterization method of the feedforward controller in claim 6, and setting the initial parameter P of the feedforward controller F 0 When b is greater than b 0 Is set as the reciprocal of the nominal mass of the controlled object, and the initial values of other parameters are set as zero.
The first derivative of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho is in rho j Value of (A)
The estimation method comprises the following steps:
first derivative of the feedforward controller F on the feedforward controller parameter p
The product of the reference trajectory r is denoted as gamma; setting the reference track r of the servo control system to be zero, and setting the track tracking error e j Adding the processed signal to the input end of the controlled object after the inverse sequence processing, recording the position signal y of the output end of the controlled object, and recording the result of the inverse sequence processing of the position signal y as Λ j ；-2Γ T Λ j Is that
The feedforward controller parameterOptimizing Hessian matrix of an objective function J to a feedforward controller parameter rho at rho j Inverse of the value of
The estimation method comprises the following steps:
note B j Optimizing an objective function J for the feedforward controller parameter and a Hessian matrix of the feedforward controller parameter rho at rho j Inverse of the value of
When j =0, B 0 Is a unit matrix; when j is not equal to 0, calculating the parameter rho of the j iteration feedforward controller j With the (j-1) th iteration feedforward controller parameter p j-1 Is recorded as Δ j (ii) a Calculating the first derivative of the jth iteration feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Value of (A)
The first derivative of the parameter optimization objective function J of the feedforward controller on the parameter rho of the feedforward controller in the J-1 th iteration feedforward controller is in the rho j-1 Value of (a)
Is marked as ζ j ；B j The estimation method comprises the following steps:
the iteration termination condition may be:
wherein epsilon is more than or equal to 0 and is determined according to the actual control requirement of the servo control system.
The iteration termination condition may also be:
wherein tau is more than or equal to 0 and is determined according to the actual control requirement of the servo control system.
The servo control system comprises an addition and subtraction arithmetic unit, a feedback controller, a feedforward controller, an addition arithmetic unit and a controlled object, wherein parameters of the feedforward controller are iteratively optimized according to a reference track and a track tracking error, and iteration is stopped when an iteration termination condition is met. The servo control system is designed and a track tracking task is carried out, parameters of the feedforward controller are iteratively optimized according to a reference track and a track tracking error, so that the optimal parameters of the feedforward controller are obtained, and the constraint of a modeling error on the servo performance can be avoided because the servo control system and the parameter setting method of the feedforward controller do not need to establish a mathematical model of a controlled object.
Drawings
FIG. 1 is a schematic diagram of a servo control system according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for tuning parameters of a feedforward controller according to an embodiment of the present invention;
FIG. 3 is a bode diagram of a controlled object in accordance with an embodiment of the present invention;
FIG. 4 is a diagram illustrating a fourth-order reference trajectory used in performing a trajectory tracking task in accordance with an embodiment of the present invention;
FIG. 5 is a diagram illustrating the convergence of the feedforward controller parameter optimization objective function J according to an embodiment of the present invention;
FIG. 6 is a graph showing a comparison of trajectory tracking errors for the same trajectory tracking task using the method of the present invention and a feedforward controller designed based on a model method in accordance with an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail 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.
As shown in fig. 1, the servo control system in this embodiment includes: an addition and subtraction arithmetic unit, a feedback controller C, a feedforward controller F, an addition arithmetic unit and a controlled object P;
the input end of the addition and subtraction arithmetic unit is connected with the reference track r and the output end of the controlled object P; the output end of the addition and subtraction arithmetic unit is connected with the input end of the feedback controller C; the input end of the feedforward controller F is connected with a reference track r; the output end of the feedback controller C and the output end of the feedforward controller F are connected with the input end of the addition arithmetic unit; the output end of the addition arithmetic unit is connected with the input end of the controlled object P;
the addition and subtraction arithmetic unit obtains a reference track r and a position signal y output by a controlled object, determines a track tracking error e according to the difference value of the reference track r and the position signal y, and inputs the track tracking error e into the feedback controller C;
the feedback controller C generates a feedback control signal u based on the tracking error e c (ii) a The feedforward controller F generates a feedforward control signal u based on the reference trajectory r and the feedforward controller parameter ρ f ；
The addition operator obtains a feedback control signal u output by the feedback controller C c And a feedforward control signal u output by the feedforward controller F f Feeding back the control signal u c And a feedforward control signal u f Adding the signals to obtain a master control signal u, and outputting the master control signal u to a controlled object P;
and after receiving the total control signal u output by the addition arithmetic unit, the controlled object P outputs a position signal y, and the position signal y is fed back to the addition and subtraction arithmetic unit.
In this embodiment, the feedforward controller parameter optimization objective function J is the sum of squares of the trajectory tracking error e, and the expression is:
where N is the sample length.
In this embodiment, as shown in fig. 3, the bode diagram of the controlled object P is, since the controlled object P has a rigid body mode, the parameterization method of the feedforward controller is selected as follows:
wherein z is a complex variable of the discrete transfer function; t is s In this embodiment, 0.0002s is taken as the sampling time of the servo control system; n and m are denominator polynomial order and numerator polynomial order, respectively, 0 and 4 being taken in this embodiment; feedforward controller parameter ρ = [ b ] 0 ,…,b 4 ] T 。
The parameter iteration optimization method of the feedforward controller in the embodiment comprises the following steps:
wherein j is the number of iterations; λ is learning rate, which is 0.8 in this example;
optimizing the first derivative of the objective function J on the feedforward controller parameter p at p for the feedforward controller parameter j Taking the value of (A);
optimizing the Hessian matrix of the objective function J to the feedforward controller parameter rho at rho for the feedforward controller parameter j The value of (c).
Fig. 4 shows a fourth-order reference trajectory used for the trajectory tracking task in this embodiment.
In this embodiment, since the controlled object P has a rigid body mode and the nominal mass is known, the initial parameter ρ of the feedforward controller F is set 0 When b is greater than b 0 Is set as the reciprocal of the nominal mass of the controlled object, and the initial values of other parameters are set as zero.
In the embodiment, the first derivative of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho is in rho j Value of (a)
The estimation method comprises the following steps:
first derivative of feedforward controller F on feedforward controller parameter p
The product of the reference trajectory r is denoted as gamma; setting the reference track r of the servo control system to be zero, and setting the track tracking error e j Adding the processed signal to the input end of the controlled object after the inverse sequence processing, recording the position signal y of the output end of the controlled object, and recording the result of the inverse sequence processing of the position signal y as Λ j ；-2Γ T Λ j Is that
In the embodiment, the Hessian matrix of the parameter optimization objective function J of the feedforward controller to the parameter rho of the feedforward controller is in rho j Inverse of the value of
The estimation method comprises the following steps:
note B j Optimizing an objective function J for the feedforward controller parameter and a Hessian matrix of the feedforward controller parameter rho at rho j Inverse of the value of
When j =0, B 0 Is an identity matrix; when j is not equal to 0, calculating the parameter rho of the j iteration feedforward controller j With the (j-1) th iteration feedforward controller parameter p j-1 Is recorded as Δ j (ii) a Calculating the first derivative of the jth iteration feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Value of (A)
The first derivative of the parameter optimization objective function J of the feedforward controller on the parameter rho of the feedforward controller in the J-1 th iteration feedforward controller is in the rho j-1 Value of (A)
Is marked as ζ j ；B j The calculating method comprises the following steps:
the iteration termination condition in this embodiment is:
wherein ε is not less than 0, in this example 1X 10 -5 。
The method for setting the parameters of the feedforward controller in the embodiment specifically comprises the following steps:
initializing, enabling the iteration number j =0, and setting an initial parameter rho of a feedforward controller 0 ；
Step two, in the feedforward controller F = F (rho) j Z) performing the j-th track following task, and recording the track following error e j ；
Estimating the first derivative of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Value of (A)
Step four, estimating the Hessian matrix of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Inverse of the value of
Step five, updating the parameters of the feedforward controller according to the parameter iterative optimization method of the feedforward controller to obtain rho j+1 ；
Step six, in the feed forward controller F = F (rho) j+1 Z) performing the j +1 st track following task, and recording the track following error e j+1 ；
Step seven, judging whether the result of the J +1 th track tracking task meets the iteration termination condition, if so, stopping the iteration, considering that the parameter optimization objective function J of the feedforward controller reaches the minimum value, and obtaining the parameter rho of the feedforward controller j+1 Is an optimal parameter; otherwise, let j = j +1, jump to step three.
In this embodiment, with the tuning of the feedforward controller parameter, the convergence condition of the feedforward controller parameter optimization objective function J is as shown in fig. 5, the feedforward controller parameter optimization objective function J gradually converges, and the iteration termination condition is already satisfied during the 6 th iteration, and the iteration can be stopped.
The application result of the method of the present invention in this embodiment is shown in fig. 6, and compared with the existing feedforward controller designed based on the model method, when the same trajectory tracking task is performed, the method of the present invention has the advantages of small trajectory tracking error, high trajectory tracking precision, and can effectively realize the high-performance motion control of the servo control system.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that several changes and modifications may be made without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description. 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.
Claims (10)
1. A servo control system comprising: an addition and subtraction arithmetic unit, a feedback controller C, a feedforward controller F, an addition arithmetic unit and a controlled object P;
the input end of the addition and subtraction arithmetic unit is connected with the reference track r and the output end of the controlled object P; the output end of the addition and subtraction arithmetic unit is connected with the input end of the feedback controller C; the input end of the feedforward controller F is connected with a reference track r; the output end of the feedback controller C and the output end of the feedforward controller F are connected with the input end of the addition arithmetic unit; the output end of the addition arithmetic unit is connected with the input end of the controlled object P;
the addition and subtraction arithmetic unit obtains a reference track r and a position signal y output by a controlled object, determines a track tracking error e according to the difference value of the reference track r and the position signal y, and inputs the track tracking error e into the feedback controller C;
the feedback controller C generates a feedback control signal u based on the tracking error e c (ii) a The feedforward controller F generates a feedforward control signal u based on the reference trajectory r and the feedforward controller parameter ρ f (ii) a The parameter rho of the feedforward controller is iteratively optimized according to the reference track r and the track tracking error e, iteration is stopped when an iteration termination condition is met, and the obtained parameter of the feedforward controller is an optimal parameter;
the addition operator acquires a feedback control signal u output by the feedback controller C c And a feedforward control signal u output by the feedforward controller F f Feeding back the control signal u c And a feedforward control signal u f Adding the signals to obtain a master control signal u, and outputting the master control signal u to a controlled object P;
and after receiving the master control signal u output by the addition arithmetic unit, the controlled object P outputs a position signal y and feeds the position signal y back to the addition and subtraction arithmetic unit.
2. A method of feedforward controller parameter tuning, the method comprising: a feedforward controller parameter optimization objective function J, a feedforward controller parameterization method, a feedforward controller parameter iteration optimization method and an iteration termination condition;
the feedforward controller parameter optimization objective function J is determined according to the actual control requirement of the servo control system, and the optimal parameter of the feedforward controller is determined by minimizing the feedforward controller parameter optimization objective function J;
the feedforward controller parameterization method represents the feedforward controller F as a mathematical expression on a finite number of parameters and basis functions;
according to the feedforward controller parameter iterative optimization method, updating a feedforward controller parameter rho by adopting an iterative optimization method according to a reference track r and a track tracking error e until an iteration termination condition is met;
the iteration termination condition is a basis for judging whether the parameter rho of the feedforward controller stops iteration, if the iteration termination condition is met, the iteration is stopped, the parameter optimization objective function J of the feedforward controller can be considered to reach the minimum value, and the obtained parameter of the feedforward controller is the optimal parameter; otherwise, continuing the iteration until the iteration termination condition is met.
3. A feedforward controller parameter setting method according to claim 2, characterized in that the feedforward controller parameter optimization objective function J is a sum of squares of a trajectory tracking error e, and the expression is:
where N is the sample length.
4. A feedforward controller parameter setting method according to claim 2, wherein the feedforward controller parameterization method is:
wherein z is a complex variable of the discrete transfer function; n and m are denominator polynomial order and numerator polynomial order respectively, and natural numbers are taken; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing denominator polynomial parameters a 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
If there is an output delay in the controlled object P, the method for parameterizing the feedforward controller may be:
wherein d is the known output delay number of the controlled object P; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing denominator polynomial parameters a 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
If the controlled object P has a rigid body mode, the feedforward controller parameterization method may be:
wherein, T s Sampling time of a servo control system; feedforward controller parameter ρ = [ a = 1 ,…,a n ,b 0 ,…,b m ] T Containing denominator polynomial parameters a 1 ,…,a n And the numerator polynomial parameter b 0 ,…,b m 。
5. A feedforward controller parameter setting method according to claim 2, characterized in that the feedforward controller parameter iterative optimization method is:
wherein j is the number of iterations; λ is learning rate, and is between 0 and 1;
optimizing the first derivative of the objective function J on the feedforward controller parameter p at p for the feedforward controller parameter j Taking the value of (A);
optimizing the Hessian matrix of the objective function J to the feedforward controller parameter rho at rho for the feedforward controller parameter j The value of (c) is as follows.
6. A method for tuning parameters of a feedforward controller according to claim 2, characterized by comprising the following steps:
initializing, enabling the iteration number j =0, and setting an initial parameter rho of a feedforward controller F 0 ；
Step two, in the feedforward controller F = F (rho) j Z) performing the j-th track following task, and recording the track following error e j ；
Estimating the first derivative of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Value of (A)
Step four, estimating the Hessian matrix of the feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Inverse of the value of
Fifthly, updating the parameters of the feedforward controller according to the parameter iterative optimization method of the feedforward controller to obtain rho j+1 ；
Step six, in the feed forward controller F = F (rho) j+1 Z) performing the j +1 st track following task, and recording the track following error e j +1 ；
Step seven, judging whether the result of the J +1 th track tracking task meets the iteration termination condition, if so, stopping the iteration, considering that the parameter optimization objective function J of the feedforward controller reaches the minimum value, and obtaining the parameter rho of the feedforward controller j+1 Is the optimal parameter; otherwise, let j = j +1, jump to step three.
7. A feedforward controller parameter setting method according to claim 8, characterized in that the initial parameter ρ of the feedforward controller F 0 May be set to zero. If the object P has rigid body mode and the nominal quality is known, the feedforward controller parameterization method of claim 6 is adopted, and the method is used for the step of determining the feedforward controller parameterizationSetting an initial parameter ρ of a feedforward controller F 0 When b is greater than 0 Is set as the reciprocal of the nominal mass of the controlled object, and the initial values of other parameters are set as zero.
8. A feedforward controller parameter tuning method according to claim 8, wherein the first derivative of the feedforward controller parameter optimization objective function J on the feedforward controller parameter ρ is at ρ j Value of (A)
The estimation method comprises the following steps:
first derivative of the feedforward controller F on the feedforward controller parameter p
The product of the reference trajectory r is denoted as gamma; setting the reference track r of the servo control system to be zero, and setting the track tracking error e j Adding the processed signal to the input end of the controlled object after the inverse sequence processing, recording the position signal y of the output end of the controlled object, and recording the result of the inverse sequence processing of the position signal y as Λ j ；-2Γ T Λ j Is that
9. A feedforward controller parameter setting method according to claim 8, characterized in that the Hessian matrix of the feedforward controller parameter optimization objective function J to the feedforward controller parameter p is at p j Inverse of the value of
The estimation method comprises the following steps:
note B j Optimizing the Hessian matrix of the objective function J to the feedforward controller parameter rho at rho for the feedforward controller parameter j Inverse of the value of
When j =0, B 0 Is an identity matrix; when j is not equal to 0, calculating the parameter rho of the j iteration feedforward controller j With the (j-1) th iteration feedforward controller parameter p j-1 Is recorded as Δ j (ii) a Calculating the first derivative of the jth iteration feedforward controller parameter optimization objective function J to the feedforward controller parameter rho at rho j Value of (A)
The first derivative of the parameter optimization objective function J of the feedforward controller on the parameter rho of the feedforward controller in the J-1 th iteration feedforward controller is in the rho j-1 Value of (A)
Is marked as ζ j ；B j The estimation method comprises the following steps:
10. a feedforward controller parameter tuning method according to claim 2 and claim 8, wherein the iteration end condition may be:
wherein epsilon is more than or equal to 0 and is determined according to the actual control requirement of the servo control system.
The iteration termination condition may also be:
wherein tau is more than or equal to 0 and is determined according to the actual control requirement of the servo control system.
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