Two-dimensional adaptive iterative learning control method for magnetic control shape memory alloy actuator

Abstract

The invention discloses a two-dimensional adaptive iterative learning control method of a magnetic control shape memory alloy actuator, and belongs to the technical field of tracking control of the magnetic control shape memory alloy actuator. According to the method, on-line data of a magnetic control shape memory alloy actuator is directly utilized for data driving modeling, a mathematical model of a system does not need to be known in advance, the system is described as a tight-format dynamic linearization model, and a self-adaptive controller is designed. And then, in order to effectively utilize information on an iteration axis, combining an adaptive controller on a time axis with classical P-type iteration learning control, and designing a two-dimensional adaptive iteration learning controller. According to the controller, the control law is continuously updated on the iteration axis, the defect of open-loop control of the one-dimensional iteration learning controller on the time axis is overcome, and disturbance on the time axis is effectively dealt with.

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] With the rapid development of smart materials and precision drive technologies, magnetic shape memory alloy actuators (MSA) have shown promising applications in precision manufacturing, medical devices, aerospace, and other fields due to their high strain, high response speed, and high energy density. However, as a typical multi-physics coupled nonlinear system, the dynamic characteristics of MSA actuators exhibit multi-dimensional complexity. On the one hand, the inherent characteristics of the material, such as time-varying hysteresis, creep effects, and dynamic response delays, make system modeling difficult. On the other hand, factors such as external ambient temperature fluctuations and sudden load changes further exacerbate the uncertainty of system control. Therefore, it is necessary to design an effective controller tailored to the characteristics of MSA actuators.

[0003] Existing control research on magnetically controlled shape memory alloy actuators (MSHAA) has largely focused on compensating for hysteretic nonlinearity. For example, feedforward control schemes that employ the Preisach or Prandtl-Ishlinskii models to construct hysteresis inverse models can improve trajectory tracking performance, but are not robust to unmodeled disturbances, noise, or parameter variations, and therefore cannot correct the error between the desired and actual outputs in real time. Adaptive control methods based on state observers, while capable of updating model parameters online, still rely on a precise mathematical model of the MSHAA actuator. This high reliance on the model can lead to degraded control performance in practical applications. Traditional model-based control methods rely heavily on precise mathematical descriptions, but real-world industrial scenarios often involve unmodeled dynamic characteristics and unmeasured disturbances, leading to challenges with tracking accuracy and interference rejection. Iterative learning control technology is an intelligent control strategy that does not rely on a precise mathematical model and can simply handle highly uncertain dynamic systems. It has been widely used in the field of micro- and nano-scale positioning and tracking control. However, traditional one-dimensional iterative learning control only updates the control law on the iteration axis and is still an open-loop control structure on the time axis. It is difficult to suppress real-time disturbances, and the convergence speed is limited by the choice of initial control parameters. Data-driven control is a control method that relies only on the actual data of the controlled system. It does not rely on an explicit mathematical model of the system, but directly designs the controller through online and offline data collection or knowledge acquired through data processing. This means that data-driven control can design a controller for the system even when an accurate model of the system is not available or even impossible to model, laying the foundation for the design of model-free controllers. Currently, the academic community is actively exploring innovative paths that combine time-domain data-driven control with iterative learning control.

[0004] In response to the above problems, the present invention proposes a high-precision control method for a magnetically controlled shape memory alloy actuator based on two-dimensional adaptive iterative learning control. Summary of the Invention

[0005] To address the shortcomings of existing technologies and address optimization needs, this proposal designs a data-driven hybrid control strategy for magnetically controlled shape memory alloy actuator systems. This strategy integrates a model-free adaptive controller with an iterative learning controller. Its core advantage lies in eliminating dependence on actuator model parameters. By collecting system operating data to design a model-free adaptive controller, adaptive adjustment of control algorithm parameters is achieved. By integrating the temporally robust nature of model-free adaptive control with an iterative learning mechanism, this hybrid control approach effectively improves the system's tracking accuracy for preset trajectories, demonstrating high-precision control advantages, particularly in repetitive motion scenarios.

[0006] The steps of the technical solution adopted by the present invention are:

[0007] 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;

[0008] The magnetically controlled shape memory alloy actuator system is shown below:

[0009] y k (t+1)=f(u k (t),y k (t),t) (1)

[0010] 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.

[0011] 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 the following compact dynamic linearization model:

[0012] y k (t+1)=y k (t)+φ k (t)△u k (t) (2)

[0013] where 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;

[0014] 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;

[0015] At the kth iteration, the following control input criterion function is considered on the time axis:

[0016] J(u k (t))=|y r (t+1)-y k (t+1)| 2 +υ|u k (t)-u k (t-1)| 2 (3)

[0017] 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 (3), u k (t) and set it equal to zero, thus obtaining the adaptive control law on the time axis, as shown below:

[0018]

[0019] Among them, ρ∈(0,1] is the step size factor;

[0020] 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:

[0021]

[0022] Among them, μ>0; for J(φ k (t)) Find φ k The partial derivative of (t) is set equal to zero, so the estimated value of the pseudo partial derivative is:

[0023]

[0024] Among them, η∈(0,1] is the step factor, △y k (t) = y k (t)-y k (t-1);

[0025] Step 3: Combined with P-type iterative learning control, the control law of two-dimensional adaptive iterative learning control is obtained to enhance the anti-interference ability of the one-dimensional iterative learning controller on the time axis;

[0026] To further optimize the control performance of adaptive control in the time domain, it is combined with a P-type iterative learning controller. On the iterative axis, the control law is:

[0027]

[0028] Among them, ψ is the learning parameter, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the systematic error;

[0029] Finally, combining formula (4) and formula (7), the control law of two-dimensional adaptive iterative learning control is proposed as follows:

[0030]

[0031] The beneficial effects of the present invention are:

[0032] 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 describes the magnetically controlled shape memory alloy actuator as a tight-form dynamic linearized model that does not require advance modeling. On this basis, the controller uses classic P-type iterative learning control on the iteration axis, and can update the control law based on the information of previous iterations; while using an adaptive controller on the time axis, the control signal is calculated based on the information in the time domain, that is, the P-type iterative learning control and adaptive control update the control law between batches and within batches respectively. Introducing time axis closed-loop control in the iterative process greatly enhances the anti-interference ability of the one-dimensional iterative learning controller on the time axis, thereby improving the overall tracking effect of the iterative learning controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the magnetically controlled shape memory alloy actuator of the present invention;

[0034] Figure 2 This is a schematic diagram of the magnetically controlled shape memory alloy actuator of the present invention;

[0035] Figure 3 This is a structural diagram of the two-dimensional adaptive iterative learning control method of the present invention;

[0036] 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;

[0037] Figure 5This is a comparison diagram of the system target trajectory and actual trajectory tracking when the input signal frequency of the present invention is 2Hz;

[0038] 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;

[0039] 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;

[0040] 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;

[0041] 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;

[0042] Figure 10 A 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;

[0043] 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

[0044] In order to make the control method proposed by the present invention clearer, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] 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, a micrometer (including a driver module and a sensor module), a temperature sensor, a computer, and a vibration isolation table.

[0046] The experimental platform structure diagram for case implementation is as follows Figure 2As shown in the figure, the working process of the magnetic shape memory alloy actuator control system is as follows: generate a control signal in the Matlab / Simulink environment, input it into the data acquisition card to convert it into an analog quantity, and the magnetic shape memory alloy actuator generates a displacement after receiving the analog signal. The displacement is measured by the sensor module and input into the computer for data processing, and finally the control process of the magnetic shape memory alloy actuator is completed. During the control process, the magnetic shape memory alloy actuator is always located on the vibration isolation table. After many debugging, the specific parameters of the controller in the experiment are selected as follows: the maximum number of iterations is 15 times, ψ=0.9, ρ=0.6, υ=10, η=0.02, μ=10,

[0047] Next, design the controller. The structural block diagram of the controller is as follows Figure 3 shown.

[0048] The magnetically controlled shape memory alloy actuator system is represented as follows:

[0049] y k (t+1)=f(u k (t),y k (t),t) (1)

[0050] Among them, y k (t) and u k (t) are the output displacement and input signal of the system at the t-th sampling time at the k-th iteration, respectively. f(·) is the unknown nonlinear function of the magnetic shape memory alloy actuator system. Furthermore, the magnetic shape memory alloy actuator is represented as the following compact dynamic linearization model:

[0051] y k (t+1)=y k (t)+φ k (t)△u k (t) (2)

[0052] where φ k (t) is a pseudo partial derivative and is bounded, i.e. |△u k (t)|=|u k (t)-u k (t-1)|≠0;

[0053] At the kth iteration, the following control input criterion function is considered on the time axis:

[0054] J(u k (t))=|y r (t+1)-y k (t+1)| 2 +υ|u k(t)-u k (t-1)| 2 (3)

[0055] 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 (3), u k (t) and set it equal to zero, thus obtaining the adaptive control law on the time axis, as shown below:

[0056]

[0057] Among them, ρ∈(0,1] is the step size factor;

[0058] The pseudo partial derivative estimation criterion function is as follows:

[0059]

[0060] Among them, μ>0; for J(φ k (t)) Find φ k The partial derivative of (t) is set equal to zero, so the estimated value of the pseudo partial derivative is:

[0061]

[0062] Among them, η∈(0,1] is the step factor, △y k (t) = y k (t)-y k (t-1);

[0063] On the iteration axis, the control law is:

[0064]

[0065] Among them, ψ is the learning parameter, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the systematic error;

[0066] Finally, combining formula (4) and formula (7), the control law of two-dimensional adaptive iterative learning control is proposed as follows:

[0067]

[0068] Finally, the effectiveness of the two-dimensional adaptive iterative learning control method of the magnetically controlled shape memory alloy actuator proposed in this invention is verified through the magnetically controlled shape memory alloy actuator control system.

[0069] The sine wave with frequency of 0.5Hz and 2Hz, the triangular wave with variable amplitude and the formula based on The mixed sine wave is used as the desired tracking signal for the magnetically controlled shape memory alloy actuator system.

[0070] 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.

[0071] Figure 8 、 Figure 9 、 Figure 10 and Figure 11 The 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. It can be seen that the tracking error of the controller is kept in a very small range, and excellent control effects can be achieved at high frequencies and complex waveforms.

[0072] In order to further quantify the control performance of the controller, the root mean square error and maximum absolute error of the controller at the last iteration are calculated. Table 1 shows the root mean square error and maximum absolute error of the magnetically controlled shape memory alloy actuator under different input signals.

[0073] Table 1

[0074] Expected Output Root mean square error (μm) Maximum absolute error (%) f = 0.5 Hz sine wave 4.7170 6.4035 f = 2Hz sine wave 6.6240 10.3681 Mixed sine waves 3.9355 18.3402 triangle wave 2.2233 4.1193

[0075] It can be seen from the experimental diagrams and performance indicators that the control method proposed in the present invention can effectively suppress the hysteresis nonlinear characteristics of the magnetically controlled shape memory alloy actuator and has an excellent control effect.

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 the following compact dynamic linearization model: y k (t+1)=y k (t)+φ k (t)△u k (t) (2) where 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; 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 (3) 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 (3), 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; 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, so 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 3: Combined with P-type iterative learning control, the control law of two-dimensional adaptive iterative learning control is obtained to enhance the anti-interference ability of the one-dimensional iterative learning controller on the time axis; To further optimize the control performance of adaptive control in the time domain, it is combined with a P-type iterative learning controller. On the iterative axis, the control law is: Among them, ψ is the learning parameter, e k-1 (t+1)=y r (t+1)-y k-1 (t+1) represents the systematic error; Finally, combining formula (4) and formula (7), the control law of two-dimensional adaptive iterative learning control is proposed as:

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