Uncertainty and disturbance estimation control method for shape memory alloy actuators

Abstract

The present application belongs to the technical field of robot control, and particularly relates to an uncertainty and disturbance estimation control method for a shape memory alloy driver. The method of the present application controls the shape memory alloy driver by using a control signal as follows: the present application combines a shape memory alloy rate-dependent Prandtl-Ishlinskii model with an uncertainty and disturbance estimation control method to realize tracking control of the shape memory alloy driver, improve robust performance, and has a good application prospect.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to an uncertainty and disturbance estimation control method for shape memory alloy actuators. Background Technology

[0002] In recent years, with the rapid development of intelligent manufacturing, shape memory alloys (SMAs), as a smart material, have attracted great interest and have been widely used in the field of intelligent manufacturing. They have advantages such as high power-to-weight ratio, simple single-drive circuit, low voltage, small size, light weight, no pollution, and noiseless drive transmission sensors.

[0003] Shape memory alloys (SMEs) can recover their initial shape and size after being heated to a certain threshold temperature. They consist of two distinct solid phases: a martensitic phase at low temperatures and an austenitic phase at high temperatures. The shape memory effect of SMEs is achieved through the interconversion between martensite and austenite. However, this interconversion leads to the nonlinear hysteresis characteristics of SMEs. Due to the uncertainties and hysteresis nonlinearities in SME actuator models, improving the positioning control accuracy and robustness of SME actuators has been a key research focus.

[0004] Zhang and Zhao et al. combined the advantages of self-tuning control and sliding mode control to propose a novel robust adaptive control method for uncertain nonlinear systems, which was successfully applied to the control of shape memory alloy actuator systems. Shi and Tian et al. proposed a multi-feedback control method for actuators based on shape memory alloys and hyperelastic shape memory alloy linear feedback. In their research, to improve the system's accuracy and stability, a support function-based data fusion algorithm was used to fuse the multi-feedback data. Then, they verified the accuracy and stability of the control through multi-order response, sinusoidal tracking, and force disturbance tests. Recently, Patterson et al. proposed a robust control method for shape memory alloy-driven soft robots. They used a static beam bending model to approximate the soft limb as an LTI system, while employing a singular value decomposition compensator method to decouple multi-axis motion and using anti-strain elements to achieve actuator saturation.

[0005] However, these existing methods are overly complex in describing the hysteresis behavior of shape memory alloys, requiring numerous parameters. Furthermore, existing control methods often ignore real-world environmental factors, focusing only on nonlinear systems to improve the control accuracy of shape memory alloy actuators. This results in poor robustness and speed performance of existing shape memory alloy actuator control methods. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides an uncertainty and disturbance estimation control method for shape memory alloy actuators. The aim is to utilize a simpler model to construct a control method for shape memory alloy actuators, thereby achieving tracking control of the shape memory alloy actuators and improving robustness.

[0007] An uncertainty and disturbance estimation control method for a shape memory alloy actuator, wherein the shape memory alloy actuator is controlled by the following control signal:

[0008]

[0009] in, For control signals, r Let be the radius of the axis of rotation. J Let be the moment of inertia of the axis of rotation.

[0010] ,

[0011] in, It is the inverse operator of the Laplace transform. K The error feedback gain matrix is... To track errors, The shrinkage amount of the shape memory alloy actuator. This is the reference shrinkage amount for the shape memory alloy actuator. Let be the transfer function of the filter. s The symbol for the Laplace transform operator is...

[0012] , k Let be the spring constant of the load spring. c is the damping coefficient of the rotating shaft.

[0013] Preferably, the The expression is:

[0014] .

[0015] The present invention also provides a shape memory alloy actuator, the movement of which is controlled by the above-described control method.

[0016] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-described control method when executing the program.

[0017] The present invention also provides a motion system based on a shape memory alloy actuator, which includes a motion mechanism, a shape memory alloy actuator, and the computer device as described in claim 4. The motion mechanism and the shape memory alloy actuator are connected by a transmission mechanism, and the shape memory alloy actuator and the computer device are connected by a signal transmission device.

[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon for implementing the above-described control method.

[0019] In this invention, the "control signal" refers to the voltage input to the shape memory alloy driver.

[0020] By adopting the above technical solution, the present invention has the following beneficial effects:

[0021] (1) The hysteresis behavior of the shape memory alloy actuator is described using a rate-dependent Prandtl-Ishlinskii (RDPI) model. Relevant parameters are identified using a genetic algorithm, allowing for accurate calculation of the physical parameters of the governing equations without requiring extensive measurements. This model can simply and efficiently describe the hysteretic nonlinear behavior of the shape memory alloy actuator. In this invention, this model is primarily established on a host computer to simulate the hysteretic nonlinear behavior of the shape memory alloy online. Therefore, this invention proposes a shape memory alloy actuator control method with fast convergence speed and low control workload, offering better flexibility and applicability.

[0022] (2) Compared with existing robust control methods for shape memory alloy actuators, the uncertainty and disturbance estimation control method of the present invention is a superior robust control strategy. It only uses a first-order filter to estimate uncertainties and disturbances, and it is unaffected by modeling errors and does not require prior disturbance knowledge. This makes the method of the present invention more robust and simpler to use in practical applications.

[0023] Obviously, based on the above description of the present invention, and according to common technical knowledge and conventional methods in the field, various other modifications, substitutions or alterations can be made without departing from the basic technical concept of the present invention.

[0024] The following detailed embodiments further illustrate the above-described content of the present invention. However, this should not be construed as limiting the scope of the present invention to the following examples. All technologies implemented based on the above-described content of the present invention fall within the scope of the present invention. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the hardware structure of the control system in Embodiment 1 of the present invention;

[0026] Figure 2This section presents the 0.05 Hz sinusoidal trajectory tracking performance of the UDE-based SMA driver in Experiment Example 1. (a) SMA tracking performance, with blue representing the actual SMA trajectory and red representing the reference trajectory. (b) Tracking error e(t). (c) Control signal v(t). (d) Uncertainty ud(t) and its estimation ud(t).

[0027] Figure 3 This section presents the 0.1 Hz sinusoidal trajectory tracking performance of the UDE-based SMA driver in Experiment Example 1. (a) SMA tracking performance, with blue representing the actual SMA trajectory and red representing the reference trajectory. (b) Tracking error e(t). (c) Control signal v(t). (d) Uncertainty ud(t) and its estimation ud(t).

[0028] Figure 4 This study investigates the 0.1 Hz sinusoidal trajectory tracking performance of an SMA driver based on a UDE controller. The data includes: (a) SMA tracking performance, with blue representing the actual SMA trajectory and red representing the reference trajectory; (b) tracking error e(t); and (c) control output signal v(t) and input disturbance vd(t). Detailed Implementation

[0029] It should be noted that the algorithms for data acquisition, transmission, storage and processing steps not specifically described in the embodiments, as well as the hardware structures and circuit connections not specifically described, can all be implemented using content already disclosed in the prior art.

[0030] Example 1: Uncertainty and Disturbance Estimation Control Method for Shape Memory Alloy Actuators

[0031] This embodiment is performed in the following control system, such as... Figure 1 As shown, specifically:

[0032] SMA stands for shape memory alloy; potentiometer is an encoder that measures the trajectory of the SMA; PC is a computer used to design control algorithms; V / I is a power electronic device used to amplify and convert control signals; YX-SPACE is a controller used to receive encoder data and output control algorithms in real time; Force sensor is a force sensor used to measure the output force of the SMA; spring load is a spring load used to simulate changes in load gravity.

[0033] In the above control system, the control signal of the shape memory alloy actuator is derived in this embodiment as follows:

[0034] I. Prandtl-Ishlinskii (PI) Model:

[0035] The PI model is a linear superposition of play or stopping operators with different weights. The output of the play operator depends not only on the threshold r and the weights w, but also on the historical input values. Furthermore, the accuracy of the PI model is highly dependent on the number of operators, but increasing the number of operators reduces the model's computational speed. Therefore, choosing an appropriate number of operators is crucial to ensuring both the accuracy and computational speed of the PI model. Let... It is localized as A set of piecewise monotonically continuous functions. When the control signal... When the threshold r0 is reached, the linear Play operator Pr can be defined as:

[0036] (1)

[0037] in

[0038] (2)

[0039] in It is the output of the operator. The region Divide into N sub-intervals, each sub-interval Input in It is monotonically continuous. The initial value of equation (1) is defined as:

[0040] (3)

[0041] 4

[0042] in These are the initial conditions for the linear Play operator.

[0043] II. Rate-dependent Prandtl-Ishlinskii (RDPI) model:

[0044] The classic PI model cannot effectively characterize the rate-dependent characteristics of SMA. To express the influence of input frequency on output, this invention employs the RDPI model to characterize the system's rate-dependent hysteresis characteristics. The RDPI model is built upon the classic PI model. It introduces a dynamic threshold related to the input rate of change, and the rate-dependent characteristics of the system are characterized by adjusting the changes in this dynamic threshold.

[0045] The output of the RDPI model is as follows:

[0046] (5)

[0047] In the formula, For control signals, N is the number of RDPI model playback operators. and These are the weighting constants for the input and play operators, respectively. A genetic algorithm (GA) is used to identify the measurement data. Control signals are used... and dynamic threshold function Construct a rate-dependent Play operator:

[0048] ⑹

[0049] Dynamic threshold function The threshold should be strictly increased so that the play operator can consider the direction of cooling and heating paths based on the system input and its rate (excitation frequency). Therefore, in the dynamic threshold function... A constraint was specified above:

[0050] 7.

[0051] Dynamic threshold It is a threshold function related to the rate of change of the input voltage, as shown below:

[0052] (8)

[0053] In the RDPI model, and For positive integers, The number of play operators.

[0054] III. Control System Design

[0055] Figure 1 The dynamic state equations of the SMA actuator platform shown are as follows:

[0056] (9)

[0057] x 1 represents the contraction amount of the SM driver. x 2 represents the contraction speed of the SMA actuator; These are the radius, damping coefficient, and moment of inertia of the shaft, respectively. Unknown disturbance Let v(t) be the output of the RDPI model.

[0058] The dynamic model of the SMA actuator (9) is reconstructed as follows:

[0059] 10

[0060] in .

[0061] RDPI hysteresis model control signals and unknown disturbance terms It can be represented as a lumped uncertainty vector :

[0062] 11

[0063] Combining (9) and (10):

[0064] 12

[0065] To ensure the closed-loop system meets the required specifications, a stable reference model (RM) in the following controllable specification form can be selected:

[0066] , ⒀

[0067] in It is the reference state vector. It is a piecewise continuous and uniformly bounded instruction for the reference system. .

[0068] The goal is to design a controller. ,make asymptotic tracking reference trajectory Tracking error It converges asymptotically to zero.

[0069] In this embodiment, the desired error dynamics are specified as:

[0070] , 14

[0071] The form of the error feedback gain matrix is: .

[0072] Therefore, control signal Should meet:

[0073] , 12

[0074] Lumped uncertainty and disturbance term It can be represented as:

[0075] 13

[0076] This indicates that the lumped term can be obtained from the known SMA driver dynamics and input voltage. However, directly using this relationship results in an algebraic loop, and the control law cannot be formulated. Due to the advantage of uncertainty and disturbance estimation controllers, any signal can be recovered through a filter with a sufficiently wide bandwidth covering the signal's spectrum. If the filter... It is strictly stable, and If it has unity gain and zero phase shift on the spectrum, and zero gain elsewhere, then... It can be precisely expressed as:

[0077] , ⒄

[0078] in yes The estimated value of ) Here is the time-domain expression for the filter. It is a convolution operator. Therefore, If the bandwidth coverage of the filter is appropriately selected The spectrum.

[0079] In (15) Replace with The result is:

[0080] 18.

[0081] By order ,Then:

[0082] , 18

[0083] In the formula It is the inverse operator of the Laplace transform. Note that (18) can be rewritten as:

[0084] ,

[0085] Then, a UDE-based SMA driver system controller is established:

[0086] .

[0087] It is worth noting that in UDE-based controller design, there is no need for hysteresis nonlinearity constraints and other information.

[0088] To further illustrate the technical effects of the present invention, experimental examples are provided below to further demonstrate the technical effects of the present invention.

[0089] Experiment Example 1: Sine Track Tracking Performance of an SMA Driver Based on ude

[0090] I. Experimental Methods

[0091] The results were obtained through testing on the experimental platform: .

[0092] Therefore, the dynamic equation of the system is:

[0093]

[0094] In the formula, u(t) is the RDPI hysteresis output fed back from the control signal v(t). The SMA driver platform, such as... Figure 1 As shown, voltage, encoder, and force sensor values ​​are acquired via YX-SPACE and used as the system's input and output.

[0095] Error feedback gain matrix:

[0096] The reference system is:

[0097] .

[0098] The input signal is set as follows: ,frequency The frequencies are 0.05Hz and 0.1Hz.

[0099] First-order filter:

[0100] II. Experimental Results

[0101] from Figure 2 , Figure 3 (a) It can be seen that, given the input RDPI lag H[v](t), the system output follows the desired output trajectory very well. Figure 2 , Figure 3 (b) shows that the maximum tracking error is 0.05 mm, meaning the relative tracking error is approximately 0.5%. From... Figure 2 , Figure 3 (c) It can be seen that the input voltage v(t) changes with the tracking frequency. From Figure 2 , Figure 3 (d) It can be seen that UDE provides good estimation of uncertainties and unknown disturbances for the SMA driver platform. Thus, the UDE-based controller can compensate for the lumped term ud(v(t)), thereby successfully completing the trajectory tracking task. It is worth noting that from... Figure 4 (c) It can be seen that even with disturbances in the input control quantity, the SMA driver can still track the reference signal very well. Figure 4 (a) Therefore, the proposed ude-based controller exhibits such good performance even with the presence of hysteresis uncertainty H[v](t).

[0102] As can be seen from the above embodiments, this invention employs a shape memory alloy rate-dependent Prandtl-Ishlinskii model combined with an uncertainty and disturbance estimation control method to achieve tracking control of the shape memory alloy actuator, thereby improving robustness. Therefore, this invention has excellent application prospects.

Claims

1. A method for uncertainty and disturbance estimation control in shape memory alloy actuators, characterized in that: The shape memory alloy actuator is controlled by the following control signals: in, For control signals, r Let be the radius of the axis of rotation. J Let be the moment of inertia of the axis of rotation. For custom parameters, it is represented as: ， in, It is the inverse operator of the Laplace transform. K The error feedback gain matrix is... To track errors, The shrinkage amount of the shape memory alloy actuator. This is the reference shrinkage amount for the shape memory alloy actuator. Let be the transfer function of the filter. s The symbol for the Laplace transform operator is... , k Let be the spring constant of the load spring. c is the damping coefficient of the rotating shaft.

2. The control method according to claim 1, characterized in that: The The expression is: 。 3. A shape memory alloy actuator, characterized in that: Its movement is controlled by the control method described in claim 1 or 2.

4. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the control method according to claim 1 or 2.

5. A motion system based on a shape memory alloy actuator, characterized in that: It includes a motion mechanism, a shape memory alloy actuator, and the computer device as described in claim 4, wherein the motion mechanism and the shape memory alloy actuator are connected by a transmission mechanism, and the shape memory alloy actuator and the computer device are connected by a signal transmission device.

6. A computer-readable storage medium, characterized in that: It stores a computer program for implementing the control method described in claim 1 or 2.

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