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

Abstract

The present invention relates to the field of control methods and is directed to solving the problem that existing model-free adaptive control methods cannot effectively improve the dynamic response performance of a controlled system and cannot effectively utilize the dynamic linearization error in the model-free adaptive control process to suppress disturbances. The method of the present invention considers the dynamic linearization error in the control process to establish an extended full-format dynamic linearization data model of the controlled system, compensates the controlled object based on this, estimates the extended pseudo-gradient of the controlled system based on the recursive augmented least squares method, obtains a model-free adaptive controller based on the extended full-format dynamic linearization data model at time k based on an improved criterion function, inputs the compensated controlled object control input signal into the controlled object, calculates the system dynamic linearization error difference, and performs 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 advancements in science and technology, more and more control systems are required to meet performance requirements such as high precision, high dynamics, and stable operation, especially for servo control systems. In practical industrial applications, the vast majority of systems employ model-based control methods, which use a precise mathematical model of the controlled object as prior knowledge for controller design. However, because the system is inevitably affected by interference, saturation nonlinearity, mechanical resonance, and other factors, resulting in inaccurate or complex mathematical models, traditional model-based control methods have difficulty improving accuracy.

[0003] However, during the operation of actual industrial systems, a large amount of process data is constantly generated. This I / O data contains all kinds of useful information, including disturbances and device status. Data-driven control directly designs controllers using online or offline system data. This offers unique advantages in situations where models are difficult to obtain, have low accuracy, or are high-order and complex. It can design controllers "model-free" to meet control requirements and effectively suppress unmodeled disturbances.

[0004] Model-free adaptive control, a data-driven control approach for discrete-time nonlinear systems, uses dynamic linearization to establish an equivalent linearized data model of the original nonlinear system at each operating point of the closed-loop system at the sampling moment. This approach allows controller design and parameter estimation using only the system's I / O data. However, traditional model-free adaptive control alone cannot effectively improve the control system's bandwidth or achieve effective disturbance rejection, making it difficult to meet the control requirements of practical industrial systems.

[0005] Chinese invention patent CN114442488A, a model-free adaptive control technology based on an extended state observer, discloses an extended state observer for estimating unmodeled nonlinear uncertainties and external disturbances in a model-free adaptive control system. Chinese invention patent CN112925208A, a data-driven disturbance compensation method for an electro-hydraulic servo system of a water well drilling rig, addresses the inherent parameter uncertainty and unknown load disturbance issues of the electro-hydraulic servo system and designs a model-free adaptive controller. These patent documents aim to design disturbance compensation schemes for model-free adaptive controllers, but fail to 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] 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 is to solve the above technical problems using the following technical solutions:

[0009] 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, comprising the following steps:

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

[0011]

[0012] Among them, the expanded sliding window vector It 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 , ρ u , ρ e are all positive integers, indicating 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 to expand the estimated value of pseudo gradient of the controlled system and the previous ρ e The dynamic linearization error sequence of the time system is used to calculate the compensation signal Δδ(k) to compensate for the control input of the controlled object;

[0018] Step 6: Input the controlled object control input signal after the 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: Calculate 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, set 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 perturbations 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] Where f(·) is a nonlinear function. Indicates the existence of k i The system output after step lag, k i is an integer and k i ∈[0,k θ ], Indicates the existence of k j The controller output after step lag, k j is an integer and k j ∈[0,k u ], Indicates the existence of k pThe dynamic linearization error caused by the system being disturbed by external factors 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 , ρ u , ρ e Satisfying the relationship ρ θ ≤k θ , ρ u ≤k u , ρ 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 between the control output u(k) and the system output θ(k+1), respectively, and β>0 is a parameter for |Δu(k)| 2 The penalty factor for the item, is a target for |Δθ(k+1)| 2 The penalty factor of 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 meets 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 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 estimation of the problem, the specific calculation process is:

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

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

[0043] The calculation law of the system extended pseudo gradient estimate at time k:

[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 Introducing an adaptive penalty factor:

[0048]

[0049] Where Δθ max is a set threshold, is a constant, ω>0;

[0050] Update the output criterion function to:

[0051]

[0052] According to the optimal conditions, 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 input signal u0(k) of the controlled object after compensation in step 6 is: u0(k)=u(k)-Δδ(k).

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

[0060] Use k moments to estimate the pseudo gradient of the system and 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. Take the 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 has a program module corresponding to the steps of the method described in any of the above technical solutions, and executes the steps in 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. In addition to 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 for 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 needs of 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 Flowchart 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 This 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 1 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 present invention, exemplary embodiments or examples of the present invention will be described below with reference to the accompanying drawings. Obviously, the described embodiments or examples are only some of the embodiments or examples of the present invention, and not all of them. Based on the embodiments or examples of the present invention, all other embodiments or examples obtained by those skilled in the art 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 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] Where f(·) is a nonlinear function. Indicates the existence of k i The system output after step lag, k i is an integer and k i ∈[0,kθ ], Indicates the existence of k j The controller output after step lag, k j is an integer and k j ∈[0,k u ], Indicates the existence of k p The dynamic linearization error caused by the system being disturbed by external factors 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 expanded sliding window vector It 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 , ρ u , ρ e are all positive integers, indicating the pseudo-order of the controlled system; ρ θ , ρ u , ρ e Satisfying the relationship ρ θ ≤k θ , ρ u ≤k u , ρ 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 between the control output u(k) and the system output θ(k+1), respectively, and β>0 is a parameter for |Δu(k)| 2 The penalty factor for the item, is a target for |Δθ(k+1)| 2 The penalty factor of 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 meets 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 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 estimation of the problem, the specific calculation process is:

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

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

[0103] The calculation law of the system extended pseudo gradient estimate at time k:

[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: Set the partial derivative of the controller output criterion function with respect to the control output at time k to 0. According to the optimal condition, obtain a 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 Introducing an adaptive penalty factor:

[0108]

[0109] Where Δθ max is a set threshold, is a constant, ω>0;

[0110] Update the output criterion function to:

[0111]

[0112] According to the optimal conditions, 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 to expand the estimated value of pseudo gradient of the controlled system and the previous ρ eThe dynamic linearization error sequence of the time system is used to calculate the compensation signal Δδ(k) to compensate for 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: Input the controlled object control input signal u0(k)=u(k)-Δδ(k) after compensation in step 5 into the controlled object, record the output signal of the controlled system at the current time k, and store the controlled system output signal θ(k) in a 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 moments to estimate the pseudo gradient of the system and 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. Take the 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, set 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 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 is used to generate a control instruction signal for 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 external disturbances or parameter estimation errors in the system;

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

[0132] The data processing module 102 is configured to obtain the data at the previous moment from the data storage module 103 or obtain the data sequence at the previous moment from the historical data sequence acquisition module 104, and use the data or data sequence to calculate the system extended pseudo gradient estimate, 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 estimate meets the reset condition;

[0133] The measurement module 105 is used to measure the output signal of the controlled object, including but 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 storing 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 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 the 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 a 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 system's angular output signal 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 angular output signal respectively. The three unknown parameters τ in the simplified mechanism model are estimated using 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, motor control systems driven by permanent magnet synchronous motors are primarily subject to disturbance torques such as cogging torque, electromagnetic torque, friction torque, and eccentric load torque. Analysis of the mechanism of these disturbances reveals that the resulting disturbance torque exhibits characteristics related to angular position. The D / A output curves of the system are measured under the excitation of different constant speed signals. Position-domain fast Fourier transform analysis of the D / A output signals reveals the primary position-domain frequencies of the disturbances. These disturbances can be represented as a superposition of sinusoidal signals with different frequency components but 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. In order 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 existing proportional-integral-differential (PID) control and the full-format dynamic linearization data model-based model-free adaptive control (FFDL-MFAC) method. At the same time, a disturbance with a constant power spectral density in the entire frequency domain is introduced into the control loop, and the following is obtained: Figure 4 The tracking error curve is shown and the experimental data is shown in Table 1.

[0146] Table 1

[0147]

[0148] In this embodiment, the root mean square error (RMS) of a disturbance whose power spectral density is constant across the entire frequency domain introduced into the control loop is 1.4153. Experimental results show that the RMS error reflected by the disturbance in the output of the system controlled by the method of the present invention is approximately 20% to 30% of that of the prior art PID and FFDL-MFAC. Furthermore, the transition time for the system controlled by the method of the present invention to track a step signal is approximately 40% of that of the prior art PID and FFDL-MFAC. The system controlled by the method of the present invention significantly outperforms the prior art PID and FFDL-MFAC methods in both disturbance rejection and step signal tracking response speed.

[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 As shown in the figure, 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 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 shown.

[0155] From Figure 6 From the tracking trajectory shown, it can be seen 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 suddenly changes, 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 in controlling nonlinear systems is significantly better than that of the prior art methods.

[0156] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention 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 scope of protection 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 a controlled motor control system under a disturbance, and includes the following steps: Step 1: Establish an extended full-format dynamic linearized data model of the controlled system: ； Among them, the expanded sliding window vector is a system output sequence with different lengths , controller output sequence And the dynamic linearization error sequence caused by external disturbances or parameter estimation errors Sliding window; represents the extended pseudo gradient of the controlled system, are all positive integers, indicating 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 extend the pseudo gradient of the controlled system Make estimates; Step 4: Obtain the 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 ; Step 5: Combine step 3 to expand the estimated value of pseudo gradient of the controlled system and the previous Compensation signal calculation of the dynamic linearization error sequence of the time system , to compensate for the control input of the controlled object; Step 6: Input the controlled object control input signal after the compensation in step 5 into the controlled object, and record the output signal of the controlled system at the current time k; Step 7: Calculate 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, set time k=k+1 and repeat steps 3 to 7. The specific steps of step 4 include: In the output criteria function Introducing an adaptive penalty factor: ； in, is a set threshold, is a constant, ; Update the output criterion function to: ； According to the optimal conditions, let the above improved control output criterion function be about the control output The partial derivative of is 0, without loss of generality, in the derivation process, we assume , substitute into the definition of the above adaptive penalty factor , the control algorithm is: ； in, It is an adjustable parameter.

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 perturbations or parameter estimation errors: ； in, is a nonlinear function, Indicates existence The system output with step lag, is an integer and , Indicates existence The controller output with step lag, is an integer and , Indicates existence The step lag is the dynamic linearization error caused by external disturbances or parameter estimation errors. is an integer and , is the set of real numbers; If the nonlinear function in the controlled system There are continuous partial derivatives about all independent variables, and the dynamic linearization error of the controlled system is is bounded, and the controlled system satisfies the generalized Lipschiz condition, then the controlled system is transformed into an extended full-format dynamic linearized data model: ； 、 、 Satisfaction relationship 、 、 .

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: ； in, Indicates that the system is The tracking error at the moment, and Respectively represent the control output With system output The first-order forward difference of It is a target The penalty factor of the item, It is a target The penalty factor of the item, Indicates that the system is Time command signal.

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 into: Seeking an estimate of the system's expanded pseudo-gradient So that it meets 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, Includes sequence The output observation data matrix, is the dimension of the observation data, ; 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 estimation of the problem, the specific calculation process is: Iterative update law of gain vector at time k: ; Iterative update law of the inverse correlation matrix at k moments: ; The calculation law of the system extended pseudo gradient estimate at time k: ; System expansion pseudo gradient estimation reset law: , the system's extended pseudo gradient is reset to its initial value ,in, 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 compensation signal is calculated in step 5 The specific steps include: Obtaining partial system extended pseudo gradient sequence With the previous Time system dynamic linearization error difference sequence The discrete convolution of the controller is used as the compensation signal of the controller output : 。 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 controlled input signal of the controlled object after compensation in step 6 for: .

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 calculation of the system dynamic linearization error difference at the current time k described in step 7 includes the following specific steps: Use k moments to estimate the pseudo gradient of the system and 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 of the output signal of the controlled system at time k is The predicted value of the forward difference of the output signal of the controlled system at time k Take the difference as the system dynamic linearization error difference at the current k moment: 。 8. A dynamic linearization error-assisted model-free adaptive control system based on recursive augmented least squares, characterized by: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 7 above, and executes the steps in the above-mentioned dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares during operation.

9. 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 of the dynamic linearization error-assisted model-free adaptive control method based on recursive augmented least squares according to any one of claims 1 to 7 when called by a processor.

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