Dynamic linearization error-assisted model-free adaptive control method and system based on recursive augmented least squares, and storage medium

Abstract

The invention discloses a recursive augmented least square-based dynamic linearization error-assisted model-free adaptive control method and system, and a storage medium, relates to the field of control methods, and aims to solve the problem that the dynamic response performance of a controlled system cannot be effectively improved by an existing model-free adaptive control method. And dynamic linearization errors in a model-free adaptive control process cannot be effectively utilized to suppress disturbance. According to the method, an expansion full-format dynamic linearization data model of a controlled system is established by considering a dynamic linearization error in a control process, a controlled object is compensated based on the expansion full-format dynamic linearization data model, and an expansion pseudo gradient of the controlled system is estimated based on a recursive augmented least square method; and obtaining a model-free adaptive controller based on the expanded full-format dynamic linearization data model at the moment k based on the improved criterion function, inputting the compensated control input signal of the controlled object into the controlled object, calculating the dynamic linearization error difference of the system, and carrying out model-free adaptive control.

Description

Technical Field

[0001] The present invention relates to the field of control methods, and in particular to a dynamic linearization error-assisted model-free adaptive control method, system and storage medium based on recursive augmented least squares. Background Art

[0002] With the development of industry and the advancement of science and technology, more and more control systems need to meet performance requirements such as high precision, high dynamics and stable operation, especially for servo control systems. In actual industrial applications, most systems use model-based control methods, which use the precise mathematical model of the controlled object as prior knowledge for controller design. However, since the system is inevitably affected by interference, saturation nonlinearity, mechanical resonance, etc., resulting in inaccurate mathematical models or complex models, it is difficult to improve the accuracy of traditional model-based control methods.

[0003] However, in the actual operation of industrial systems, a large amount of process data is generated all the time. These I / O data contain all useful information including disturbances, equipment status, etc. Data-driven control uses online or offline system data to directly design controllers. In cases where models are difficult to obtain, the accuracy is not high, or the model order is high and complex, data-driven control has unique advantages. It can design controllers "without models" to meet control requirements, and can also effectively suppress unmodeled disturbances.

[0004] As a data-driven control method for discrete-time nonlinear systems, the model-free adaptive control method introduces a dynamic linearization method to establish an equivalent linearized data model of the original nonlinear system at each operating point of the closed-loop system at the sampling time, and only uses the system's I / O data to complete the design of the controller and the estimation of parameters. However, the simple use of traditional model-free adaptive control methods cannot effectively improve the bandwidth of the control system, cannot achieve a good disturbance suppression effect, and is difficult to meet the control needs of actual industrial systems.

[0005] Chinese invention patent CN114442488A, a model-free adaptive control technology based on an extended state observer, discloses an extended state observer to estimate the unmodeled nonlinear uncertainty and external disturbance of the model-free adaptive control system. Chinese invention patent CN112925208A, a data-driven disturbance compensation method for the electro-hydraulic servo system of a water well drilling rig, discloses a data-driven disturbance compensation method for the electro-hydraulic servo system of a water well drilling rig in view of the parameter uncertainty and unknown load disturbance problems existing in the electro-hydraulic servo system itself, and designs a model-free adaptive controller. The above patent documents aim to design a disturbance compensation scheme for a model-free adaptive controller, but do not effectively utilize the dynamic linearization error in the model-free adaptive control process, and do not consider the dynamic response performance of the system controlled by the model-free adaptive control method. Summary of the invention

[0006] The technical problems to be solved by the present invention are:

[0007] The existing model-free adaptive control methods cannot effectively improve the dynamic response performance of the controlled system, and cannot effectively utilize the dynamic linearization error in the model-free adaptive control process to suppress disturbances.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] In order to solve the above technical problems, the present invention provides a dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares. The control method runs on a hardware platform to control a controlled motor control system under disturbance, and includes the following steps:

[0010] Step 1: Establish an extended full-format dynamic linearized data model of the controlled system:

[0011]

[0012] Among them, the extended sliding window vector is a sliding window of system output sequences {θ(k)}, controller output sequences {u(k)}, and dynamic linearization error sequences {ξ(k)} caused by external disturbances or parameter estimation errors.

[0013] represents the extended pseudo gradient of the controlled system, ρ θ , u , e are all positive integers, representing the pseudo-order of the controlled system;

[0014] Step 2: Set the controller output criterion function and set the initial values ​​of each parameter and variable;

[0015] Step 3: Use the recursive augmented least squares method to extend the pseudo gradient of the controlled system Make estimates;

[0016] Step 4: Obtain a model-free adaptive controller based on the extended full-format dynamic linearized data model at time k through the controller output criterion function set in step 2, and calculate the control output u(k);

[0017] Step 5: Combine step 3 with the estimated value of the pseudo gradient of the controlled system and the previous ρ e The dynamic linearization error sequence of the system at each moment calculates the compensation signal Δδ(k) to compensate the control input of the controlled object;

[0018] Step 6, input the controlled object control input signal after compensation in step 5 into the controlled object, and record the output signal of the controlled system at the current time k;

[0019] Step 7, calculating the system dynamic linearization error difference at the current time k;

[0020] Step 8: Determine whether the dynamic linearization error-assisted model-free adaptive control process based on recursive augmented least squares is terminated or ended. If so, complete the model-free adaptive control process. If not, time k=k+1 and repeat steps 3 to 7.

[0021] Furthermore, the process of establishing the extended full-format dynamic linearized data model of the controlled system in step 1 specifically includes the following steps:

[0022] Construct a single-input, single-output discrete-time nonlinear system subject to external disturbances or parameter estimation errors:

[0023] θ(k+1)=f(θ(k),…,θ(kk θ ),u(k),…,u(kk u ),ξ(k),…,ξ(kk e ))

[0024] Among them, f(·) is a nonlinear function, Indicates that there is k i The system output after step lag, k i is an integer and k i ∈[0,k θ ], Indicates that there is k j The controller output after one step lag, k j is an integer and k j ∈[0,k u ], Indicates that there is k pThe dynamic linearization error caused by external disturbances or parameter estimation errors is k p is an integer and k p ∈[0,k e ], is the set of real numbers;

[0025] If the nonlinear function f(·) in the controlled system has continuous partial derivatives with respect to all independent variables, the dynamic linearization error ξ(k) of the controlled system is bounded, and the controlled system satisfies the generalized Lipschiz condition, then the controlled system is transformed into an extended full-format dynamic linearization data model:

[0026]

[0027] ρ θ , u , e Satisfying the relationship ρ θ ≤k θ , u ≤k u , e ≤k e .

[0028] Furthermore, in step 2, the controller output criterion function is set as:

[0029]

[0030] Where, e(k+1)=θ d (k+1)-θ(k+1) represents the tracking error of the system at time k+1, Δu(k)=u(k)-u(k-1) and Δθ(k+1)=θ(k+1)-θ(k) represent the first-order forward difference of the control output u(k) and the system output θ(k+1), respectively, and β>0 is a constant for |Δu(k)| 2 The penalty factor for the item, is a target for |Δθ(k+1)| 2 The penalty factor for the term, θ d (k+1) represents the command signal of the system at time k+1.

[0031] Furthermore, the specific steps of step 3 include:

[0032] Expanding the full-format dynamic linearization data model can be transformed into: seeking an estimate of the system's expanded pseudo-gradient So that it satisfies the conditions:

[0033]

[0034] Then, the expanded full-format dynamic linearized data model is transformed into a linear least squares problem;

[0035] The cost function of the linear least squares problem is defined as:

[0036]

[0037] in, Includes sequence The input observation data matrix is is the output observation data matrix including the sequence {Δθ(i)}, m is the dimension of the observation data, i = k-1, k-2, …, km;

[0038] Let the cost function be the estimated value of the pseudo gradient of the system expansion The partial derivative of is 0, so:

[0039]

[0040] The recursive augmented least squares method is used to The specific calculation process of the problem is:

[0041] Iterative update law of gain vector at time k:

[0042] Iterative update law of the inverse correlation matrix at time k:

[0043] The calculation law of the pseudo-gradient estimate value of the system expansion at time k is:

[0044] System expansion pseudo gradient estimation reset law:

[0045] when or or or When , the system's extended pseudo gradient is reset to the initial value Among them, ε is a positive number close to 0, Represents the system extended pseudo gradient estimate vector The i-th item of .

[0046] Furthermore, the specific steps of step 4 include:

[0047] In the output criteria function Introduce an adaptive penalty factor:

[0048]

[0049] Among them, Δθ max is a set threshold value, is a constant, ω>0;

[0050] Update the output criterion function to:

[0051]

[0052] According to the optimal condition, let the partial derivative of the above improved control output criterion function with respect to the control output u(k) be 0. Without loss of generality, assume that Δθ(k+1)<Δθ in the derivation process. max , substitute into the definition of the above adaptive penalty factor The control algorithm is obtained as:

[0053]

[0054] Among them, α i (i=1,2,…,ρ θ +ρ u ) is an adjustable parameter.

[0055] Furthermore, the specific steps of calculating the compensation signal Δδ(k) in step 5 include:

[0056] Obtaining partial system extended pseudo gradient sequence The dynamic linearization error difference sequence {Δξ(k-ρ e ),…,Δξ(k-1)} as the compensation signal Δδ(k) output by the controller:

[0057]

[0058] Furthermore, the controlled object after compensation in step 6 controls the input signal u 0 (k) is: u 0 (k) = u(k) - Δδ(k).

[0059] Furthermore, the calculation of the system dynamic linearization error difference at the current time k described in step 7 specifically includes the following steps:

[0060] Use k moment to estimate the pseudo gradient of the system The extended sliding window difference vector at time k-1 The inner product of is used as the prediction of the forward difference of the output signal of the controlled system at time k:

[0061]

[0062] The forward difference Δθ(k) of the output signal of the controlled system at time k is combined with the predicted value of the forward difference of the output signal of the controlled system at time k. Make a difference as the system dynamic linearization error difference at the current k moment:

[0063]

[0064] Furthermore, a dynamic linearization error-assisted model-free adaptive control system based on recursive augmented least squares is provided, the system having a program module corresponding to the steps of the method described in any one of the above technical solutions, and executing the steps of the above-mentioned dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares during operation.

[0065] A computer-readable storage medium stores a computer program, wherein the computer program is configured to implement the steps of the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares described in any one of the above technical solutions when called by a processor.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] The method of the present invention is a data-driven control method. Except for the sampling period, no other information is required as a priori information for the control system design. The method of the present invention can effectively avoid the complex process of modeling the controlled object, and can reduce the influence of the accuracy of the model built by the controlled object on the control effect of the controller. Compared with the traditional model-free adaptive control method, the method of the present invention takes into account the dynamic linearization error in the control process, and designs a compensation scheme based on this, thereby reducing the adverse effects of external disturbances and parameter estimation errors on the control effect. At the same time, the extended pseudo-gradient estimation based on the recursive augmented least squares method and the model-free adaptive control law based on the improved criterion function effectively improve the dynamic response performance of the controlled object, thereby meeting the control requirements in actual industrial processes.

[0068] Numerical simulations have shown that the accuracy and dynamic performance of the method of the present invention in controlling linear and nonlinear systems are superior to those of existing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of a dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares in an embodiment of the present invention;

[0070] Figure 2 It is a control block diagram of a dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares in an embodiment of the present invention;

[0071] Figure 3 Schematic diagram of a system for implementing the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares in an embodiment of the present invention;

[0072] Figure 4A tracking error comparison curve of the method of the present invention and the prior art method applied in a motor control system in an embodiment of the present invention;

[0073] Figure 5 A tracking trajectory comparison curve of the method of the present invention and the prior art method applied in a motor control system in an embodiment of the present invention;

[0074] Figure 6 It is a comparison curve of tracking trajectories of the method of the present invention and the prior art method for controlling a nonlinear system in an embodiment of the present invention. DETAILED DESCRIPTION

[0075] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0076] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0077] Example 1

[0078] like Figure 1 and Figure 2 As shown, the present invention provides a dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares. The control method runs on a hardware platform to control a controlled motor control system under disturbance, and performs the following steps:

[0079] Step 1: Establish an extended full-format dynamic linearized data model of the controlled system:

[0080] Construct a single-input-single-output discrete-time nonlinear system that is subject to external disturbances or parameter estimation errors. The specific steps include:

[0081] θ(k+1)=f(θ(k),…,θ(kk θ ),u(k),…,u(kk u ),ξ(k),…,ξ(kk e ))

[0082] Among them, f(·) is a nonlinear function, Indicates that there is k i The system output after step lag, k i is an integer and k i ∈[0,kθ ], Indicates that there is k j The controller output after one step lag, k j is an integer and k j ∈[0,k u ], Indicates that there is k p The dynamic linearization error caused by external disturbances or parameter estimation errors is k p is an integer and k p ∈[0,k e ], is the set of real numbers;

[0083] If the nonlinear function f(·) in the controlled system has continuous partial derivatives with respect to all independent variables, the dynamic linearization error ξ(k) of the controlled system is bounded, and the controlled system satisfies the generalized Lipschiz condition, then the controlled system is transformed into an extended full-format dynamic linearization data model:

[0084]

[0085] Among them, the extended sliding window vector is a sliding window of system output sequences {θ(k)}, controller output sequences {u(k)}, and dynamic linearization error sequences {ξ(k)} caused by external disturbances or parameter estimation errors.

[0086] represents the extended pseudo gradient of the controlled system, ρ θ , u , e are all positive integers, indicating the pseudo-order of the controlled system; ρ θ , u , e Satisfying the relationship ρ θ ≤k θ , u ≤k u , e ≤k e .

[0087] Step 2: Set the controller output criterion function and set the initial values ​​of each parameter and variable;

[0088] Furthermore, the controller output criterion function is:

[0089]

[0090] Where, e(k+1)=θ d(k+1)-θ(k+1) represents the tracking error of the system at time k+1, Δu(k)=u(k)-u(k-1) and Δθ(k+1)=θ(k+1)-θ(k) represent the first-order forward difference of the control output u(k) and the system output θ(k+1), respectively, and β>0 is a constant for |Δu(k)| 2 The penalty factor for the item, is a target for |Δθ(k+1)| 2 The penalty factor for the term, θ d (k+1) represents the command signal of the system at time k+1.

[0091] Step 3: Use the recursive augmented least squares method to extend the pseudo gradient of the controlled system To make an estimate, the specific steps include:

[0092] Expanding the full-format dynamic linearization data model can be transformed into: seeking an estimate of the system's expanded pseudo-gradient So that it satisfies the conditions:

[0093]

[0094] Then, the expanded full-format dynamic linearized data model is transformed into a linear least squares problem;

[0095] The cost function of the linear least squares problem is defined as:

[0096]

[0097] in, Includes sequence The input observation data matrix is is the output observation data matrix including the sequence {Δθ(i)}, m is the dimension of the observation data, i = k-1, k-2, …, km;

[0098] Let the cost function be the estimated value of the pseudo gradient of the system expansion The partial derivative of is 0, so:

[0099]

[0100] The recursive augmented least squares method is used to The specific calculation process of the problem is:

[0101] Iterative update law of gain vector at time k:

[0102] Iterative update law of the inverse correlation matrix at time k:

[0103] The calculation law of the pseudo-gradient estimate value of the system expansion at time k is:

[0104] The system expands the pseudo-gradient estimation to reset the law:

[0105] when or or or When , the system's extended pseudo gradient is reset to the initial value Among them, ε is a positive number close to 0, Represents the system extended pseudo gradient estimate vector The i-th item of .

[0106] Step 4: Let the partial derivative of the controller output criterion function with respect to the control output at time k be 0, and according to the optimal conditions, obtain the model-free adaptive controller based on the extended full-format dynamic linearization data model at time k, calculate the control output u(k) at the current time k, and store the controller output at the current time k in the data storage. The specific steps include:

[0107] In the output criteria function Introduce an adaptive penalty factor:

[0108]

[0109] Among them, Δθ max is a set threshold value, is a constant, ω>0;

[0110] Update the output criterion function to:

[0111]

[0112] According to the optimal condition, let the partial derivative of the above improved control output criterion function with respect to the control output u(k) be 0. Without loss of generality, assume that Δθ(k+1)<Δθ in the derivation process. max , substitute into the definition of the above adaptive penalty factor The control algorithm is obtained as:

[0113]

[0114] Among them, α i (i=1,2,…,ρ θ +ρ u ) is an adjustable parameter that makes the algorithm design more flexible.

[0115] Step 5: Combine step 3 with the estimated value of the pseudo gradient of the controlled system and the previous ρ eThe dynamic linearization error sequence of the system at each moment calculates the compensation signal Δδ(k) to compensate the control input of the controlled object;

[0116] Furthermore, the specific steps of calculating the compensation signal Δδ(k) include:

[0117] Obtaining partial system extended pseudo gradient sequence The dynamic linearization error difference sequence {Δξ(k-ρ e ),…,Δξ(k-1)} as the compensation signal Δδ(k) output by the controller:

[0118]

[0119] Step 6: The controlled object after compensation in step 5 is controlled to input signal u 0 (k) = u(k) - Δδ(k) inputs the controlled object, records the output signal of the controlled system at the current time k, and stores the output signal θ(k) of the controlled system into the data storage;

[0120] Step 7: Calculate the system dynamic linearization error difference at the current time k, and store the calculated value ξ(k) in a data storage device. The specific steps include:

[0121] Use k moment to estimate the pseudo gradient of the system The extended sliding window difference vector at time k-1 The inner product of is used as the prediction of the forward difference of the output signal of the controlled system at time k:

[0122]

[0123] The forward difference Δθ(k) of the output signal of the controlled system at time k is combined with the predicted value of the forward difference of the output signal of the controlled system at time k. Make a difference as the system dynamic linearization error difference at the current k moment:

[0124]

[0125] Step 8: Determine whether the dynamic linearization error-assisted model-free adaptive control process based on recursive augmented least squares is terminated or ended. If so, complete the model-free adaptive control process. If not, time k=k+1 and repeat steps 3 to 7.

[0126] Example 2

[0127] The present invention provides a dynamic linearization error-assisted model-free adaptive control system based on recursive augmented least squares. The system has a program module corresponding to the steps of the method described in Example 1, and executes the steps of the above-mentioned dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares during operation.

[0128] like Figure 3 As shown, the control system includes:

[0129] A control instruction generation module 101, used to generate a control instruction signal of a model-free adaptive control system;

[0130] The data storage module 103 is used to store the system output sequence {θ(k)}, the controller output sequence {u(k)} and the dynamic linearization error difference sequence {Δξ(k)} caused by the external disturbance of the system or the parameter estimation error;

[0131] The historical data sequence acquisition module 104 acquires data from the data storage module 103 and splices the data into a data sequence that meets the processing requirements of the data processing module 102;

[0132] The data processing module 102 is used to obtain the data of the previous moment from the data storage module 103 or obtain the data sequence of the previous moment from the historical data sequence acquisition module 104, and use the data or the data sequence to calculate the system extended pseudo gradient estimation value, the system dynamic linearization error difference, the controller control output signal, the compensation signal of the controller control output, etc., and determine whether the system extended pseudo gradient estimation value meets the reset condition;

[0133] The measuring module 105 is used to measure the output signal of the controlled object, the output signal includes but is not limited to angle, position, speed, torque, voltage, current, temperature, etc., and store the measured output signal of the controlled object in the data storage module 103, and feed it back to the data processing module 102;

[0134] and the accused 106.

[0135] Example 3

[0136] The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps of the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares described in any one of Embodiment 1 when called by a processor.

[0137] Example 4

[0138] In this embodiment, a numerical simulation is performed on a motor control system with periodic disturbances in the position domain as a controlled object for the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares proposed in the present invention.

[0139] Considering the motor control system driven by a permanent magnet synchronous motor, its simplified mechanism model can be expressed as:

[0140]

[0141] Among them, τ m is the mechanical time constant, τ e is the electrical time constant and K is the gain.

[0142] Using sinusoidal signals of different frequencies as excitation, the angle output signal of the system is measured in an open loop. The amplitude ratio and phase angle difference of the two signals are obtained by fast Fourier transform of the excitation signal and the angle output signal. The three unknown parameters τ in the simplified mechanism model are estimated by the system identification method based on least squares. m , τ e , K, the mathematical model of the motor control system driven by the permanent magnet synchronous motor can be obtained.

[0143] During operation, the motor control system driven by a permanent magnet synchronous motor is mainly disturbed by disturbance torques such as cogging ripple torque, electromagnetic ripple torque, friction torque, and eccentric load torque. By analyzing the mechanism of the disturbance, it is found that the disturbance resultant torque shows characteristics related to the angular position. Under the excitation of different constant speed signals, the D / A output curve of the system is measured, and the position domain fast Fourier transform analysis of the D / A output signal can be performed to obtain the main position domain frequency of the disturbance. The disturbance can be expressed as the superposition of sinusoidal signals with different frequency components with different phases.

[0144] It is worth noting that the above-mentioned mechanism model of the motor control system driven by the permanent magnet synchronous motor and the analysis of the position domain periodic disturbance therein are only used for subsequent numerical simulation verification and are not used for the design of the controller of the method of the present invention.

[0145] In terms of controlling linear systems with nonlinear disturbances, a motor control system driven by a permanent magnet synchronous motor is taken as an example to illustrate the effectiveness of the method of the present invention in improving anti-disturbance performance and dynamic performance. Under the excitation of a step signal, the method of the present invention is compared with the prior art proportional-integral-differential (PID) control and the full form dynamic linearization based model-free adaptive control (FFDL-MFAC) method. At the same time, a disturbance whose power spectral density is a constant in the entire frequency domain is introduced into the control loop, and the following is obtained: Figure 4 The tracking error curves are shown and the experimental data are shown in Table 1.

[0146] Table 1

[0147]

[0148] In this embodiment, the root mean square error of the disturbance whose power spectrum density is constant in the whole frequency domain introduced into the control loop is 1.4153. It can be seen from the experimental results that the root mean square error reflected by the disturbance of the output of the system controlled by the method of the present invention is about 20% to 30% of that of the prior art PID and FFDL-MFAC, and the transition process time of the system controlled by the method of the present invention tracking the step signal is about 40% of that of the prior art PID and FFDL-MFAC. The system controlled by the method of the present invention is significantly superior to the prior art PID and FFDL-MFAC methods in terms of disturbance suppression and response speed of tracking step signals.

[0149] Example 5

[0150] The motor control system driven by the permanent magnet synchronous motor in Example 4 is used as the controlled object for numerical simulation. Under the excitation of a 3 Hz sinusoidal signal, the tracking trajectory of the system controlled by the prior art PID, FFDL-MFAC method and the method of the present invention is as follows: Figure 5 It can be seen that under the excitation of a 3 Hz sinusoidal signal, the amplitude attenuation of the system controlled by the prior art FFDL-MFAC method is close to 30%, while the control effect of the method of the present invention is similar to that of the prior art PID controller, and it can better track dynamic signals and show good dynamic performance.

[0151] Example 6

[0152] In order to illustrate the excellent performance of the method of the present invention in controlling nonlinear systems, in this embodiment, a nonlinear system As the controlled object, the control input The numerical simulation is performed for the excitation signal, where T s is the sampling period, and the disturbance in the nonlinear system is defined as:

[0153]

[0154] Get as Figure 6 The tracking trajectory is shown.

[0155] From Figure 6 It can be seen from the tracking trajectory shown that: under the action of disturbance, the tracking error of the nonlinear system controlled by the method of the present invention is approximately 50% of the tracking error of the nonlinear system controlled by the prior art FFDL-MFAC method, and when the state of the controlled nonlinear system changes suddenly, the method of the present invention can better suppress the oscillation of the tracking trajectory. The tracking effect of the method of the present invention when controlling a nonlinear system is significantly better than that of the prior art method.

[0156] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares, characterized in that: The control method is run on a hardware platform to control the controlled motor control system under disturbance, and includes the following steps: Step 1: Establish an extended full-format dynamic linearized data model of the controlled system: Among them, the extended sliding window vector is a sliding window of system output sequences {θ(k)}, controller output sequences {u(k)}, and dynamic linearization error sequences {ξ(k)} caused by external disturbances or parameter estimation errors. represents the extended pseudo gradient of the controlled system, ρ θ , u , e are all positive integers, representing the pseudo-order of the controlled system; Step 2: Set the controller output criterion function and set the initial values ​​of each parameter and variable; Step 3: Use the recursive augmented least squares method to expand the pseudo gradient of the controlled system Make estimates; Step 4: Obtain a model-free adaptive controller based on the extended full-format dynamic linearized data model at time k through the controller output criterion function set in step 2, and calculate the control output u(k); Step 5: Combine step 3 with the estimated value of the pseudo gradient of the controlled system and the previous ρ e The dynamic linearization error sequence of the system at each moment calculates the compensation signal Δδ(k) to compensate the control input of the controlled object; Step 6, input the controlled object control input signal after compensation in step 5 into the controlled object, and record the output signal of the controlled system at the current time k; Step 7, calculating the system dynamic linearization error difference at the current time k; Step 8: Determine whether the dynamic linearization error-assisted model-free adaptive control process based on recursive augmented least squares is terminated or ended. If so, complete the model-free adaptive control process. If not, time k=k+1 and repeat steps 3 to 7.

2. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The process of establishing the extended full-format dynamic linearized data model of the controlled system described in step 1 specifically includes the following steps: Construct a single-input, single-output discrete-time nonlinear system subject to external disturbances or parameter estimation errors: θ(k+1)=f(θ(k),…,θ(kk θ ),u(k),…,u(k u ),ξ(k),…,ξ(kk e )) Among them, f(~) is a nonlinear function, Indicates that there is k i The system output after step lag, k i is an integer and k i ∈[0,k θ ], Indicates that there is k j The controller output after one step lag, k j is an integer and k j ∈[0,k u ], Indicates that there is k p The dynamic linearization error caused by the external disturbance or parameter estimation error of the system after one step lag, k p is an integer and k p ∈[0,k e ], is the set of real numbers; If the nonlinear function f(~) in the controlled system has continuous partial derivatives with respect to all independent variables, the dynamic linearization error ξ(k) of the controlled system is bounded, and the controlled system satisfies the generalized Lipschiz condition, then the controlled system is transformed into an extended full-format dynamic linearization data model: ρ θ , u , e Satisfying the relationship ρ θ ≤k θ , u ≤k u , e ≤k e .

3. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: In step 2, the controller output criterion function is set as: Where, e(k+1)=θ d (k+1)-θ(k+1) represents the tracking error of the system at time k+1, Δu(k)=u(k)-u(k-1) and Δθ(k+1)=θ(k+1)-θ(k) represent the first-order forward difference of the control output u(k) and the system output θ(k+1), respectively, and β>0 is a constant for |Δu(k)| 2 The penalty factor for the item, is a target for |Δθ(k+1)| 2 The penalty factor for the term, θ d (k+1) represents the command signal of the system at time k+1.

4. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The specific steps of step 3 include: Expanding the full-format dynamic linearization data model can be transformed into: seeking an estimate of the system's expanded pseudo-gradient So that it satisfies the conditions: Then, the expanded full-format dynamic linearized data model is transformed into a linear least squares problem; The cost function of the linear least squares problem is defined as: in, Includes sequence The input observation data matrix is is the output observation data matrix including the sequence {Δθ(i)}, m is the dimension of the observation data, i = k-1, k-2, …, km; Let the cost function be the estimated value of the pseudo gradient of the system expansion The partial derivative of is 0, so: The recursive augmented least squares method is used to The specific calculation process of the problem is: Iterative update law of gain vector at time k: Iterative update law of the inverse correlation matrix at time k: The calculation law of the pseudo-gradient estimate value of the system expansion at time k is: System expansion pseudo gradient estimation reset law: when or or or When , the system's extended pseudo gradient is reset to the initial value Among them, ε is a positive number close to 0, Represents the system extended pseudo gradient estimate vector The i-th item of .

5. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The specific steps of step 4 include: In the output criteria function Introduce an adaptive penalty factor: Among them, Δθ max is a set threshold, is a constant, ω>0; Update the output criterion function to: According to the optimal condition, let the partial derivative of the above improved control output criterion function with respect to the control output u(k) be 0. Without loss of generality, assume that Δθ(k+1)<Δθ in the derivation process. max , substitute into the definition of the above adaptive penalty factor The control algorithm is obtained as: Among them, αi (i=1,2,…,ρ θ +ρ u ) is an adjustable parameter.

6. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The specific steps of calculating the compensation signal Δδ(k) in step 5 include: Obtaining partial system extended pseudo gradient sequence The discrete convolution with the system dynamic linearization error difference sequence {Δξ(k-ρe),…,Δξ(k-1)} at the previous ρe moment is used as the compensation signal Δδ(k) of the controller control output:

7. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The controlled input signal u0(k) of the controlled object after compensation in step 6 is: u0(k)=u(k)-Δδ(k).

8. The dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to claim 1, characterized in that: The step 7 is to calculate the system dynamic linearization error difference at the current time k, and the specific steps include: Use k moment to estimate the pseudo gradient of the system The extended sliding window difference vector at time k-1 The inner product of is used as the prediction of the forward difference of the output signal of the controlled system at time k: The forward difference Δθ(k) of the output signal of the controlled system at time k is combined with the predicted value of the forward difference of the output signal of the controlled system at time k. Make a difference as the system dynamic linearization error difference at the current k moment:

9. A dynamic linearization error-assisted model-free adaptive control system based on recursive augmented least squares, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 8, and executes the steps of the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares during operation.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps in the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to any one of claims 1 to 8 when called by a processor.

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