CN112612211A - Servo system residual vibration suppression method based on parametric feedforward - Google Patents

Servo system residual vibration suppression method based on parametric feedforward Download PDF

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CN112612211A
CN112612211A CN202011556719.5A CN202011556719A CN112612211A CN 112612211 A CN112612211 A CN 112612211A CN 202011556719 A CN202011556719 A CN 202011556719A CN 112612211 A CN112612211 A CN 112612211A
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feedforward
parameterized
control
servo system
residual vibration
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杨亮亮
张晖
叶佳保
陶之源
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Zhejiang University of Technology ZJUT
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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

Servo system residual vibration suppression method based on parametric feedforward
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:
Figure BDA0002857619040000021
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:
Figure BDA0002857619040000022
Figure BDA0002857619040000023
then the basis function is selected for the parameterized input shaping filter
Figure BDA0002857619040000024
And a feedforward controller
Figure BDA0002857619040000025
Figure BDA0002857619040000026
Basis functions
Figure BDA0002857619040000027
Is composed of
Figure BDA0002857619040000028
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
Figure BDA0002857619040000031
Representing the i-th derivative of the input signal.
Parameterized input shaping filter
Figure BDA0002857619040000032
And a feedforward controller
Figure BDA0002857619040000033
Comprises the following steps:
Figure BDA0002857619040000034
Figure BDA0002857619040000035
the j iteration knows
Figure BDA0002857619040000036
Figure BDA0002857619040000037
Figure BDA0002857619040000038
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，
Figure BDA0002857619040000039
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:
Figure BDA00028576190400000310
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
Figure BDA00028576190400000311
Then
Figure BDA00028576190400000312
Figure BDA00028576190400000313
Figure BDA00028576190400000314
Namely, it is
Figure BDA00028576190400000315
uj+1＝uj+ψLθΔ
Δu＝ψLθΔ
Wherein
Figure BDA0002857619040000041
Figure BDA0002857619040000042
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
Figure BDA0002857619040000043
The derivation can identify that:
Figure BDA0002857619040000044
therefore, the identification parameter update formula is:
Figure BDA0002857619040000045
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
Figure BDA0002857619040000046
And a feedforward controller
Figure BDA0002857619040000047
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:
Figure BDA0002857619040000048
according to
Figure BDA0002857619040000049
As known from the knowledge of the non-singularities and norms,
Figure BDA00028576190400000410
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:
Figure BDA0002857619040000051
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
Figure BDA0002857619040000061
Figure BDA0002857619040000062
Wherein
Figure BDA0002857619040000063
Figure BDA0002857619040000064
Figure BDA0002857619040000065
Figure BDA0002857619040000066
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
Figure BDA0002857619040000067
Representing the i-th derivative of the input signal.
Parameterized input shaping filter
Figure BDA0002857619040000068
And a feedforward controller
Figure BDA0002857619040000069
Comprises the following steps:
Figure BDA00028576190400000610
Figure BDA00028576190400000611
j th iteration measurement data
Figure BDA00028576190400000612
uj，yjIt can be known that
Figure BDA00028576190400000613
Figure BDA00028576190400000614
Figure BDA00028576190400000615
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，
Figure BDA0002857619040000071
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:
Figure BDA0002857619040000072
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
Figure BDA0002857619040000073
Then
Figure BDA0002857619040000074
Figure BDA0002857619040000075
Figure BDA0002857619040000076
Namely, it is
Figure BDA0002857619040000077
uj+1＝uj+ψLθΔ
Δu＝ψLθΔ
Wherein
Figure BDA0002857619040000078
Figure BDA0002857619040000079
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
Figure BDA00028576190400000710
The derivation can identify that:
Figure BDA00028576190400000711
therefore, the identification parameter update formula is:
Figure BDA0002857619040000081
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
Figure BDA0002857619040000082
And a feedforward controller
Figure BDA0002857619040000083
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:
Figure BDA0002857619040000084
according to
Figure BDA0002857619040000085
As known from the knowledge of the non-singularities and norms,
Figure BDA0002857619040000086
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
Figure BDA0002857619040000087
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)

1.一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，1. a servo system residual vibration suppression method based on parameterized feedforward, is characterized in that, 包括以下步骤：Include the following steps: 步骤一：连接好伺服控制系统，设置好相关控制器参数，将参数下载到运动控制卡上的芯片中；Step 1: Connect the servo control system, set the relevant controller parameters, and download the parameters to the chip on the motion control card; 步骤二：根据伺服控制系统的时不变离散状态空间要求，下载控制器参数，并使能伺服系统，使电机闭环；Step 2: Download the controller parameters according to the time-invariant discrete state space requirements of the servo control system, enable the servo system, and close the motor loop; 步骤三：在伺服控制系统信号输入端输入理想轨迹信号r(t)，通过参数化输入整形滤波器产生整形后的输入轨迹信号ry(t)，规定采样周期Ts，采集输出轨迹信号y(t)与控制信号u(t)，采集采样点，整形输入信号ry(t)减去输出信号y(t)为误差信号ey(t)，并运用输出信号y(t)与控制信号u(t)来消除对模型的依赖，利用基函数参数化前馈控制器，通过输入轨迹和参数化前馈控制器计算前馈力uff(t)，规定伺服系统的响应调节时间；Step 3: Input the ideal track signal r(t) at the signal input end of the servo control system, generate the shaped input track signal r y (t) through the parameterized input shaping filter, specify the sampling period T s , and collect the output track signal y (t) and the control signal u(t), collect the sampling points, shape the input signal ry (t) and subtract the output signal y (t) to obtain the error signal e y (t), and use the output signal y(t) and control The signal u(t) is used to eliminate the dependence on the model, the basis function is used to parameterize the feedforward controller, the feedforward force u ff (t) is calculated by the input trajectory and the parameterized feedforward controller, and the response adjustment time of the servo system is specified; 步骤四：根据最优控制理论引入参数化前馈控制算法的性能目标函数进行辨识输入整形滤波器与前馈控制器的参数θ，并选择合适的约束参数ρ，λ实现对伺服系统的残余振动抑制；Step 4: According to the optimal control theory, the performance objective function of the parameterized feedforward control algorithm is introduced to identify the parameters θ of the input shaping filter and the feedforward controller, and select the appropriate constraint parameters ρ, λ to realize the residual vibration of the servo system inhibition; 步骤五：对参数化前馈控制的误差与辨识参数θ的收敛性进行分析；Step 5: Analyze the error of the parameterized feedforward control and the convergence of the identification parameter θ; 步骤六：求取各个参数的最优值，根据选取初始参数，利用迭代寻优法对所测量的误差，控制信号，输出轨迹数据来进行迭代辨识参数θ，利用迭代辨识的参数来计算驱动力重新下发到运动控制卡，反复此迭代实现系统的残余振动抑制。Step 6: Obtain the optimal value of each parameter, and use the iterative optimization method to iteratively identify the parameter θ for the measured error, control signal, and output trajectory data according to the selected initial parameters, and use the iteratively identified parameters to calculate the driving force. Re-delivery to the motion control card, and repeat this iteration to achieve residual vibration suppression of the system. 2.如权利要求1所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，步骤二，未知模型的运动控制器系统时不变离散状态空间表达式为：2. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 1, is characterized in that, in step 2, the time-invariant discrete state space expression of the motion controller system of unknown model is:
Figure FDA0002857619030000011
Figure FDA0002857619030000011
 其中，uj＝[u(0)，…，u(N-1)]T为有限离散控制输入指令，yj＝[y(0)，…，y(N-1)]T为有限离散系统输出信号，j代表迭代次数，N为采样点数；理想轨迹为r(t)，迭代的时间跨度为t∈[0，T]。Among them, u j =[u(0),...,u(N-1)] T is the finite discrete control input command, y j =[y(0),...,y(N-1)] T is the finite discrete The output signal of the system, j represents the number of iterations, N is the number of sampling points; the ideal trajectory is r(t), and the time span of the iteration is t∈[0, T]. 3.如权利要求1所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，步骤三，参数化前馈控制算法如下：3. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 1, is characterized in that, step 3, parameterized feedforward control algorithm is as follows:
Figure FDA0002857619030000012
Figure FDA0002857619030000012
Figure FDA0002857619030000013
Figure FDA0002857619030000013
 则选用基函数进行参数化输入整形滤波器
Figure FDA0002857619030000014
和前馈控制器
Figure FDA0002857619030000015
Then the basis function is used to parameterize the input shaping filter
Figure FDA0002857619030000014
and feedforward controller
Figure FDA0002857619030000015
Figure FDA0002857619030000021
Figure FDA0002857619030000021
 基函数
Figure FDA0002857619030000022
为basis function
Figure FDA0002857619030000022
for
Figure FDA0002857619030000023
Figure FDA0002857619030000023
 其中，θ为参数化输入整形滤波器与前馈控制器的辨识参数，na，nb为组成Ty和Tff的基函数的个数，基函数
Figure FDA0002857619030000024
表示对输入信号的i阶导数；Among them, θ is the identification parameter of the parameterized input shaping filter and feedforward controller, n a , n b are the number of basis functions that make up Ty and T ff , and the basis functions
Figure FDA0002857619030000024
represents the i-order derivative with respect to the input signal; 参数化输入整形滤波器
Figure FDA0002857619030000025
和前馈控制器
Figure FDA0002857619030000026
为：Parametric Input Shaping Filter
Figure FDA0002857619030000025
and feedforward controller
Figure FDA0002857619030000026
for:
Figure FDA0002857619030000027
Figure FDA0002857619030000027
Figure FDA0002857619030000028
Figure FDA0002857619030000028
 第j次迭代可知The jth iteration knows that
Figure FDA0002857619030000029
Figure FDA0002857619030000029
Figure FDA00028576190300000210
Figure FDA00028576190300000210
Figure FDA00028576190300000211
Figure FDA00028576190300000211
 Sr与SPr都跟参数模型有关，为了消除对模型的依赖，将其转化为基于数据驱动的形式，则Both Sr and SPr are related to the parametric model. In order to eliminate the dependence on the model and convert it into a data-driven form, then Sr＝T-1uj Sr=T -1 u j SPr＝T-1yj SPr=T -1 y j 其中，S＝(1+PCfb)-1，
Figure FDA00028576190300000212
Among them, S=(1+PC fb ) -1 ,
Figure FDA00028576190300000212
 4.如权利要求1所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，步骤四，最优控制理论引入参数化前馈控制算法的性能目标函数如下：4. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 1, is characterized in that, step 4, the performance objective function that optimal control theory introduces parameterized feedforward control algorithm is as follows:
Figure FDA00028576190300000213
Figure FDA00028576190300000213
 由于参考轨迹在稳定段时间内ry＝r，即可知ey＝ry-y＝e，故目标函数可写为Since the reference trajectory is ry = r in the stable period, it can be known that e y = ry -y = e, so the objective function can be written as
Figure FDA00028576190300000214
Figure FDA00028576190300000214
 则but
Figure FDA00028576190300000215
Figure FDA00028576190300000215
Figure FDA00028576190300000216
Figure FDA00028576190300000216
Figure FDA0002857619030000031
Figure FDA0002857619030000031
 即which is
Figure FDA0002857619030000032
Figure FDA0002857619030000032
 uj+1＝uj+ψLθΔ u j+1 =u j +ψ L θ Δ Δu＝ψLθΔ Δu=ψ L θ Δ 其中in
Figure FDA0002857619030000033
Figure FDA0002857619030000033
Figure FDA0002857619030000034
Figure FDA0002857619030000034
 5.如权利要求4所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，5. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 4 is characterized in that, 基于性能目标函数，进行参数化输入整形滤波器与前馈控制器的设计，由于θΔ为函数Jj +1的变量，令
Figure FDA0002857619030000035
经推导可辨识得出：Based on the performance objective function, a parameterized input shaping filter and a feedforward controller are designed. Since θ Δ is a variable of the function J j +1 , let
Figure FDA0002857619030000035
It can be identified by derivation that:
Figure FDA0002857619030000036
Figure FDA0002857619030000036
 因此辨识参数更新公式为：Therefore, the identification parameter update formula is:
Figure FDA0002857619030000037
Figure FDA0002857619030000037
 6.如权利要求5所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，6. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 5 is characterized in that, 对控制信号约束参数ρ进行优化设计，其限制控制信号能量的大小和影响误差收敛值，ρ为大于等于0的任意实数，ρ为0时即不限制控制信号能量。The control signal constraint parameter ρ is optimally designed, which limits the energy of the control signal and affects the convergence value of the error. ρ is any real number greater than or equal to 0. When ρ is 0, the control signal energy is not limited. 7.如权利要求6所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，7. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 6 is characterized in that, 对控制变化量约束参数λ进行优化设计，其限制控制信号变化步长和影响收敛速度，λ为大于等于0的任意实数，λ为0时即不限制控制信号变化步长。The control variation constraint parameter λ is optimally designed, which limits the control signal change step size and affects the convergence speed. λ is any real number greater than or equal to 0. When λ is 0, the control signal change step size is not limited. 8.如权利要求1所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，8. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 1 is characterized in that, 步骤五，参数化前馈算法中输入整形滤波器
Figure FDA0002857619030000038
和前馈控制器
Figure FDA0002857619030000039
均为有限脉冲响应滤波器，并且误差ey与有限脉冲响应滤波器参数成线性关系，可知误差ey是全局收敛的，因此：Step 5: Input shaping filter in parameterized feedforward algorithm
Figure FDA0002857619030000038
and feedforward controller
Figure FDA0002857619030000039
Both are finite impulse response filters, and the error e y has a linear relationship with the parameters of the finite impulse response filter. It can be seen that the error e y is globally convergent, so:
Figure FDA00028576190300000310
Figure FDA00028576190300000310
 根据
Figure FDA00028576190300000311
是非奇异和范数知识可知，according to
Figure FDA00028576190300000311
It can be known from the non-singularity and norm knowledge,
Figure FDA0002857619030000041
Figure FDA0002857619030000041
 因此，辨识参数θ是收敛的。Therefore, the identification parameter θ is convergent. 9.如权利要求1所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，9. a kind of servo system residual vibration suppression method based on parameterized feedforward as claimed in claim 1 is characterized in that, 步骤六：利用上位机仿真软件MATLAB来辨识参数化输入整形滤波器和前馈控制器的参数，计算前馈力和输入轨迹信号；运动控制系统为直流无刷电机，上位机为电脑或工控机。Step 6: Use the host computer simulation software MATLAB to identify the parameters of the parameterized input shaping filter and feedforward controller, and calculate the feedforward force and input trajectory signal; the motion control system is a DC brushless motor, and the host computer is a computer or industrial computer . 10.如权利要求9所述的一种基于参数化前馈的伺服系统残余振动抑制方法，其特征在于，10. A method for suppressing residual vibration of servo system based on parameterized feedforward as claimed in claim 9, wherein, 上位机为电脑，电脑应用已经很普遍，直接利用电脑做上位机，不需要增加额外投资，减少生产成本。The host computer is a computer, and computer applications are already very common. Using the computer directly as the host computer does not require additional investment and reduces production costs.
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113655713A (en) * 2021-06-17 2021-11-16 中国人民解放军海军工程大学 An optimization method for shock resistance of active vibration control system
CN114153148A (en) * 2021-11-30 2022-03-08 哈尔滨工业大学 A Gradient Iterative Feedforward Tuning Method with Variable Learning Step Size
CN115248554A (en) * 2021-11-24 2022-10-28 浙江理工大学 An optimal iterative feedforward parameter tuning method and system for motion control system
CN115356932A (en) * 2022-08-26 2022-11-18 中国地质大学（武汉） Servo control system and feedforward controller parameter setting method
CN116107221A (en) * 2023-04-14 2023-05-12 河北工业大学 Control method of servo control system
CN118759830A (en) * 2024-09-03 2024-10-11 佛山大学 Vibration control method, system and device based on adaptive filtering algorithm

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106325072A (en) * 2016-10-12 2017-01-11 浙江理工大学 Method for controlling mechanical residual vibration of linear servo system
CN107272409A (en) * 2017-07-04 2017-10-20 浙江理工大学 A kind of linear servo system vibration suppressing method based on iterative learning

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106325072A (en) * 2016-10-12 2017-01-11 浙江理工大学 Method for controlling mechanical residual vibration of linear servo system
CN107272409A (en) * 2017-07-04 2017-10-20 浙江理工大学 A kind of linear servo system vibration suppressing method based on iterative learning

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
杨亮亮等: "直线伺服系统正交投影迭代学习控制器参数辨识与优化", 《中国机械工程》 *
薄雨蒙等: "结合前馈调参与迭代学习的数据驱动控制方法", 《控制理论与应用》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113655713A (en) * 2021-06-17 2021-11-16 中国人民解放军海军工程大学 An optimization method for shock resistance of active vibration control system
CN113655713B (en) * 2021-06-17 2023-08-29 中国人民解放军海军工程大学 A shock resistance optimization method for active vibration control system
CN115248554A (en) * 2021-11-24 2022-10-28 浙江理工大学 An optimal iterative feedforward parameter tuning method and system for motion control system
CN114153148A (en) * 2021-11-30 2022-03-08 哈尔滨工业大学 A Gradient Iterative Feedforward Tuning Method with Variable Learning Step Size
CN115356932A (en) * 2022-08-26 2022-11-18 中国地质大学（武汉） Servo control system and feedforward controller parameter setting method
CN116107221A (en) * 2023-04-14 2023-05-12 河北工业大学 Control method of servo control system
CN118759830A (en) * 2024-09-03 2024-10-11 佛山大学 Vibration control method, system and device based on adaptive filtering algorithm

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