Two-dimensional adaptive iterative learning control method for magnetic control shape memory alloy actuator
Through the two-dimensional adaptive iterative learning control method, combined with model-free adaptive control and iterative learning control, the nonlinear control problem of magnetron shape memory alloy actuators is solved, and the rapid convergence and high-precision trajectory tracking effect is achieved.
Patent Information
- Application Number
- CN202510457547.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-14
- Publication Date
- 2025-08-15
AI Technical Summary
Magnet-controlled shape memory alloy actuators have hysteresis characteristics and multi-factor highly coupled nonlinear characteristics in high-end equipment manufacturing, which leads to difficulty in precise control. Traditional control strategies are difficult to take into account both rapid convergence and high precision, and the fixed learning rate parameters lead to insufficient adaptability.
A two-dimensional adaptive iterative learning control method is adopted, combined with model-free adaptive control and iterative learning control, through a tight-form dynamic linearization model and an adaptive parameter learning mechanism, a double closed-loop adjustment is formed on the time and iterative axis to achieve real-time adjustment of the learning rate.
It improves the trajectory tracking accuracy and system robustness of magnetron shape memory alloy actuators, adapts to different environmental changes, and achieves rapid convergence and high-precision control.
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Figure CN120491447A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of tracking control of magnetically controlled shape memory alloy actuators, and specifically designs a two-dimensional adaptive iterative learning control method. Technical Background
[0002] In recent years, intelligent actuators based on magnetically controlled shape memory alloys (MSAs) have demonstrated significant advantages in high-end equipment manufacturing. With advantages such as large output displacement, high response frequency, and strong load capacity, these devices have gradually become core drive components in scenarios such as precision machining and spacecraft precision adjustment. However, MSA actuators not only exhibit hysteresis, but their system characteristics are also affected by multiple factors, including input current, driving magnetic field, signal frequency, load size, and ambient temperature. These highly coupled nonlinear characteristics pose a significant challenge to precise control.
[0003] Current control strategies for magnetically controlled shape memory alloy actuators primarily follow two technical approaches: First, controllers that rely on hysteresis models can improve trajectory tracking accuracy, but require the establishment of a system model, which is impractical in many industrial scenarios. Second, control strategies that do not rely on models, such as iterative learning controllers and data-driven controllers, are highly effective in industrial scenarios where the same task must be repeated. However, traditional iterative learning control has a drawback: it can only adjust the control law after each iteration and cannot be adjusted in real time. With the rapid development of model-free adaptive control theory, controllers can be designed directly on the timeline through online and offline data collection, or knowledge acquired through data processing. Therefore, researchers have combined model-free adaptive controllers and iterative learning controllers to design two-dimensional adaptive iterative learning control. By leveraging the ability of iterative learning control to continuously optimize its control performance, the control accuracy of model-free adaptive control is continuously improved during iterations.
[0004] During the iterative process, the constant pursuit of improved control accuracy often leads to neglect of system convergence performance, resulting in slow convergence and excessive jitter amplitude during convergence, severely impacting control performance. The learning rate plays a crucial role in the control effectiveness of iterative learning control. Choosing too high a learning rate can cause the system to gradually diverge during the iteration process, while choosing too low a learning rate can lead to excessive iterations and low control accuracy. This parameter sensitivity necessitates multiple experiments to obtain ideal parameters in practical applications. Even if ideal parameter values are achieved, their fixed gain characteristics still have inherent limitations: dynamic adjustment at different stages of the iterative process is impossible, making it difficult to achieve both rapid convergence and high-precision control. This fixed parameter mechanism inherently restricts the control system's ability to adapt to environmental conditions. Therefore, exploring learning rate adjustment mechanisms with time-varying characteristics has become an important research direction. Therefore, in practice, selecting an appropriate learning rate often requires considerable effort. Even if a relatively suitable learning rate is ultimately found, its fixed value often makes it difficult to achieve both convergence performance and control accuracy during the iteration process.
[0005] Based on this, the present invention proposes a two-dimensional adaptive iterative learning control strategy with adaptive learning parameters, constructs a dual closed-loop regulation mechanism in the time domain and iteration domain to form a composite control scheme, and proposes a learning parameter adjustment mechanism, which can integrate information on the time axis and the iteration axis to quickly improve the control performance. Summary of the Invention
[0006] In response to the limitations of traditional control methods, this study proposed an innovative data-driven composite control scheme. This scheme integrates the dual advantages of model-free adaptive control and iterative learning control, greatly reducing the dependence of traditional control strategies on system models. The core innovations of the two-dimensional adaptive iterative learning controller are: 1. By introducing model-free adaptive control on the time axis, the anti-interference ability of the one-dimensional iterative learning control is enhanced, forming a time axis closed-loop state; 2. The fixed learning parameters in the iterative learning controller greatly impair the tracking performance of the magnetically controlled shape memory alloy actuator. An adaptive parameter learning mechanism is designed, which integrates the information of the iterative axis and the time axis to quickly improve the system performance. Ultimately, this composite control architecture fully utilizes the real-time robustness of model-free adaptive control and the periodic optimization capability of iterative learning control, achieving significant improvements in trajectory tracking accuracy. It is particularly suitable for repetitive motion scenarios and provides a new solution for actuator control.
[0007] The steps of the technical solution adopted by the present invention are:
[0008] A two-dimensional adaptive iterative learning control method, the steps of the method are as follows:
[0009] Step 1: Construct a dynamic linearization expression with pseudo partial derivative parameters and establish a compact dynamic linearization model of the magnetically controlled shape memory alloy actuator based on online data;
[0010] The magnetically controlled shape memory alloy actuator system is shown below:
[0011] y k (t+1)=f(u k (t),y k (t),t) (1)
[0012] Among them, y k (t) and u k (t) are the output displacement and input signal of the system at the t-th sampling moment in the k-th iteration, respectively. f(·) is the unknown nonlinear function of the magnetically controlled shape memory alloy actuator system.
[0013] Assuming that the partial derivatives of the unknown nonlinear function f(·) with respect to u are continuous, the system satisfies the generalized Lipschitz condition, i.e., ||y(t1+1)-y(t2+1)||≤Υ||u(t1)-u(t2)||, where Υ represents a positive integer; the system can be described as a compact dynamic linearization model:
[0014] y k (t+1)=y k (t)+φ k (t)△u k (t) (2)
[0015] Among them, φ k (t) is a pseudo partial derivative and is bounded, i.e. |△u k (t)|=|u k (t)-u k (t-1)|≠0; Represents φ k (t) Upper bound of pseudo partial derivative;
[0016] Next, we need to use the system's real-time input and output data to calculate φ k Estimated value of (t) The pseudo partial derivative estimation criterion function is as follows:
[0017]
[0018] Among them, μ>0; for J(φ k (t)) Find φ k The partial derivative of (t) is set equal to zero, and the estimated value of the pseudo partial derivative is:
[0019]
[0020] Among them, η∈(0,1] is the step factor, △y k (t) = y k (t)-y k (t-1);
[0021] Step 2: Obtain the adaptive control law on the time axis through the control input criterion function, and use the real-time input and output data of the system to obtain the estimated value of the pseudo partial derivative;
[0022] At the kth iteration, the following control input criterion function is considered on the time axis:
[0023] J(u k (t))=|y r (t+1)-y k (t+1)| 2 +υ|u k (t)-u k (t-1)| 2 (5)
[0024] Among them, υ>0 is used to constrain the change value of the control quantity to make the control input smoother; after substituting formula (2) into formula (5), u k Taking the derivative of (t) and setting it equal to zero, we can obtain the adaptive control law on the time axis as shown below:
[0025]
[0026] Among them, ρ∈(0,1] is the step size factor;
[0027] Step 3: Combine the learning control law on the iterative axis to obtain a two-dimensional adaptive iterative learning control law to optimize the control performance of the adaptive control in the time domain;
[0028] To further optimize the control performance of adaptive control in the time domain, the information on the iteration axis is fully utilized and combined with the iterative learning controller; on the iteration axis, the control law is:
[0029]
[0030] Among them, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the system error, ψ k (t) is the designed adaptive learning parameter, and the update law is as follows;
[0031]
[0032] Finally, combining formula (6) and formula (7), the control law of two-dimensional adaptive iterative learning control is obtained as follows:
[0033]
[0034] The beneficial effects of the present invention are:
[0035] Based on the characteristics of magnetically controlled shape memory alloy actuators, the present invention proposes a two-dimensional adaptive iterative learning control method. The present invention first innovatively adopts a tight-form dynamic linearization method to achieve a model-free description of magnetically controlled shape memory alloy actuators. Based on this model, the controller introduces adaptive control in the time axis dimension and designs an iterative learning controller with an adaptive learning parameter update law in the iteration dimension. The adaptive adjustment capability of the learning parameters enables real-time adjustment of the control law according to the dynamic changes of the system, and the control law can fully utilize the information of the system on the iteration axis and the time axis for optimization, effectively enhancing the adaptability and robustness of the controller. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] Figure 1 Schematic diagram of the magnetically controlled shape memory alloy actuator of the present invention;
[0037] Figure 2 This is a schematic diagram of the magnetically controlled shape memory alloy actuator of the present invention;
[0038] Figure 3 This is a structural diagram of the two-dimensional adaptive iterative learning control method of the present invention;
[0039] Figure 4 This is a comparison diagram of the system target trajectory and actual trajectory tracking when the input signal frequency of the present invention is 0.5Hz;
[0040] Figure 5 This is a comparison diagram of the system target trajectory and actual trajectory tracking when the input signal frequency of the present invention is 2Hz;
[0041] Figure 6 This is a comparison diagram of the system target trajectory and actual trajectory tracking when the input signal of the present invention is a mixed sine wave;
[0042] Figure 7 This is a comparison diagram of the target trajectory and actual trajectory tracking of the system when the input signal of the present invention is a variable amplitude triangular wave;
[0043] Figure 8 This is a curve diagram of the tracking error between the target trajectory and the actual trajectory of the system when the input signal frequency is 0.5 Hz;
[0044] Figure 9 This is a curve diagram of the tracking error between the target trajectory and the actual trajectory of the system when the input signal frequency is 2 Hz;
[0045] Figure 10A curve diagram of the tracking error between the target trajectory and the actual trajectory of the system when the input signal of the present invention is a mixed sine wave;
[0046] Figure 11 This is a curve diagram of the tracking error between the system target trajectory and the actual trajectory when the input signal of the present invention is a variable amplitude triangular wave. DETAILED DESCRIPTION
[0047] In order to make the control method proposed in the present invention clearer, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.
[0048] The two-dimensional adaptive iterative learning control method designed by the present invention is applied to Figure 1 The experimental platform for the magnetically controlled shape memory alloy actuator control system shown in the figure includes the following components: a magnetically controlled shape memory alloy actuator, a PCI-1716 data acquisition card, an integrated positioning controller (including a driver module and a sensor module), a temperature sensor, a computer, and a vibration isolation platform.
[0049] Figure 2 The system architecture of the experimental platform is presented. The control system uses Matlab / Simulink software in the computer as the core control unit. Its working mechanism is as follows: the control instructions are converted from digital to analog by the data acquisition card to drive the actuator to generate displacement. The displacement is collected by the sensor unit and fed back to the computer for real-time processing, forming a complete closed-loop control circuit. To ensure the accuracy of the experiment, the actuator is placed on the vibration isolation platform for operation throughout the process. Through repeated experimental verification, the parameter configuration of the controller and pseudo-partial derivative is finally determined as follows: the maximum number of iterations is 15 times, the sampling frequency is 1kHz, ρ=0.6, υ=14, η=0.02, μ=0.9,
[0050] Next, design the controller. The structural block diagram of the controller is as follows Figure 3 shown.
[0051] The magnetically controlled shape memory alloy actuator system is shown below:
[0052] y k (t+1)=f(u k (t),y k (t),t) (1)
[0053] Among them, y k (t) and u k (t) are the output displacement and input signal of the system at the t-th sampling moment in the k-th iteration, respectively. f(·) is the unknown nonlinear function of the magnetically controlled shape memory alloy actuator system.
[0054] Assuming that the partial derivatives of the unknown nonlinear function f(·) with respect to u are continuous, the system satisfies the generalized Lipschitz condition, i.e., ||y(t1+1)-y(t2+1)||≤Υ||u(t1)-u(t2)||, where Υ represents a positive integer; the system can be described as a compact dynamic linearization model:
[0055] y k (t+1)=y k (t)+φ k (t)△u k (t) (2)
[0056] Among them, φ k (t) is a pseudo partial derivative and is bounded, i.e. |△u k (t)|=|u k (t)-u k (t-1)|≠0;
[0057] Next, we need to use the system's real-time input and output data to calculate φ k Estimated value of (t) The pseudo partial derivative estimation criterion function is as follows:
[0058]
[0059] Among them, μ>0; for J(φ k (t)) Find φ k The partial derivative of (t) is set equal to zero, and the estimated value of the pseudo partial derivative is:
[0060]
[0061] Among them, η∈(0,1] is the step factor, △y k (t) = y k (t)-y k (t-1);
[0062] At the kth iteration, the following control input criterion function is considered on the time axis:
[0063] J(u k (t))=|y r (t+1)-y k (t+1)| 2 +υ|u k (t)-u k (t-1)| 2 (5)
[0064] Among them, υ>0 is used to constrain the change value of the control quantity to make the control input smoother; after substituting formula (2) into formula (5), uk Taking the derivative of (t) and setting it equal to zero, we can obtain the adaptive control law on the time axis as shown below:
[0065]
[0066] Among them, ρ∈(0,1] is the step size factor;
[0067] To further optimize the control performance of adaptive control in the time domain, the information on the iteration axis is fully utilized and combined with the iterative learning controller. On the iteration axis, the control law is designed as follows:
[0068]
[0069] Among them, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the system error, ψ k (t) is the designed adaptive learning parameter, and the update law is as follows;
[0070]
[0071] Finally, combining formula (6) and formula (7), the control law of two-dimensional adaptive iterative learning control is proposed as:
[0072]
[0073] Finally, the performance of the proposed two-dimensional adaptive iterative learning control scheme was verified through a magnetically controlled shape memory alloy actuator experimental platform.
[0074] The target tracking trajectory of the magnetically controlled shape memory alloy actuator system is set to a sine wave with a frequency of 0.5 Hz and 2 Hz, a triangular wave with a variable amplitude, and a A mixed sine wave.
[0075] Figure 4 、 Figure 5 、 Figure 6 and Figure 7 The following are comparison diagrams of the system target trajectory and actual trajectory tracking when the input frequencies are 0.5Hz and 2Hz sine waves, variable amplitude triangle waves, and mixed sine waves. It can be seen that the control method of the present invention can enable the magnetically controlled shape memory alloy actuator system to track the target trajectory well.
[0076] Figure 8 、 Figure 9 、 Figure 10 and Figure 11The following are the tracking error curves of the system target trajectory and the actual trajectory when the input frequencies are 0.5Hz and 2Hz sine waves, variable amplitude triangle waves, and mixed sine waves. The experimental results show that the control method achieves the expected effect in trajectory tracking, fully confirming its feasibility and superiority.
[0077] In order to evaluate the control effect, the root mean square error and maximum absolute error are used as quantitative indicators of the two-dimensional adaptive iterative learning controller, and the final iterative results are statistically analyzed. Table 1 shows the error data of the magnetically controlled shape memory alloy actuator under different expected outputs under the action of the controller.
[0078] Expected Output Root mean square error (μm) Maximum absolute error (%) f = 0.5 Hz sine wave 3.4279 5.6017 f = 2Hz sine wave 5.2535 8.3590 Mixed sine waves 3.6809 18.1172 Variable amplitude triangle wave 1.8167 3.6760
[0079] Experimental results show that the control scheme effectively overcomes the nonlinear characteristics of the system and exhibits significant control advantages.
Claims
1. A two-dimensional adaptive iterative learning control method for a magnetically controlled shape memory alloy actuator, characterized in that: The steps of this method are as follows: Step 1: Construct a dynamic linearization expression with pseudo partial derivative parameters and establish a compact dynamic linearization model of the magnetically controlled shape memory alloy actuator based on online data; The magnetically controlled shape memory alloy actuator system is shown below: y k (t+1)=f(u k (t),y k (t),t) (1) Among them, y k (t) and u k (t) are the output displacement and input signal of the system at the t-th sampling moment in the k-th iteration, respectively. f(·) is the unknown nonlinear function of the magnetically controlled shape memory alloy actuator system. Assuming that the partial derivatives of the unknown nonlinear function f(·) with respect to u are continuous, the system satisfies the generalized Lipschitz condition, i.e., ||y(t1+1)-y(t2+1)||≤Υ||u(t1)-u(t2)||, where Υ represents a positive integer; the system can be described as a compact dynamic linearization model: y k (t+1)=y k (t)+φ k (t)△u k (t) (2) Among them, φ k (t) is a pseudo partial derivative and is bounded, i.e. |△u k (t)|=|u k (t)-u k (t-1)|≠0; Represents φ k (t) Upper bound of pseudo partial derivative; Next, we need to use the system's real-time input and output data to calculate φ k Estimated value of (t) The pseudo partial derivative estimation criterion function is as follows: Among them, μ>0; for J(φ k (t)) Find φ k The partial derivative of (t) is set equal to zero, and the estimated value of the pseudo partial derivative is: Among them, η∈(0,1] is the step factor, △y k (t) = y k (t)-y k (t-1); Step 2: Obtain the adaptive control law on the time axis through the control input criterion function, and use the real-time input and output data of the system to obtain the estimated value of the pseudo partial derivative; At the kth iteration, the following control input criterion function is considered on the time axis: J(u k (t))=|y r (t+1)-y k (t+1)| 2 +υ|u k (t)-u k (t-1)| 2 (5) Among them, υ>0 is used to constrain the change value of the control quantity to make the control input smoother; after substituting formula (2) into formula (5), u k (t) and set it equal to zero, thus obtaining the adaptive control law on the time axis, as shown below: Among them, ρ∈(0,1] is the step size factor; Step 3: Combine the learning control law on the iterative axis to obtain a two-dimensional adaptive iterative learning control law to optimize the control performance of the adaptive control in the time domain; On the iteration axis, the control law is: Among them, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the system error, ψ k (t) is the designed adaptive learning parameter, and the update law is as follows; Finally, combining formula (6) and formula (7), the control law of two-dimensional adaptive iterative learning control is obtained as follows: