Optimal Iterative Feedforward Parameter Tuning Method and System for a Motion Control System

Abstract

The present invention discloses an optimal iterative feedforward parameter tuning method and system for a motion control system, belonging to the technical field of mechanical equipment control. Existing control methods do not balance control energy and tracking performance and cannot limit the system control energy, which may cause the energy to exceed the maximum output capacity of the actual motion control system, resulting in the system being unable to close the loop and entering an unstable state. An optimal iterative feedforward parameter tuning method for a motion control system of the present invention sets the identification parameters θ of the input shaping filter and the feedforward controller, and constrains and weights their variation amounts, which can effectively constrain the magnitude of the feedforward control signal energy and the influence on the error convergence value, as well as constrain the change step of the feedforward control signal and the influence on the convergence speed; at the same time, combining the advantages of optimal iterative learning control and parameterized feedforward, it realizes the performance of variable trajectory tracking tasks, effectively reduces the computational amount of the processor, has strong flexibility, fast operation speed, high performance, and the scheme is detailed and feasible.

Description

Technical Field

[0001] The present invention relates to an optimal iterative feedforward parameter tuning method and system for a motion control system, belonging to the technical field of mechanical equipment control. Background Art

[0002] In a motion control system, it is usually necessary to achieve the tracking of a given desired trajectory to minimize the trajectory tracking error. High speed and high precision are the pursuit goals and development trends in the field of motion control. The former improves production efficiency, shortens the production cycle, and reduces manufacturing costs. However, the flexible vibration modes included in the actual system model, and with the increasing requirement for high-speed characteristics, the acceleration and deceleration sections of the system input trajectory contain more and more high-frequency components, which are very likely to excite the neglected flexible vibration modes, resulting in continuous vibration during the motion process of the motion control system and after reaching the end position. The common control strategies of motion control systems include only feedback and feedforward plus feedback control strategies. The control strategy with only feedback uses a traditional PID feedback controller. The feedback control has a slow response speed and is corrected according to the system error, with hysteresis and cannot meet the requirements of high response speed. For the two-degree-of-freedom control strategy of feedback plus feedforward, the feedback controller is used to ensure the system stability, and the feedforward control improves the trajectory tracking performance. Because the feedforward has characteristics such as high response speed and high positioning accuracy, and the feedforward corrects the system before the error occurs, with a certain degree of predictability. Therefore, the two-degree-of-freedom control strategy of feedback plus feedforward is a standard configuration for high-speed and high-precision motion control systems.

[0003] In the two-degree-of-freedom control strategy, the feedback controller generally uses PID, and there are many methods for designing the feedforward controller, which have been widely studied by domestic and foreign scholars. At present, the feedforward control methods are mainly divided into iterative learning control and model-based feedforward control. The iterative learning control algorithm can achieve the tracking performance of repeated trajectories. Especially, the optimal iterative learning control algorithm can achieve the norm-optimal objective function, and the control signal and the change amount of the control signal are weighted and constrained in the objective function, weighing the control energy and the tracking performance. However, for variable trajectory tracking tasks, such algorithms will lead to performance deterioration; the model-based feedforward control algorithms include feedforward control based on model inversion and feedforward control based on parameterization. The feedforward controller based on model inversion depends on the mathematical model of the system and needs to go through a cumbersome and time-consuming process of identifying the system model in advance. The feedforward control algorithm based on parameterization uses basis functions to parameterize the feedforward controller, which can achieve variable trajectory tracking tasks without relying on the mathematical model, but does not weigh the control energy and the tracking performance, and cannot limit the system control energy, which will lead to the energy exceeding the maximum output capacity of the actual motion control system, resulting in the system being unable to be closed-loop and entering an unstable state. Summary of the Invention

[0004] Aiming at the defects of the prior art, the purpose of the present invention is to provide a method and system for optimal iterative feedforward parameter tuning of a motion control system, which identifies the parameter θ provided with an input shaping filter and a feedforward controller, constrains and weights its variation, can effectively constrain the magnitude of the feedforward control signal energy and affect the error convergence value, as well as constrain the change step of the feedforward control signal and affect the convergence speed; meanwhile, combining the advantages of optimal iterative learning control and parameterized feedforward, it realizes the performance of variable trajectory tracking tasks, has good trajectory tracking robustness, can balance the control signal and the tracking error, further iteratively identifies the optimal parameters in a data-driven manner, avoids cumbersome model identification, effectively reduces the computational amount of the processor, has strong flexibility, fast operation speed, and has a high-performance motion control system.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] An optimal iterative feedforward parameter tuning method for a motion control system,

[0007] including the following steps:

[0008] Step 1: Construct a motion control system and set the PID parameters of the feedback controller;

[0009] Step 2: Use the PID parameters of the feedback controller in Step 1 to enable the motion control system and close the motor loop;

[0010] Step 3: Input the desired trajectory signal r(t) into the motion control system in Step 2, and collect the output trajectory signal y(t), the control signal u(t), and the trajectory error signal e y (t);

[0011] Use the collected output trajectory signal y(t) and control signal u(t) to eliminate the dependence on the model;

[0012] Step 4: For the motion control system in Step 3, calculate the trajectory signal r y (t) after input trajectory shaping through the input shaping filter, and calculate the feedforward control signal u ff (t) through the feedforward controller, and set the execution section and stable section time of the motion control system;

[0013] Step 5: Use the trajectory signal r y (t) and the feedforward control signal u ff(t)Construct a parametric feedforward model, and combine it with the optimal iterative learning control method. Introduce the constraint terms of the identification parameters θ of the input shaping filter and the feedforward controller and their variations into the objective function of the parametric feedforward model, and weight them. Then calculate the identification parameter θ by the data-driven least squares method, and select appropriate weighting coefficients ρ and λ to achieve the trajectory tracking and variable trajectory tracking tasks of the motion control system;

[0014] The weighting coefficient ρ is the weighting coefficient for the magnitude of the identification parameter. It weights the magnitude of the identification parameter and can constrain the magnitude of the feedforward control signal energy and affect the error convergence value;

[0015] The weighting coefficient λ is the weighting coefficient for the variation of the identification parameter. It weights the variation step of the identification parameter and can constrain the variation step of the feedforward control signal and affect the convergence speed;

[0016] Step 6: Analyze the convergence of the identification parameter θ and the optimal iterative feedforward tuning error in Step 5, and obtain the optimal value of the identification parameter to achieve the optimal trajectory tracking of the motion control system.

[0017] Through continuous exploration and experiments, the present invention sets the identification parameter θ of the input shaping filter and the feedforward controller, and constrains and weights its variation, which can effectively constrain the magnitude of the feedforward control signal energy and affect the error convergence value, as well as constrain the variation step of the feedforward control signal and affect the convergence speed, effectively avoiding the situation where the energy exceeds the maximum output capacity of the actual motion control system, resulting in the system being unable to close the loop and entering an unstable state. At the same time, combining the advantages of optimal iterative learning control and parametric feedforward, it realizes the performance of variable trajectory tracking tasks, has good trajectory tracking robustness, can balance the control signal and the tracking error, and further iteratively identifies the optimal parameters in a data-driven manner, avoiding cumbersome model identification, effectively reducing the computational amount of the processor, being flexible, having a fast operation speed, having high performance, with a detailed and feasible scheme, and being easy to implement.

[0018] Furthermore, the present invention is particularly applicable to non-minimum phase systems and complex systems because the system parameterizes the feedforward controller in the form of basis functions, there is no problem of non-minimum phase zeros, and at the same time, the data-driven method does not require the system parameter model.

[0019] As a preferred technical measure:

[0020] In Step 5, the construction method of the parametric feedforward model is specifically as follows:

[0021] Use a finite impulse response (FIR) filter composed of basis function polynomials for the input shaping filter T y and the feedforward controller Tff Parametrize, and the parametric expression is as follows:

[0022]

[0023] Then, form T y With T ff The basis function polynomials A(z -1 , θ) and B(z -1 , θ) are respectively expressed as

[0024]

[0025]

[0026] Where z -1 Is the time shift operator, θ is the identification parameter of the parametric input shaping filter and the feedforward controller, n a , n b Is the number of basis functions that form T y And T ff The basis function Can decompose the input trajectory into derivatives of each order. The acceleration basis function y In T Is:

[0027] Where T s Is the sampling time.

[0028] The basis function polynomials A(z -1 , θ) and B(z -1 , θ) are FIR filters. The advantages of using FIR filters are: first, the FIR filter has no poles, so there is no instability problem; second, designing the feedforward controller with the FIR filter is a convex optimization method; third, according to the control framework of the motion control system, the system error is 0, that is

[0029] e y = r y - y = S(T y - PT ff )r = 0

[0030] Then

[0031]

[0032] To obtain the optimal trajectory tracking performance, as long as T y And T ffThe numerator and denominator of the controlled system are described, which can include the zero-pole motion characteristics of the system. When two FIR filters are inverted, it will not cause unstable poles and non-minimum phase zero problems, and can achieve better trajectory tracking effects. Therefore, the control objective is to identify the system model with two FIR filters.

[0033] When the motion control system is iterated for the jth time, the system error, control signal, and output trajectory signal are expressed as follows

[0034]

[0035]

[0036]

[0037] Among them, the system sensitivity function S=(1+PC fb ) -1 , the sensitivity function T = C fb T y +T ff , C fb is the feedback controller;

[0038] As can be seen from the above, both Sr and SPr are related to the parameter model. To eliminate the dependence on the model, Sr and SPr are transformed into a data-driven form, and their calculation formulas are as follows:

[0039] Sr = T -1 u j

[0040] SPr = T -1 y j .

[0041] As a preferred technical measure:

[0042] The optimal iterative feedforward tuning parameter method combines optimal iterative learning control under the parameterized feedforward control framework with an input shaping filter, and balances the system control signal energy and trajectory error.

[0043] The feedforward control signal is composed of basis function polynomials, which is related to the parameters corresponding to the basis functions, so that the objective function includes not only the system error, but also weights and constraints on the parameters and parameter changes of the input shaping filter and the feedforward controller. Its expression is as follows:

[0044]

[0045] Since r y = T y r, the desired trajectory is T y = 1 during the stable period, so r y= r and there is a time delay in the execution segment, and the length of the time delay is T y The number of components n of the basis function a , from which the stable segment e can be known y = r y -y = e, so the calculation formula of the objective function is as follows:

[0046]

[0047] Then, from the above, at the (j + 1)-th iteration, the system trajectory error is

[0048]

[0049] According to the parametric polynomials and data-driven expression forms of the input shaping filter and the feedforward controller, we can obtain

[0050]

[0051] where

[0052] is non-singular.

[0053] As a preferred technical measure:

[0054] The objective function identifies the parameters of the parametric input shaping filter and the feedforward controller. Since θ j+1 is a variable of the objective function J j+1 , in order to minimize the trajectory tracking error, according to the iterative learning idea, the error decreases continuously relative to the previous one until convergence at each iteration. Therefore, we find the minimum value of the objective function J j+1 , that is, we find the partial derivative of the objective function J j+1 with respect to θ j+1 , and let After derivation, the parameter θ j+1 can be identified as:

[0055]

[0056] In the formula, the robust filter Q θ and the learning filter L θ are

[0057] Q θ = [ψ T W e ψ + W θ + W Δθ -1 [ψ T W e ψ + W Δθ

[0058] L θ = [ψ​​T W e ψ + W Δθ -1 ψ T W e

[0059] Among them, W e , W θ and W Δθ are respectively the weighted matrices of the error, the identification parameter θ and the change amount Δθ of the identification parameter. The error weighted matrix is selected as W e = I, the weighted matrix of the identification parameter θ is selected as W θ = ρI, ρ is the weighted coefficient of the magnitude of the identification parameter, and the weighted matrix of the change amount Δθ of the identification parameter is selected as W Δθ = λI, λ is the weighted coefficient of the change amount of the identification parameter, and I is the identity matrix.

[0060] As a preferred technical measure:

[0061] The optimization design method of the weighted coefficient of the magnitude of the identification parameter is as follows:

[0062] The weighted coefficient of the magnitude of the identification parameter weights the magnitude of the identification parameter, which can constrain the magnitude of the feedforward control signal energy and affect the error convergence value. ρ is any real number greater than or equal to 0. When ρ is 0, the control signal energy is not restricted. The larger the weighted coefficient ρ, the greater the constraint effect. At this time, the constraint effect of the feedforward control signal is greater, and the error convergence value is larger. On the contrary, the error convergence value is smaller.

[0063] As a preferred technical measure:

[0064] The optimization design method of the weighted coefficient of the change amount of the identification parameter is as follows:

[0065] The weighted coefficient of the change amount of the identification parameter weights the change step of the identification parameter, which can constrain the change step of the feedforward control signal and affect the convergence speed. λ is any real number greater than or equal to 0. When λ is 0, the change step of the feedforward control signal is not restricted. The larger the weighted coefficient λ, the greater the constraint effect on the change amount of the parameter. The slower the speed at which the feedforward control signal iterates to the optimal value, and the slower the error convergence speed. On the contrary, the error convergence speed is faster.

[0066] As a preferred technical measure:

[0067] In step six, the optimal iterative feedforward tuning parameter error is the error e y , and its convergence is specifically analyzed as follows:

[0068] The input shaping filter T y and the feedforward controller T ff are both finite impulse response filters, and the error e y ​Is linearly related to the finite impulse response filter parameters, and the error e y Globally convergent, and the error e y The calculation formula is as follows:

[0069]

[0070] According to Based on non-singularity and norm knowledge, it is obtained that:

[0071]

[0072] Therefore, the identified parameter θ is convergent.

[0073] As a preferred technical measure:

[0074] The method for obtaining the optimal value of the identified parameter is as follows:

[0075] Select the initial parameter, and use the iterative optimization method to iteratively identify the parameter θ for the measured error, control signal, and output trajectory signal. Use the iteratively identified parameter to calculate the trajectory signal and feedforward control signal after input trajectory shaping, and re-transmit them to the motion control system. Repeat this iterative process until the optimal trajectory tracking of the motion control system is achieved.

[0076] As a preferred technical measure:

[0077] An optimal iterative feedforward parameter tuning system for a motion control system,

[0078] Includes one or more processors;

[0079] A storage device for storing one or more programs;

[0080] A motion control system equipped with an input shaping filter and a feedforward controller;

[0081] When the one or more programs are executed by the one or more processors, the one or more processors implement an optimal iterative feedforward parameter tuning method for a motion control system as described above.

[0082] As a preferred technical measure:

[0083] The motion control system is a brushless DC motor, which is connected to an upper computer, and the upper computer is a computer or an industrial control computer.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] Through continuous exploration and experimentation, the present invention sets the identification parameters θ of the input shaping filter and the feedforward controller, and constrains and weights their variation amounts, which can effectively constrain the magnitude of the feedforward control signal energy and affect the error convergence value, as well as constrain the variation step of the feedforward control signal and affect the convergence speed, effectively avoiding the energy exceeding the maximum output capacity of the actual motion control system, resulting in the system being unable to close the loop and entering an unstable state. At the same time, the present invention combines the advantages of optimal iterative learning control and parameterized feedforward, realizes the performance of variable trajectory tracking tasks, has good trajectory tracking robustness, can balance the control signal and the tracking error, and further iteratively identifies the optimal parameters in a data-driven manner, avoiding cumbersome model identification, effectively reducing the computational amount of the processor, having strong flexibility, fast operation speed, high performance, detailed solutions, being practical and feasible, and being easy to implement.

[0086] Furthermore, the present invention is particularly suitable for non-minimum phase systems and complex systems because the system parameterizes the feedforward controller in the form of basis functions, there is no problem of non-minimum phase zeros, and at the same time, the data-driven method does not require the system parameter model. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 is the block diagram of the parameterized feedforward control system with an input shaping filter according to the present invention;

[0088] Figure 2 is the schematic diagram of the reference trajectory curve according to the present invention;

[0089] Figure 3 is for the present invention when the weighting coefficient ρ = 5×10 4 , the curve graph of the two-norm of the trajectory error in the stable section under different weighting coefficients λ;

[0090] Figure 4 is for the present invention when the weighting coefficient λ = 2×10 5 , the curve graph of the two-norm of the trajectory error in the stable section under different weighting coefficients ρ;

[0091] Figure 5 is for the present invention when the weighting coefficient ρ = 5×10 4 , λ = 2×10 5 when, the curve graph of the trajectory change before and after iteration in the stable section;

[0092] Figure 6 is for the present invention when the weighting coefficient ρ = 5×10 4 , λ = 2×10 5 when, the curve graph of the change of the identification parameter θ;

[0093] Figure 7 is the curve graph of different reference trajectories for the variable trajectory test according to the present invention;

[0094] Figure 8 For the present invention, when the weighting coefficient ρ = 5×10 4 and λ = 2×10 5 , this is the change curve of the two-norm of the error in the stable section of the variable trajectory experiment. Detailed implementation manners

[0095] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention.

[0096] On the contrary, the present invention covers any alternatives, modifications, equivalent methods and solutions made within the spirit and scope of the present invention as defined by the claims. Further, in order to enable the public to have a better understanding of the present invention, in the following detailed description of the present invention, some specific details are described in detail. Those skilled in the art can fully understand the present invention without the description of these details.

[0097] Embodiment 1 of the present invention:

[0098] An optimal iterative feedforward parameter tuning method for a motion control system

[0099] comprises the following steps:

[0100] Step 1: Construct a motion control system and set the PID parameters of the feedback controller;

[0101] Step 2: Use the PID parameters of the feedback controller in Step 1 to enable the motion control system and close the motor loop;

[0102] Step 3: Input the desired trajectory signal r(t) into the motion control system in Step 2, and collect the output trajectory signal y(t), the control signal u(t) and the trajectory error signal e y (t) of the system;

[0103] Use the collected output trajectory signal y(t) and control signal u(t) to eliminate the dependence on the model;

[0104] Step 4: For the motion control system in Step 3, calculate the trajectory signal r y after input trajectory shaping through the input shaping filter, and calculate the feedforward control signal u ff (t) through the feedforward controller, and set the execution section and stable section times of the motion control system;

[0105] Step 5: Use the trajectory signal r y (t) and the feedforward control signal u ff(t)Construct a parametric feedforward model, and combine it with the optimal iterative learning control method. Introduce the constraint terms of the identification parameters θ of the input shaping filter and the feedforward controller and their variations into the objective function of the parametric feedforward model, and weight them. Then calculate the identification parameter θ by the data-driven least squares method, and select appropriate weighting coefficients ρ and λ to achieve the trajectory tracking and variable trajectory tracking tasks of the motion control system;

[0106] The weighting coefficient ρ is the weighting coefficient for the magnitude of the identification parameter. It weights the magnitude of the identification parameter, which can constrain the magnitude of the feedforward control signal energy and affect the error convergence value;

[0107] The weighting coefficient λ is the weighting coefficient for the variation of the identification parameter. It weights the variation step of the identification parameter, which can constrain the variation step of the feedforward control signal and affect the convergence speed;

[0108] Step 6: Analyze the convergence of the identification parameter θ and the optimal iterative feedforward tuning error in Step 5, and obtain the optimal value of the identification parameter to achieve the optimal trajectory tracking of the motion control system.

[0109] The present invention adopts the optimal iterative feedforward tuning method, which can be independent of the system mathematical model, avoids the cumbersome model identification process, reduces the computational workload of the processor, has a relatively fast operation speed, and at the same time the method is simple to implement, reduces the control difficulty of the motion control system, can not only achieve repeated trajectory tracking but also variable trajectory tracking, has strong application flexibility, has a certain robustness, and can meet the control requirements of high-speed and high-precision motion control systems.

[0110] The control method of the present invention is detailed, the scheme is practical and feasible, the process is simple and practical, has strong flexibility, fast operation speed, high control precision, good control effect, and can meet the control requirements of the motion control system.

[0111] Embodiment 2 of the present invention:

[0112] An optimal iterative feedforward tuning method based on a motion control system includes the following: parameterize the input shaping filter and the feedforward controller using basis functions, and calculate the feedforward force through the input trajectory and the parametric feedforward controller; combine the advantages of optimal iterative learning control and parametric feedforward control, introduce the performance objective function of optimal iterative feedforward tuning, and iteratively identify the parameters of the input shaping filter and the feedforward controller; analyze the convergence of the error of optimal iterative feedforward tuning and the identification parameters; obtain the optimal values of each parameter to achieve the optimal trajectory tracking of the motion control system.

[0113] Through continuous exploration and experimentation, the present invention adopts an optimal iterative feedforward parameter adjustment method, which can effectively reduce the control difficulty of the motion control system, reduce the computational load of the processor, has strong flexibility, fast operation speed, good robustness, good control effect, and can meet the control requirements of the motion control system.

[0114] As Figure 1-7 shown, Embodiment 3 of the present invention:

[0115] An optimal iterative feedforward parameter adjustment method for a motion control system includes the following steps:

[0116] Step 1: Build a motion control system platform, set the feedback controller PID parameters, etc. on the control interface, and download the parameters to a motion control board designed by an ARM chip.

[0117] Step 2: According to the closed-loop performance requirements of the motion control system, enable the motion control platform through the downloaded control parameters to close the motor loop.

[0118] The expression of a single-input single-output linear time-invariant motion control system with an unknown model is:

[0119]

[0120] The controlled system is in the form of a rational basis function with a numerator and denominator, and includes the zero-pole characteristics of the motion control system. The system transfer function is converted into a discrete time-invariant state space model as:

[0121]

[0122] where x(t + 1) is the state variable of the system at time t + 1, A, B, C, and D are the system state space models, and the sampling time of the system is T s , the number of sampling points is N, and the system input control signal is discretized as u = [u(0), …, u(N - 1)] T , u is the vector expression form of the input control signal, and for the convenience of representation, subsequent symbols are all represented in vector form.

[0123] Step 3: Input the desired trajectory signal r(t) at the signal input end of the motion control system, and specify the sampling period T s as 0.0005 s, there are a total of 2048 sampling points, the acquisition time is 1.0235 s, and the initial value θ 0 = [0, 0, 0, 0.1, 0] T of the input shaping filter and the feedforward controller parameters is set, and the shaped input trajectory r y (t) and the feedforward control signal u ff(t) is downloaded to the motion control card for operation, and then the system output trajectory signal y(t) and control signal u(t) are collected from the motion control board. At the same time, the trajectory error signal e y (t) is collected. It is stipulated that the execution section and stable section times of the motion control system are 0.512 s and 0.5115 s respectively;

[0124] For the optimal iterative feedforward tuning parameter method, a finite impulse response (FIR) filter composed of basis function polynomials is used to parameterize the input shaping filter T y and the feedforward controller T ff . The parameterization expressions are as follows:

[0125]

[0126] Then, the basis function polynomials A(z y and T ff ,θ) and B(z -1 ,θ) are respectively expressed as -1 ,θ) are respectively expressed as

[0127]

[0128]

[0129] where z -1 is the time-shift operator, and θ 1 ~θ 3 are the identification parameters of the parameterized input shaping filter, and θ 4 ~θ 5 are the identification parameters of the parameterized feedforward controller. n a , n b are the numbers of basis functions that make up T y and T ff are 3 and 2 respectively. The basis function can decompose the input trajectory into derivatives of each order. The basis function is selected as:

[0130]

[0131]

[0132]

[0133] The basis function polynomials A(z -1 ,θ) and B(z -1, θ) is an FIR filter. The advantages of using an FIR filter are as follows: First, the FIR filter has no poles, so there is no instability problem. Second, designing a feedforward controller using an FIR filter is a convex optimization method. Third, according to the control framework of the motion control system Figure 1 As can be seen, for the system error to be 0, that is

[0134] e y = r y - y = S(T y - PT ff )r = 0

[0135] Then

[0136]

[0137] To obtain the optimal trajectory tracking performance, as long as the T designed by two FIR filters y and T ff are used to describe the numerator and denominator of the controlled system, which can include the zero-pole motion characteristics of the system. And when the two FIR filters are inverted, it will not cause unstable poles and non-minimum phase zero-point problems, and can achieve better trajectory tracking effects. Therefore, the control objective is to identify the system model using two FIR filters.

[0138] According to Figure 1 the control block diagram, when the motion control system iterates for the jth time, the expressions of the system error, control signal, and output trajectory signal are as follows

[0139]

[0140]

[0141]

[0142] Among them, the system sensitivity function S = (1 + PC fb ) -1 , the sensitivity function T = C fb T y + T ff , C fb is the feedback controller.

[0143] As can be seen from the above, both Sr and SPr are related to the parameter model. To eliminate the dependence on the model, it is transformed into a data-driven form. Then

[0144] Sr = T -1 u j

[0145] SPr = T -1 y j

[0146] Step 4: For Figure 1 the optimal iterative feedforward tuning method shown in the block diagram of the parametric feedforward control system with an input shaping filter, combined with the optimal iterative learning control, weighs the system control signal energy and the trajectory error. Since the feedforward control signal in the optimal iterative feedforward tuning is composed of basis function polynomials, the feedforward signal is related to the parameters corresponding to the basis functions. Therefore, the system performance objective function not only includes the system error, but also imposes weighted constraints on the parameters and parameter variations of the input shaping filter and the feedforward controller. Different weighting coefficients ρ and λ are selected for the trajectory tracking experiment, and the trajectory tracking performance under different weighting coefficients is evaluated. Then, appropriate weighting coefficients ρ and λ are selected for the trajectory and variable trajectory tracking experiments.

[0147] The performance objective function of the optimal iterative feedforward tuning is as follows:

[0148]

[0149] From Figure 1 it can be seen that r y = T y r, Figure 2 it can be known that the desired trajectory is T y = 1 during the stable period, so r y = r and there is a delay in the execution section, and the length of the delay time is T y The number of components n a of the basis function. From this, it can be seen that during the stable period, e y = r y - y = e. Therefore, the performance objective function can be written as

[0150]

[0151] Then, from the above, at the (j + 1)-th iteration, the system trajectory error is

[0152]

[0153] According to the parametric polynomials and data-driven expression forms of the input shaping filter and the feedforward controller, we can obtain

[0154]

[0155] where

[0156] Assume ψ T ψ ∈ R 5×5 is non-singular.

[0157] Identify the parameters of the parametric input shaping filter and the feedforward controller. Since θ j+1 is the objective function J j+1For the variable, in order to minimize the trajectory tracking error, according to the idea of iterative learning, the error in each iteration continuously decreases relative to the previous one until convergence. Therefore, the objective function J j+1 is minimized, that is, the objective function J j+1 is differentiated with respect to θ j+1 , and let Through derivation, the parameter θ j+1 can be identified as follows:

[0158]

[0159] In the formula, the robust filter Q θ and the learning filter L θ are

[0160] Q θ =[ψ T W e ψ + W θ + W Δθ -1 [ψ T W e ψ + W Δθ

[0161] L θ =[ψ T W e ψ + W Δθ -1 ψ T W e

[0162] W e , W θ and W Δθ are the weighted matrices of the error, the identified parameter θ, and the change amount Δθ of the identified parameter respectively. Generally, the error weighted matrix is selected as W e = I; the weighted matrix of the identified parameter θ is selected as W θ = ρI, where ρ is the weighted coefficient of the identified parameter, which can constrain the magnitude of the feedforward control signal energy and affect the error convergence value. Generally, ρ is an arbitrary real number greater than or equal to 0. When ρ is 0, the control signal energy is not restricted. The larger the weighted coefficient ρ, the greater the constraint effect. At this time, the feedforward control signal has a greater constraint effect and the error convergence value is larger. On the contrary, the error convergence value is smaller; the weighted matrix of the change amount Δθ of the identified parameter is selected as W Δθ = λI, where λ is the weighted coefficient of the change amount of the identified parameter, which can constrain the change step of the feedforward control signal and affect the convergence speed. Generally, λ is an arbitrary real number greater than or equal to 0. When λ is 0, the change step of the feedforward control signal is not restricted. The larger the weighted coefficient λ, the greater the constraint effect on the parameter change amount, and the slower the feedforward control signal iterates to the optimal value and the slower the error convergence speed. On the contrary, the error convergence speed is faster; where, I is the identity matrix. ​​​

[0163] Step 5, the motion control framework is as follows Figure 1 shown. In the optimal iterative feedforward tuning parameter method, the input shaping filter T y and the feedforward controller T ff are both 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 known that the error e y is globally convergent. Therefore:

[0164]

[0165] According to nonsingularity and norm knowledge, it can be known that

[0166]

[0167] Therefore, the identified parameter θ is convergent.

[0168] Step 6: The host computer simulation software (such as: MATLAB / Simulink, VisualStudio2012) uses the error, control signal, and output trajectory signal collected by the motion control board card, and uses the data-driven least squares method to iteratively optimize and identify the parameters of the parameterized input shaping filter and the feedforward controller. Among them, the system expected input trajectory adopts Figure 2 the fourth-order S-shaped point-to-point motion trajectory shown or adopts Figure 7 different fourth-order S-shaped point-to-point expected input trajectories for variable trajectory experiments (in the variable trajectory experiment, the reference trajectory 1 is run in the first 10 iterations, and the reference trajectory 2 is run in the 11th iteration). The input shaping filter and the feedforward controller are updated through the identified parameters, and then the feedforward control signal u ff and the shaped input trajectory signal r y are calculated and the generated signals are downloaded back to the motion control board card. Repeating this iteration realizes the trajectory or variable trajectory tracking task and the convergence of the identified parameters. As shown in Figure 3 and Figure 4 shown, the present invention balances the control energy and performance of the motion control system. Different weighting coefficients λ limit the step size of the identified parameters, so that the convergence speed of the system feedforward control signal to the optimal feedforward controller becomes slower, and then affects the convergence speed of the system trajectory error. Different weighting coefficients ρ limit the magnitude of the identified parameters, so that the magnitude of the feedforward control signal is limited, and then affects the convergence value magnitude of the system trajectory error. As shown in Figure 5 and Figure 8 shown, the present invention can achieve the optimal tracking performance of the trajectory and has a certain robustness for variable trajectories. As shown in Figure 6 shown, the convergence of the parameters of the input shaping filter and the feedforward controller of the present invention.

[0169] An apparatus embodiment of applying the method of the present invention:

[0170] An optimal iterative feedforward parameter tuning system method for a motion control system, comprising:

[0171] One or more processors;

[0172] A storage device for storing one or more programs;

[0173] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned optimal iterative feedforward parameter tuning method and system for a motion control system.

[0174] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0175] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processors of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processors of the computer or other programmable data processing devices generate means for implementing the functions specified in one Figure 1 One flow or multiple flows and / or blocks Figure 1 One block or multiple blocks.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement without departing from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. An optimal iterative feedforward tuning parameter method for a motion control system, characterized in that it includes the following steps: Step 1: Construct a motion control system and set the PID parameters of the feedback controller; Step 2: Use the PID parameters of the feedback controller in Step 1 to enable the motion control system and close the motor loop; Step 3: Input the desired trajectory signal r(t) into the motion control system in Step 2, and collect the output trajectory signal y(t) and the control signal u(t); Step 4: For the motion control system in Step 3, calculate the trajectory signal r y (t) after input trajectory shaping through an input shaping filter, and calculate the feedforward control signal u ff (t) through a feedforward controller, and set the execution section and stable section times of the motion control system; Step Five: Utilize the trajectory signal r y (t) and the feedforward control signal u ff (t) to construct a parametric feedforward model, and combine the optimal iterative learning control method. Introduce the constraint terms of the identification parameters θ of the input shaping filter and the feedforward controller and their variation amounts into the objective function of the parametric feedforward model and weight them. Then, calculate the identification parameter θ through the data-driven least squares method, and select appropriate weighting coefficients ρ and λ to achieve the trajectory tracking and variable trajectory tracking tasks of the motion control system; The weighting coefficient ρ is the weighting coefficient for the size of the identification parameter. It weights the size of the identification parameter, can constrain the energy of the feedforward control signal, and affect the error convergence value; The weighting coefficient λ is the weighting coefficient for the change amount of the identification parameter. It weights the change step of the identification parameter, can constrain the change step of the feedforward control signal, and affect the convergence speed; Step 6: Analyze the convergence of the identification parameter θ and the optimal iterative feedforward tuning parameter error in Step 5, and obtain the optimal value of the identification parameter to achieve the optimal trajectory tracking of the motion control system.

2. An optimal iterative feedforward tuning parameter method for a motion control system according to claim 1, characterized in that in Step 5, the construction method of the parameterized feedforward model is specifically as follows: The input shaping filter T is parameterized by a finite impulse response filter composed of basis function polynomials y and the feedforward controller T ff The parameterization expressions are as follows: Then, the composition of T y and T ff The basis function polynomials A(z -1 , θ) and B(z -1 , θ) are respectively expressed as where z -1 is the time-shift operator, θ is the identification parameter of the parametric input shaping filter and the feedforward controller, n a , n b is the number of basis functions that make up T y and T ff . The basis functions decompose the input trajectory into derivatives of each order. The acceleration basis function y in T is as follows: where T s is the sampling time; The basis function polynomials A(z -1 , θ) and B(z -1 , θ) are FIR filters, Its system error is 0, that is e y = r y -y = S(T y - PT ff )r = 0 then When the motion control system iterates for the jth time, the error, control signal and output trajectory signal expressions of the system are as follows Among them, the system sensitive function S = (1 + PC fb ) -1 , and the sensitive function T = C fb T y + T ff , where C fb is the feedback controller; Convert Sr and SPr into a data-driven form, and its calculation formula is as follows: Sr = T -1 u j SPr = T -1 y j 。 3. An optimal iterative feedforward tuning parameter method for a motion control system according to claim 1, characterized in that The feedforward control signal is composed of basis function polynomials, which is related to the parameters corresponding to the basis functions, so that the objective function weights and constrains the parameters and parameter change amounts of the input shaping filter and the feedforward controller. Its expression is as follows: Since r y = T y r, the desired trajectory is within the stable period T y = 1, so r y = r and there is a delay in the execution segment, and the length of the delay time is T y The number of components n of the basis function a , thus the stable segment e y = r y - y = e, so the calculation formula of the objective function is as follows: Then it can be obtained from the above that when iterating for the j + 1th time, the system trajectory error is According to the parameterized polynomial and data-driven expression form of the input shaping filter and the feedforward controller, it can be obtained where Nonsingular; Among them, W e , W θ and W Δθ are the weighted matrices of the error, the identification parameter θ, and the change amount Δθ of the identification parameter respectively. The error weighted matrix is selected as W e = I, the weighted matrix of the identification parameter θ is selected as W θ = ρI, ρ is the weighted coefficient of the identification parameter magnitude, and the weighted matrix of the change amount Δθ of the identification parameter is selected as W Δθ = λI, λ is the weighted coefficient of the change amount of the identification parameter, and I is the identity matrix.

4. An optimal iterative feedforward tuning parameter method for a motion control system according to claim 3, characterized in that The objective function identifies the parameters of the parameterized input shaping filter and the feedforward controller. Since θ j+1 is the variable of the objective function J j+1 , in order to minimize the trajectory tracking error, according to the idea of iterative learning, the error decreases continuously relative to the previous one in each iteration until convergence. Therefore, the minimum value of the objective function J j+1 is sought, that is, the partial derivative of the objective function J j+1 with respect to θ j+1 is calculated and set to After derivation and identification, the parameter θ j+1 is obtained as follows: In the formula, the robust filter Q θ and the learning filter L θ are 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 feedforward tuning parameter method for a motion control system according to claim 4, characterized in that The optimization design method of the weighting coefficient for the size of the identification parameter is as follows: The weighting coefficient ρ for the size of the identification parameter is any real number greater than or equal to 0. When ρ is 0, the energy of the control signal is not restricted. The larger the weighting coefficient ρ, the greater the constraint effect. At this time, the constraint effect of the feedforward control signal is greater, and the error convergence value is greater. On the contrary, the error convergence value is smaller.

6. An optimal iterative feedforward tuning parameter method for a motion control system according to claim 4, characterized in that The optimization design method of the weighting coefficient for the change amount of the identification parameter is as follows: The weighting coefficient λ for the change amount of the identification parameter is any real number greater than or equal to 0. When λ is 0, the change step of the feedforward control signal is not restricted. The larger the weighting coefficient λ, the greater the constraint effect on the parameter change amount. The slower the feedforward control signal iterates to the optimal value, and the slower the error convergence speed. On the contrary, the error convergence speed is faster.

7. The optimal iterative feedforward parameter tuning method for a motion control system as described in claim 1, characterized in that, In the sixth step, the optimal iterative feedforward tuning parameter error is the error e y , and its convergence is analyzed as follows: Input shaping filter T y and feedforward controller T ff are both finite impulse response filters, and the error e y is linearly related to the finite impulse response filter parameters, and the error e y globally converges, and the error e y is calculated as follows: According to it is obtained from non-singular and norm knowledge that:

8. The optimal iterative feedforward parameter tuning method for a motion control system as described in any one of claims 1-7, characterized in that, The method for obtaining the optimal value of the identification parameter is as follows: Select the initial parameter, use the iterative optimization method to iteratively identify the parameter θ for the measured error, control signal, and output trajectory signal, use the iteratively identified parameter to calculate the trajectory signal and the feedforward control signal after input trajectory shaping, and re-transmit them to the motion control system. Repeat this iterative process until the optimal trajectory tracking of the motion control system is achieved.

9. An optimal iterative feedforward parameter tuning system for a motion control system, characterized in that, comprising one or more processors; a storage device for storing one or more programs; a motion control system provided with an input shaping filter and a feedforward controller; when the one or more programs are executed by the one or more processors, the one or more processors implement the optimal iterative feedforward parameter tuning method for a motion control system as described in any one of claims 1-8.

10. An optimal iterative feedforward parameter tuning system for a motion control system as described in claim 9, characterized in that, the motion control system is a DC brushless motor, which is connected to an upper computer, and the upper computer is a computer or an industrial control computer.

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