CN115248554A - Optimal iteration feedforward parameter adjusting method and system for motion control system - Google Patents
Optimal iteration feedforward parameter adjusting method and system for motion control system Download PDFInfo
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Abstract
The invention discloses an optimal iteration feedforward parameter adjusting method and system of a motion control system, and belongs to the technical field of mechanical equipment control. The existing control method does not balance control energy and tracking performance, cannot limit system control energy, and can cause the energy to exceed the maximum output capacity of an actual motion control system, so that the system cannot be closed and enters a destabilization state. The optimal iterative feedforward parameter adjusting method of the motion control system, provided by the invention, sets the identification parameter theta of the input shaping filter and the feedforward controller, and restrains and weights the variable quantity of the identification parameter theta, so that the energy of a feedforward control signal and the convergence value of an influence error can be effectively restrained, and the change step length and the convergence speed of the feedforward control signal are restrained; meanwhile, the advantages of optimal iterative learning control and parameterized feedforward are combined, the performance of the track-changing tracking task is realized, the calculated amount of a processor is effectively reduced, the flexibility is strong, the operation speed is high, the performance is high, the scheme is detailed, and the method is practical and feasible.
Description
Technical Field
The invention relates to an optimal iterative feedforward parameter adjusting method and system of a motion control system, and belongs to the technical field of mechanical equipment control.
Background
In motion control systems, it is often desirable to achieve tracking for a given desired trajectory to minimize trajectory tracking errors. High speed and high precision are pursuit targets and development trends in the motion control field, the former improves production efficiency, shortens production period and reduces manufacturing cost, but flexible vibration modes contained in an actual system model and requirements on high speed characteristics are improved, and an acceleration and deceleration section of a system input track contains more and more high-frequency components, so that the ignored flexible vibration modes are easily excited, and continuous vibration of the motion control system in the motion process and after the motion control system reaches a terminal point is caused. The control strategy commonly used by the motion control system comprises two control strategies of only feedback and feedforward plus feedback, the control strategy of only feedback adopts a traditional PID feedback controller, the response speed of feedback control is slow, correction is carried out according to system errors, and the motion control system has hysteresis and cannot meet the requirement of high response speed. The two-degree-of-freedom control strategy of feedback plus feedforward ensures the stability of the system through a feedback controller, and the feedforward control improves the track tracking performance because the feedforward has the characteristics of high response speed, high positioning accuracy and the like, and the feedforward corrects the system before errors are not generated, so that the method has certain predictability. Therefore, the two-degree-of-freedom control strategy of feedback plus feedforward is a standard configuration of a high-speed high-precision motion control system.
In a two-degree-of-freedom control strategy, a feedback controller generally adopts PID (proportion integration differentiation), a plurality of methods are designed for a feedforward controller, and extensive research is carried out by scholars at home and abroad, the current feedforward control method mainly comprises iterative learning control and model-based feedforward control, the iterative learning control algorithm can realize the tracking performance of a repeated track, particularly the optimal iterative learning control algorithm can realize a target function with the optimal norm, weighting constraint is carried out on a control signal and a control signal variable quantity in the target function, the control energy and the tracking performance are balanced, but the algorithm can cause performance deterioration for a track-changing tracking task; the feedforward control algorithm based on the model comprises feedforward control based on model inversion and feedforward control based on parameterization, the feedforward controller based on the model inversion depends on a mathematical model of a system and needs to experience a process of identifying the system model in a complicated and time-consuming manner in advance, and the feedforward control algorithm based on the parameterization adopts a basis function to carry out the parameterization feedforward controller, so that an orbital-varying tracking task can be realized without depending on the mathematical model, but control energy and tracking performance are not balanced, the control energy of the system cannot be limited, and the energy exceeds the maximum output capacity of an actual motion control system, so that the system cannot be closed-loop and enters a destabilization state.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an identification parameter theta provided with an input shaping filter and a feedforward controller, and the variable quantity of the identification parameter theta is restrained and weighted, so that the energy of a feedforward control signal can be effectively restrained, the convergence value of an influence error can be effectively restrained, and the change step length of the feedforward control signal and the convergence speed of the influence can be restrained; meanwhile, the optimal iterative learning control and parameterized feedforward advantages are combined, the performance of an orbital transfer tracking task is realized, the method has good track tracking robustness, control signals and tracking errors can be balanced, optimal parameters are iteratively identified in a data-driven mode, complex model identification is avoided, the calculated amount of a processor is effectively reduced, the flexibility is high, the operation speed is high, and the optimal iterative feedforward parameter adjusting method and the system of the motion control system have high performance.
In order to achieve the purpose, the technical scheme of the invention is as follows:
an optimal iterative feedforward parameter adjusting method of a motion control system,
the method comprises the following steps:
the method comprises the following steps: constructing a motion control system and setting PID parameters of a feedback controller;
step two: enabling a motion control system by using the PID parameters of the feedback controller in the step one to enable a motor of the motion control system to be closed;
step three: inputting the expected track signal r (t) into the motion control system in the second step, and collecting the output track signal y (t), the control signal u (t) and the track error signal e of the system y (t)；
Eliminating the dependence on the model by utilizing the acquired output track signal y (t) and the control signal u (t);
step four, for the motion control system in the step three, the track signal r after the input track shaping is calculated through the input shaping filter y (t) and calculating a feedforward control signal u by the feedforward controller ff (t) setting the execution period and the stabilization period of the motion control system;
step five: using the track signal r in step four y (t) and a feedforward control signal u ff (t) constructing a parameterized feedforward model, combining an optimal iterative learning control method, introducing an identification parameter theta of an input shaping filter and a feedforward controller and a constraint term of variable quantity of the identification parameter theta into a target function of the parameterized feedforward model, weighting the identification parameter theta, calculating the identification parameter theta by a data-driven least square method, and selecting a proper weighting coefficient rho and a weighting coefficient lambda to realize track tracking and track-changing tracking tasks of a motion control system;
the weighting coefficient rho is an identification parameter size weighting coefficient, weights the identification parameter size and can restrict the energy of the feedforward control signal and influence an error convergence value;
the weighting coefficient lambda is an identification parameter variation weighting coefficient which weights the identification parameter variation step length and can restrict the feedforward control signal variation step length and influence the convergence speed;
step six: and analyzing the identification parameter theta and the convergence of the optimal iterative feedforward parameter adjusting error in the step five, and solving the optimal value of the identification parameter to realize the optimal trajectory tracking of the motion control system.
Through continuous exploration and test, the invention sets the identification parameter theta of the input shaping filter and the feedforward controller, and restrains and weights the variation of the identification parameter theta, thereby effectively restraining the energy of the feedforward control signal and influencing the error convergence value, and restraining the variation step length and influencing the convergence speed of the feedforward control signal, and effectively avoiding the energy from exceeding the maximum output capacity of the actual motion control system, thereby leading the system to be incapable of closing the loop and entering the unstable state. Meanwhile, the advantages of optimal iterative learning control and parameterized feedforward are combined, the performance of the variable-track tracking task is realized, good track tracking robustness is achieved, control signals and tracking errors can be balanced, optimal parameters are iteratively identified in a data-driven mode, complex model identification is avoided, the calculated amount of a processor is effectively reduced, the flexibility is high, the operation speed is high, the performance is high, the scheme is detailed, the implementation is feasible, and the implementation is convenient.
Furthermore, the invention is particularly suitable for non-minimum phase systems and complex systems, because the system adopts a basis function mode to parameterize the feedforward controller, the problem of non-minimum phase zero point does not exist, and simultaneously, a data driving mode does not need a system parameter model.
As a preferable technical measure:
in the fifth step, the method for constructing the parameterized feedforward model specifically comprises the following steps:
finite Impulse Response (FIR) filter pair input shaping filter T composed of basis function polynomials y And a feedforward controller T ff Parameterizing, wherein the parameterized expression is as follows:
then, form T y And T ff Is a polynomial of a (z) -1 Theta) and B (z) -1 θ) are respectively represented as
Wherein z is -1 For the time shift operator, theta is an identification parameter of the parameterized input shaping filter and the feedforward controller, n a ，n b To form T y And T ff Number of basis functions, basis functions
The input trajectory can be decomposed into derivatives of various orders, at T y Acceleration basis function of
Comprises the following steps:
Polynomial of basis function A (z) -1 Theta) and B (z) -1 Theta) is an FIR filter, and the FIR filter has the advantages that firstly, the FIR filter has no pole, so the instability problem does not exist; secondly, designing a feedforward controller by an FIR filter is a convex optimization method; thirdly, according to the control framework of the motion control system, the system error is 0, namely
e y ＝r y -y＝S(T y -PT ff )r＝0
Then
To obtain the optimum track tracking performance, only two FIR filters are used for designing T y And T ff The numerator denominator of the controlled system can be described, the zero-pole motion characteristic of the system can be contained, when the two FIR filters work for inversion, the problems of unstable poles and non-minimum phase zeros cannot be caused, and a better track tracking effect can be realized, so that the control target is to use the two FIR filters to identify the system model.
When the motion control system iterates for the jth time, the expressions of the system error, the control signal and the output track signal are as follows
Wherein, the system sensitivity function S = (1 + PC) fb ) -1 Sensitivity function T = C fb T y +T ff ，C fb Is a feedback controller;
from the above, sr and SPr are related to a parametric model, and in order to eliminate the dependence on the model, sr and SPr are converted into a form based on data driving, and the calculation formula is as follows:
Sr＝T -1 u j
SPr＝T -1 y j 。
as a preferable technical measure:
the optimal iterative feedforward parameter adjusting method combines optimal iterative learning control under a parameterized feedforward control framework with an input shaping filter, and balances system control signal energy and trajectory errors.
The feedforward control signal is composed of a basis function polynomial, and is related to parameters corresponding to the basis functions, so that the objective function comprises a system error, and the parameters and parameter variation of the input shaping filter and the feedforward controller are weighted and constrained, and the expression is as follows:
due to r y ＝T y r, expected trajectory during the settling period T y =1, then r y = r and there is a delay of the execution section, the length of the delay time being T y Number of components n of basis function a From this, the stable segment e is known y ＝r y -y = e, so the design of the objective functionThe calculation formula is as follows:
then, the error of the system track is obtained from the above step when the iteration is performed for the (j + 1) th time
Then according to the parameterized polynomial of the input shaping filter and the feedforward controller and the expression form of data drive, the method can obtain
Wherein
As a preferable technical measure:
the objective function identifies the parameters of the parameterized input shaping filter and the feedforward controller due to θ j+1 As an objective function J j+1 In order to minimize the track tracking error, according to the iterative learning idea, the iterative error of each iteration is continuously reduced relative to the previous iteration until convergence, so that the objective function J is solved j+1 To a minimum value of, i.e. to find the objective function J j+1 To theta j+1 Is a partial derivative of
Derived and identified to obtain a parameter theta j+1 ：
In the formula, a robust filter Q θ And a learning filter L θ Is composed of
Q θ ＝[ψ T W e ψ+W θ +W Δθ ] -1 [ψ T W e ψ+W Δθ ]
L θ ＝[ψ T W e ψ+W Δθ ] -1 ψ T W e
Wherein, W e ，W θ And W Δθ Respectively, the error, the identification parameter theta and the identification parameter variation delta theta, and selecting the error weighting matrix as W e Selecting W as identification parameter theta weighting matrix θ Rho is a weight coefficient of the size of the identification parameter, and a weight matrix of the variation delta theta of the identification parameter is selected as W Δθ And = λ I, λ is a recognition parameter variation weighting coefficient, and I is an identity matrix.
As a preferable technical measure:
the optimal design method of the identification parameter size weighting coefficient comprises the following steps:
the identification parameter size weighting coefficient weights the identification parameter size, the size of feedforward control signal energy and an influence error convergence value can be constrained, rho is any real number which is larger than or equal to 0, the control signal energy is not limited when rho is 0, the greater the weighting coefficient rho is, the greater the constraint effect is, the greater the feedforward control signal constraint effect is, the greater the error convergence value is, and otherwise, the smaller the error convergence value is.
As a preferable technical measure:
the optimal design method for identifying the parameter variation weighting coefficient comprises the following steps:
the identification parameter variation weighting coefficient weights the identification parameter variation step length, can constrain the feedforward control signal variation step length and influence the convergence speed, lambda is any real number more than or equal to 0, the feedforward control signal variation step length is not limited when lambda is 0, the larger the weighting coefficient lambda is, the larger the parameter variation constraint effect is, the slower the feedforward control signal iteration speed to the optimal value is, the slower the error convergence speed is, otherwise, the faster the error convergence speed is.
As a preferable technical measure:
step six, optimal iterative feedforward adjustmentThe parameter error is error e y The convergence is specifically analyzed as follows:
input shaping filter T y And a feedforward controller T ff Are all finite impulse response filters, and error e y Linear with finite impulse response filter parameters, error e y Global convergence, error e y The calculation formula of (a) is as follows:
according to
Non-singular and norm knowledge yields:
therefore, the recognition parameter θ is converged.
As a preferable technical measure:
the method for solving the optimal value of the identification parameter comprises the following steps:
selecting initial parameters, carrying out iterative identification parameters theta on the measured errors, the control signals and the output track signals by using an iterative optimization method, calculating the track signals and the feedforward control signals after input track shaping by using the iterative identification parameters, sending the track signals and the feedforward control signals to the motion control system again, and repeating the iterative process until the optimal track tracking of the motion control system is realized.
As a preferable technical measure:
an optimal iterative feedforward parameter adjusting system of a motion control system,
comprising one or more processors;
storage means for storing one or more programs;
the motion control system is provided with an input shaping filter and a feedforward controller;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement an optimal iterative feed-forward parameter tuning method for a motion control system as described above.
As a preferable technical measure:
the motion control system is a direct current brushless motor and is connected with an upper computer, and the upper computer is a computer or an industrial personal computer.
Compared with the prior art, the invention has the following beneficial effects:
through continuous exploration and test, the invention sets the identification parameter theta of the input shaping filter and the feedforward controller, and restrains and weights the variation of the identification parameter theta, thereby effectively restraining the energy of the feedforward control signal and influencing the error convergence value, and restraining the variation step length and influencing the convergence speed of the feedforward control signal, and effectively avoiding the energy from exceeding the maximum output capacity of the actual motion control system, thereby leading the system to be incapable of closing the loop and entering the unstable state. Meanwhile, the invention combines the advantages of optimal iterative learning control and parameterized feedforward, realizes the performance of the variable-track tracking task, has good track tracking robustness, can balance control signals and tracking errors, further iteratively identifies optimal parameters in a data-driven mode, avoids fussy model identification, effectively reduces the calculated amount of a processor, has strong flexibility, high operation speed, high performance, detailed scheme, feasibility and convenient realization.
Furthermore, the invention is particularly suitable for non-minimum phase systems and complex systems, because the system adopts a basis function mode to parameterize the feedforward controller, the problem of non-minimum phase zero point does not exist, and simultaneously, a data driving mode does not need a system parameter model.
Drawings
FIG. 1 is a block diagram of a parameterized feedforward control system with an input shaping filter according to the present invention;
FIG. 2 is a schematic diagram of a reference trajectory according to the present invention;
FIG. 3 shows the weighting factor ρ =5 × 10 according to the present invention 4 A curve chart of two norms of track errors of the stable section under different weighting coefficients lambda;
FIG. 4 shows the weighting factor λ =2 × 10 according to the present invention 5 A curve diagram of two norms of track errors of the stable section under different weighting coefficients rho;
FIG. 5 shows the weighting factor ρ =5 × 10 according to the present invention 4 ，λ＝2×10 5 Then, a trajectory change curve chart before and after the iteration of the stable section is obtained;
FIG. 6 shows the weighting factor ρ =5 × 10 according to the present invention 4 ，λ＝2×10 5 Identifying a parameter theta change curve chart;
FIG. 7 is a graph of different reference trajectories for the apodization test of the present invention;
FIG. 8 shows the weighting factor ρ =5 × 10 according to the present invention 4 ，λ＝2×10 5 And in time, a two-norm change curve diagram of errors of a stable section of the variable-trajectory experiment is obtained.
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.
an optimal iterative feedforward parameter adjusting method of a motion control system,
the method comprises the following steps:
the method comprises the following steps: constructing a motion control system and setting PID parameters of a feedback controller;
step two: enabling a motion control system by using the PID parameters of the feedback controller in the step one to enable a motor of the motion control system to be closed-loop;
step three: inputting a desired track signal r (t) toIn the motion control system in the step two, the output track signal y (t), the control signal u (t) and the track error signal e of the system are collected y (t)；
Eliminating the dependence on the model by utilizing the acquired output track signal y (t) and the control signal u (t);
step four, for the motion control system in the step three, the track signal r after the input track shaping is calculated through the input shaping filter y (t) and calculating a feedforward control signal u by the feedforward controller ff (t) setting the execution period and the stabilization period of the motion control system;
step five: using the track signal r in step four y (t) and a feedforward control signal u ff (t) constructing a parameterized feedforward model, combining an optimal iterative learning control method, introducing a constraint term of an identification parameter theta and a variable quantity of the identification parameter theta of an input shaping filter and a feedforward controller into a target function of the parameterized feedforward model, weighting the constraint term, calculating the identification parameter theta by a data-driven least square method, selecting a proper weighting coefficient rho and a weighting coefficient lambda, and realizing the track tracking and the track-variant tracking tasks of a motion control system;
the weighting coefficient rho is an identification parameter size weighting coefficient, weights the identification parameter size and can restrict the energy of the feedforward control signal and influence an error convergence value;
the weighting coefficient lambda is an identification parameter variation weighting coefficient which weights the identification parameter variation step length and can restrict the feedforward control signal variation step length and influence the convergence speed;
step six: and analyzing the identification parameter theta and the convergence of the optimal iterative feedforward parameter adjusting error in the step five, and solving the optimal value of the identification parameter to realize the optimal trajectory tracking of the motion control system.
The optimal iterative feedforward parameter adjusting method is adopted, a system mathematical model can be not depended on, a complex model identification process is avoided, the operation amount of a processor is reduced, the operation speed is high, meanwhile, the method is simple to implement, the control difficulty of a motion control system is reduced, not only can the repeated trajectory tracking be realized, but also the variable trajectory tracking can be realized, the method is high in application flexibility and has certain robustness, and the control requirement of a high-speed high-precision motion control system can be met.
The control method of the invention is detailed, the scheme is feasible, the process is simple and practical, the flexibility is strong, the operation speed is fast, the control precision is high, the control effect is good, and the control requirement of the motion control system can be met.
an optimal iterative feedforward parameter adjusting method based on a motion control system comprises the following steps: parameterizing an input shaping filter and a feedforward controller by using a basis function, and calculating a feedforward force through an input track and the parameterized feedforward controller; combining the advantages of optimal iterative learning control and parameterized feedforward control, introducing a performance objective function of optimal iterative feedforward parameter adjustment, and iteratively identifying parameters input into a shaping filter and a feedforward controller; analyzing the error of the optimal iterative feedforward parameter adjustment and the convergence of the identification parameters; and solving the optimal value of each parameter to realize the optimal trajectory tracking of the motion control system.
Through continuous exploration and test, the optimal iterative feedforward parameter adjusting method is adopted, the control difficulty of the motion control system can be effectively reduced, the calculated amount of a processor is reduced, the flexibility is strong, the operation speed is high, the robustness is good, the control effect is good, and the control requirement of the motion control system can be met.
As shown in fig. 1 to 7, inventive example 3:
an optimal iterative feedforward parameter adjusting method of a motion control system comprises the following steps:
the method comprises the following steps: and (3) a motion control system platform is built, PID parameters of a feedback controller and the like are set on a control interface, and the parameters are downloaded to a motion control board card designed by an ARM chip.
Step two: and enabling the motion control platform through the downloaded control parameters according to the closed-loop performance requirement of the motion control system to enable the motor to be closed-loop.
The expression of the single-input single-output linear time-invariant motion control system of the unknown model is as follows:
the controlled system is in the form of rational basis functions in the form of numerators and contains the pole-zero characteristics of the motion control system. The system transfer function is converted into a discrete time invariant state space model as follows:
wherein, x (T + 1) is the state variable of the system at the T +1 moment, A, B, C and D are the system state space model, and the sampling time of the system is T s With the number of sampling points being N, discretizing the system input control signal into u = [ u (0), …, u (N-1)] T U is a vector representation of the input control signal, and for convenience of representation subsequent symbols are represented in vector form.
Step three: inputting a desired track signal r (T) at the signal input end of the motion control system, and defining a sampling period T s Is 0.0005s, 2048 sampling points in total, 1.0235s acquisition time, and initial values theta of input shaping filter and feedforward controller parameters are set 0 ＝[0,0,0,0.1,0] T Calculating the input trajectory r after shaping y (t) and a feedforward control signal u ff (t), downloading to the motion control card for operation, and then collecting the system output track signal y (t) and the control signal u (t) from the motion control board card, and simultaneously collecting the track error signal e of the system y (t) defining the execution period and the stabilization period of the motion control system to be 0.512s and 0.5115s, respectively, in the collection;
an optimal iterative feedforward parameter regulating method, which adopts Finite Impulse Response (FIR) filter composed of basis function polynomial to input shaping filter T y And a feedforward controller T ff Parameterizing, wherein the parameterized expression is as follows:
then, form T y And T ff Is a polynomial of a (z) -1 θ) and B (z) -1 And theta) are respectively represented by
Wherein z is -1 As time shift operator, θ 1 ～θ 3 For parameterizing the identification parameter, theta, of the input shaping filter 4 ～θ 5 For parameterizing the identification parameter of the feedforward controller, n a ，n b To form T y And T ff The number of basis functions of (1) is 3 and 2, respectively
The input trajectory may be decomposed into various derivatives, with the basis functions selected as:
polynomial of basis function A (z) -1 Theta) and B (z) -1 Theta) is an FIR filter, and the FIR filter has the advantages that firstly, the FIR filter has no pole, so the instability problem does not exist; secondly, designing a feedforward controller by an FIR filter is a convex optimization method; thirdly, as can be seen from the control framework of the motion control system in fig. 1, the system errorThe difference is about 0, i.e.
e y ＝r y -y＝S(T y -PT ff )r＝0
Then
To obtain the optimum track tracking performance, only two FIR filters are used for designing T y And T ff The numerator denominator of the controlled system can be described, the zero-pole motion characteristic of the system can be contained, when the two FIR filters work for inversion, the problems of unstable poles and non-minimum phase zeros cannot be caused, and a better track tracking effect can be realized, so that the control target is to use the two FIR filters to identify the system model.
According to the control block diagram of FIG. 1, the expressions of the system error, control signal and output track signal during the jth iteration of the motion control system are as follows
Wherein, the system sensitivity function S = (1 + PC) fb ) -1 Sensitivity function T = C fb T y +T ff ，C fb Is a feedback controller.
From the above, it is known that both 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 -1 u j
SPr＝T -1 y j
Step four: aiming at the optimal iteration feedforward parameter adjusting method shown in the figure 1, under the block diagram of a parameterization feedforward control system with an input shaping filter, optimal iteration learning control is combined, system control signal energy and track errors are balanced, and a feedforward control signal in the optimal iteration feedforward parameter adjusting method is composed of a basis function polynomial, so that the feedforward signal is related to parameters corresponding to the basis function, a system performance target function comprises the system errors, weighting constraint is also carried out on parameters and parameter variable quantities of the input shaping filter and a feedforward controller, different weighting coefficients rho and lambda are selected for carrying out a track tracking experiment, and under different weighting coefficients, track tracking performance is selected, and appropriate weighting coefficients rho and lambda are selected for carrying out a track and track-changing tracking experiment.
The performance objective function of the optimal iterative feedforward parameter adjustment is as follows:
as can be seen from FIG. 1, r y ＝T y r, FIG. 2 shows that the expected trajectory is T in the stable period y =1, then r y = r and there is a delay of the execution section, the length of the delay time being T y Number of components n of basis function a From this, the stable segment e is known y ＝r y Y = e, so the performance objective function can be written as
Then, the error of the system track is obtained from the above step when the iteration is performed for the (j + 1) th time
Then obtaining the expression form according to the parameterized polynomial and data drive of the input shaping filter and the feedforward controller
Wherein
Identifying the parameters of the parameterized input shaping filter and the feedforward controller due to θ j+1 As an objective function J j+1 In order to minimize the track tracking error, each iteration error is continuously reduced relative to the previous iteration until convergence according to the iterative learning idea, so that the objective function J is solved j+1 To a minimum value of, i.e. to find the objective function J j+1 To theta j+1 Is a partial derivative of
Derived and identified to obtain a parameter theta j+1 ：
In the formula, a robust filter Q θ And a learning filter L θ Is composed of
Q θ ＝[ψ T W e ψ+W θ +W Δθ ] -1 [ψ T W e ψ+W Δθ ]
L θ ＝[ψ T W e ψ+W Δθ ] -1 ψ T W e
W e ，W θ And W Δθ Weighting matrix of error, identification parameter theta and identification parameter variation delta theta, respectively, the general error weighting matrix is selected as W e = I; selecting the identification parameter theta weighting matrix as W θ Rho is an identification parameter weighting coefficient, the magnitude of feedforward control signal energy and an influence error convergence value can be constrained, generally rho is any real number greater than or equal to 0, and when rho is 0, the condition is not limitedControlling signal energy, wherein the larger the weighting coefficient rho is, the larger the constraint action of the feedforward control signal is at the moment, the larger the error convergence value is, and otherwise, the smaller the error convergence value is; the weight matrix for identifying the parameter variation Delta theta is selected as W Δθ The method is characterized in that = λ I, λ is an identification parameter variation weighting coefficient, and can constrain a feedforward control signal variation step length and influence convergence speed, generally λ is any real number greater than or equal to 0, the feedforward control signal variation step length is not limited when λ is 0, the larger the weighting coefficient λ is, the larger the parameter variation constraint action is, the slower the feedforward control signal is iterated to an optimal value, the slower the error convergence speed is, otherwise, the faster the error convergence speed is; wherein I is an identity matrix.
Step five, the motion control framework is shown in figure 1, and an input shaping filter T in the optimal iteration feedforward parameter adjusting method y And a feedforward controller T ff Are all finite impulse response filters, and error e y Error e is known in linear relation to the finite impulse response filter parameters y Is 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: the upper computer simulation software (for example: MATLAB/Simulink, visual studio 2012) utilizes the error, control signal and output track signal collected by the motion control board card to carry out iterative optimization identification on the parameters of the parameterized input shaping filter and the feedforward controller by using a data-driven least square method, wherein the expected input track of the system adopts a four-order S-shaped point-to-point motion track or a four-order S-shaped point-to-point motion track shown in FIG. 2Adopting different fourth-order S-shaped point-to-point expected input tracks in the figure 7 to carry out an orbital transfer experiment (in the orbital transfer experiment, the reference track 1 is operated in the first 10 times of iteration, and the reference track 2 is operated in the 11 th iteration), updating an input shaping filter and a feedforward controller through identified parameters, and then calculating a feedforward control signal u ff And shaping the input track signal r y And the generated signals are downloaded to the motion control board card again, and the track or the track-changing tracking task and the convergence of the identification parameters are realized by repeating the iteration. As shown in FIG. 3 and FIG. 4, the invention balances the control energy and performance of the motion control system, and different weighting coefficients λ limit the step length of the identification parameter, so that the speed of the system feedforward control signal converging to the optimal feedforward controller becomes slow, and then influences the convergence speed of the system trajectory error, and different weighting coefficients ρ limit the size of the identification parameter, thereby limiting the size of the feedforward control signal, and then influences the convergence value of the system trajectory error. As shown in fig. 5 and 8, the present invention can achieve optimal tracking performance for a track and has certain robustness for a variable track. As shown in fig. 6, the convergence of the input shaping filter and feedforward controller parameters of the present invention.
An embodiment of a device to which the method of the invention is applied:
an optimal iterative feedforward parameter adjustment system method for a motion control system, comprising:
one or more processors;
storage means for storing one or more programs;
when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the optimal iterative feedforward parameter tuning method and system for a motion control system described above.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
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. An optimal iteration feedforward parameter adjusting method of a motion control system is characterized in that,
the method comprises the following steps:
the method comprises the following steps: constructing a motion control system and setting PID parameters of a feedback controller;
step two: enabling a motion control system by using the PID parameters of the feedback controller in the step one to enable a motor of the motion control system to be closed-loop;
step three: inputting the expected track signal r (t) into the motion control system in the second step, and collecting an output track signal y (t) and a control signal u (t);
step four, the motion control system in the step three is controlled byThe input shaping filter calculates the track signal r after input track shaping y (t) and calculating a feedforward control signal u by the feedforward controller ff (t) setting the execution period and the stabilization period of the motion control system;
step five: using the trace signal r in step four y (t) and a feedforward control signal u ff (t) constructing a parameterized feedforward model, combining an optimal iterative learning control method, introducing an identification parameter theta of an input shaping filter and a feedforward controller and a constraint term of variable quantity of the identification parameter theta into a target function of the parameterized feedforward model, weighting the identification parameter theta, calculating the identification parameter theta by a data-driven least square method, and selecting a proper weighting coefficient rho and a weighting coefficient lambda to realize track tracking and track-changing tracking tasks of a motion control system;
the weighting coefficient rho is an identification parameter size weighting coefficient, weights the identification parameter size and can restrict the energy of the feedforward control signal and influence an error convergence value;
the weighting coefficient lambda is an identification parameter variation weighting coefficient which weights the identification parameter variation step length and can restrict the feedforward control signal variation step length and influence the convergence speed;
step six: and analyzing the identification parameter theta and the convergence of the optimal iterative feedforward parameter adjusting error in the step five, and solving the optimal value of the identification parameter to realize the optimal trajectory tracking of the motion control system.
2. An optimal iterative feed-forward parameter tuning method for a motion control system according to claim 1,
in the fifth step, the method for constructing the parameterized feedforward model specifically comprises the following steps:
input shaping filter T using finite impulse response filter composed of basis function polynomials y And a feedforward controller T ff Parameterizing, wherein the parameterized expression is as follows:
then, form T y And T ff Is a polynomial of a (z) -1 Theta) and B (z) -1 And theta) are respectively represented by
Wherein z is -1 For the time shift operator, theta is an identification parameter of the parameterized input shaping filter and the feedforward controller, n a ，n b To form T y And T ff Number of basis functions, basis functions
Decomposing the input trajectory into derivatives of various orders, at T y Acceleration basis function of
Comprises the following steps:
Polynomial of basis function A (z) -1 Theta) and B (z) -1 And theta) is a FIR filter,
with a systematic error of 0, i.e.
e y ＝r y -y＝S(T y -PT ff )r＝0
Then
When the motion control system iterates for the jth time, the expressions of the system error, the control signal and the output track signal are as follows
Wherein, the system sensitivity function S = (1 + PC) fb ) -1 Sensitivity function T = C fb T y +T ff ，C fb Is a feedback controller;
converting Sr and SPr into a form based on data driving, the calculation formula is as follows:
Sr＝T -1 u j
SPr＝T -1 y j 。
3. an optimal iterative feed-forward parameter adjustment method for a motion control system according to claim 1,
the feedforward control signal is composed of a basis function polynomial, and is related to parameters corresponding to the basis functions, so that the objective function performs weighting constraint on parameters and parameter variation of the input shaping filter and the feedforward controller, and the expression is as follows:
due to r y ＝T y r, expected trajectory during the settling period T y =1, then r y = r and there is a delay of the execution section, the length of the delay time being T y Number of components n of basis function a Thereby stabilizing the section e y ＝r y Y = e, the objective function is calculated as follows:
then, the error of the system track is obtained from the above step when the iteration is performed for the (j + 1) th time
Then according to the parameterized polynomial of the input shaping filter and the feedforward controller and the expression form of data drive, the method can obtain
Wherein
wherein, W e ，W θ And W Δθ Respectively, the error, the identification parameter theta and the identification parameter variation delta theta, and selecting the error weighting matrix as W e Selecting W as identification parameter theta weighting matrix θ Rho is a weight coefficient of the size of the identification parameter, and a weight matrix of the variation delta theta of the identification parameter is selected as W Δθ And = λ I, λ is a recognition parameter variation weighting coefficient, and I is an identity matrix.
4. An optimal iterative feed-forward parameter tuning method for a motion control system according to claim 3,
the objective function identifies the parameters of the parameterized input shaping filter and the feedforward controller due to θ j+1 As an objective function J j+1 In order to enable trajectory trackingThe error is minimum, according to the iterative learning idea, the iterative error of each time is continuously reduced relative to the previous time until convergence, and therefore the objective function J is solved j+1 To a minimum value of, i.e. to find the objective function J j+1 To theta j+1 Is a partial derivative of
Derived and identified to obtain a parameter theta j+1 ：
In the formula, a robust filter Q θ And a learning filter L θ Is composed of
Q θ ＝[ψ T W e ψ+W θ +W Δθ ] -1 [ψ T W e ψ+W Δθ ]
L θ ＝[ψ T W e ψ+W Δθ ] -1 ψ T W e 。
5. An optimal iterative feed-forward parameter adjustment method for a motion control system according to claim 4,
the optimal design method of the identification parameter size weighting coefficient comprises the following steps:
identifying the parameter size, wherein the weighting coefficient rho is any real number greater than or equal to 0, when rho is 0, the energy of the control signal is not limited, the larger the weighting coefficient rho is, the larger the constraint effect of the feedforward control signal is, the larger the error convergence value is, and conversely, the smaller the error convergence value is.
6. An optimal iterative feed-forward parameter adjustment method for a motion control system according to claim 4,
the optimal design method for identifying the parameter variation weighting coefficient comprises the following steps:
identifying any real number of which the parameter variation weighting coefficient lambda is greater than or equal to 0, not limiting the variation step length of the feedforward control signal when lambda is 0, wherein the larger the weighting coefficient lambda is, the larger the parameter variation constraint effect is, the slower the iteration speed of the feedforward control signal to the optimal value is, the slower the error convergence speed is, and otherwise, the faster the error convergence speed is.
7. An optimal iterative feed-forward parameter adjustment method for a motion control system according to claim 1,
step six, the optimal iteration feedforward parameter adjusting error is an error e y The convergence is specifically analyzed as follows:
input shaping filter T y And a feedforward controller T ff Are all finite impulse response filters, and error e y Error e, linear with finite impulse response filter parameters y Global convergence, error e y The calculation formula of (c) is as follows:
according to
Non-singular and norm knowledge yields:
8. an optimal iterative feed-forward parameter adjustment method for a motion control system according to any one of claims 1 to 7,
the method for solving the optimal value of the identification parameter comprises the following steps:
selecting initial parameters, carrying out iterative identification parameters theta on the measured errors, the control signals and the output track signals by using an iterative optimization method, calculating the track signals and the feedforward control signals after input track shaping by using the iterative identification parameters, sending the track signals and the feedforward control signals to the motion control system again, and repeating the iterative process until the optimal track tracking of the motion control system is realized.
9. An optimal iterative feedforward parameter adjusting system of a motion control system is characterized in that,
comprising one or more processors;
storage means for storing one or more programs;
the motion control system is provided with an input shaping filter and a feedforward controller;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement an optimal iterative feed-forward parameter tuning method for a motion control system according to any of claims 1-8.
10. An optimal iterative feed-forward parameter adjustment system for a motion control system as claimed in claim 9,
the motion control system is a direct current brushless motor and is connected with an upper computer, and the upper computer is a computer or an industrial personal computer.
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