Dielectric elastomer actuator control method based on fractional order creep hysteresis model

Abstract

The invention discloses a dielectric elastomer actuator control method based on a fractional order creep hysteresis model, and relates to the field of intelligent material driving control. The method comprises the following steps: constructing a fractional order creep hysteresis model; creep inverse compensation is carried out on the fractional order creep hysteresis model through an inverse compensator; constructing a second-order system state equation of the dielectric elastomer actuator, and defining a tracking error of the dielectric elastomer actuator based on the second-order system state equation and the expected trajectory of the dielectric elastomer actuator; taking convergence of tracking errors in a preset performance boundary as a constraint condition, approaching a nonlinear function in a second-order system state equation of the dielectric elastomer driver by using a radial basis function neural network, and recursively designing a temporary control law and an adaptive law through a backstepping method; and extracting an actual control signal of the dielectric elastomer actuator through a hysteresis implicit inverse algorithm based on a temporary control law and an adaptive law of a backstepping method recursion design. The method can improve the control precision of the dielectric elastomer actuator.

Description

Technical Field

[0001] The present invention relates to the field of intelligent material drive control, and in particular to a dielectric elastomer actuator control method based on a fractional-order creep hysteresis model. Background Art

[0002] Smart materials, a class of advanced materials with sensing and actuation capabilities, show broad application prospects in areas such as biomimetic robotics, flexible actuators, precision optical alignment, and medical devices. Dielectric elastomer actuators, a typical example, have become a research hotspot in the field of flexible actuation due to their large deformation, high energy density, and lightweight design. However, smart material-driven systems generally exhibit significant nonlinear behavior, including hysteresis and creep, which severely restricts control accuracy and system stability. Dielectric elastomer actuators are a category of smart materials.

[0003] Traditional control methods face multiple challenges in addressing the nonlinearity of dielectric elastomer actuators. Robust control mitigates nonlinear effects by enhancing the system's anti-interference capabilities, but high-gain strategies can result in excessive control input signal amplitudes, hindering practical applications. While inverse model-based feedforward compensation methods can partially eliminate hysteresis, the hysteresis characteristics of dielectric elastomer actuators are typically highly nonlinear and dynamic, making them difficult to accurately describe with traditional static models. Furthermore, creep causes hysteresis behavior to vary over time, further reducing the effectiveness of compensation.

[0004] Therefore, there is an urgent need for a method to improve the control accuracy of dielectric elastomer actuators. Summary of the Invention

[0005] Therefore, it is necessary to provide a control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model to address the above technical issues. This method can improve the control accuracy of the dielectric elastomer actuator.

[0006] The present invention adopts the following technical solutions: The present invention provides a control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model, comprising: Based on the GL fractional-order integral operator and the KP hysteresis model, a fractional-order creep hysteresis model is constructed; the KP hysteresis model is used to describe the hysteresis behavior of the dielectric elastomer actuator under input action; the GL fractional-order integral operator is used to describe the creep characteristics of the dielectric elastomer actuator; The fractional-order creep hysteresis model is subjected to creep inverse compensation through an inverse compensator; the inverse compensator is used to reconstruct and offset the creep nonlinear term in the fractional-order creep hysteresis model; Based on the fractional-order creep hysteresis model after creep inverse compensation, a second-order system state equation of the dielectric elastomer actuator is constructed. Based on the second-order system state equation and the desired trajectory of the dielectric elastomer actuator, the tracking error of the dielectric elastomer actuator is defined. The second-order system state equation is used to describe the state behavior of the dielectric elastomer actuator. With the tracking error of the dielectric elastomer actuator converging within the preset performance boundary as the constraint, a radial basis function neural network is used to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, and the temporary control law and adaptive law are recursively designed through the backstepping method. Based on the temporary control law and adaptive law designed recursively by backstepping method, the actual control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm.

[0007] Preferably, based on the GL fractional-order integral operator and the KP hysteresis model, a fractional-order creep hysteresis model is constructed, including: The output of the KP hysteresis model Convert to , and substitute into the initial fractional-order creep hysteresis model ,get: ; in, is the density function, is the kernel function under different parameters, is a fractional-order operator, is the output of the KP hysteresis model; Will After transformation, the fractional-order creep hysteresis model is obtained as follows: ; in, is the number of combinations, For the distance walk length, Indicates the segmented rounding of the time interval. Represents the cumulative effect of a function delayed over time.

[0008] Preferably, the inverse compensator is: ; in, and is the discretization step size, and Indicates time The piecewise rounding operation, Indicates input voltage The influence of time-varying creep properties, k =0,1,..., , j =0,1,..., , α is the fractional-order integral operator parameter.

[0009] Preferably, creep inverse compensation is performed on the fractional-order creep hysteresis model by an inverse compensator, specifically including: Get the negative fractional order inverse compensator; The coefficients of the fractional-order operation of -α order are integrated through the quadratic coefficient relationship; the quadratic coefficient relationship is: ; when hour, ; when When , the -α-order fractional-order inverse compensator reconstructs and offsets the creep nonlinear term in the fractional-order creep hysteresis model through integral calculation to achieve creep inverse compensation for the fractional-order creep hysteresis model.

[0010] Preferably, with the tracking error of the dielectric elastomer actuator converging within a preset performance boundary as a constraint, a radial basis function neural network is used to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, and a temporary control law and an adaptive law are recursively designed by backstepping, specifically including: For the second-order system state equation, the preset performance function is introduced into the first Lyapunov function of the backstepping method by combining the preset performance control and the backstepping method, and a virtual control law is designed to make the first Lyapunov function positive definite and the derivative negative definite; A radial basis function neural network is used to approximate the nonlinear terms in the state equation of a second-order system. The adaptive law of the radial basis function neural network and the density function is introduced into the second Lyapunov function. A temporary control law and an adaptive law are designed to make the second Lyapunov function positive definite and its derivative negative definite. The second Lyapunov function is composed of polynomials, which include errors, weight estimation errors, and density function estimation errors. Based on the stability analysis of the first Lyapunov function, the virtual control law is derived by controlling the negative derivative of the first Lyapunov function. , to ensure the first-order error convergence; Using radial basis function neural network to analyze the nonlinear function in the state equation of the second order system and Make an approximation; Design of temporary control law based on virtual control law The weight estimation is adjusted online through the adaptive law, and through parameter adjustment and adaptive law design, the derivative of the second Lyapunov function is made less than zero, satisfying the Lyapunov stability, achieving global stability and tracking error convergence.

[0011] Preferably, the second-order system state equation is: ; in, is the output of the fractional-order creep hysteresis model, is the input voltage of the dielectric elastomer actuator, is a bounded perturbation, is the displacement of the dielectric elastomer actuator, is the velocity of the dielectric elastomer actuator, represents the unknown continuous nonlinear mapping of coupled electromechanical effects, Smooth unknown function describing the hyperelastic properties.

[0012] Preferably, the temporary control law and adaptive law designed based on the backstepping method are recursively designed, and the actual control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm, which specifically includes: A controller is constructed; the controller integrates the kernel function of the fractional-order creep hysteresis model with the parameter estimates and relates the adaptive law, the state behavior of the dielectric elastomer actuator, and the tracking error of the dielectric elastomer actuator; the parameter estimates are updated using the adaptive law; the controller is: in, is the weight estimate of the neural network, , are the design parameters of the controller, is the virtual control law, is the velocity of the dielectric elastomer actuator, and is the basis function, is the KP kernel function, is the estimated value of the density function; Obtain the adaptive law of the density function; the adaptive law of the density function is: Get the constraints that the controller satisfies at all times; the constraints are: in, for The maximum value of for The minimum value of is the actual input range of the hysteresis operator; Defining temporary control signals And the hysteresis response corresponding to the temporary control signal ,parameter represents the optimal step length adjustment; Taking the temporary control law as the basis of the hysteresis implicit inverse algorithm, when When the control signal of the dielectric elastomer actuator is ; when When the control signal of the dielectric elastomer actuator is ; when When the initial value Start increasing the adjustment amount and generate a temporary control signal through iterative calculation and its corresponding hysteresis response , when the conditions are met The iteration stops when the condition is met. The value is set to , and define Corresponding control signal of dielectric elastomer actuator .

[0013] The present invention provides a dielectric elastomer actuator control device based on a fractional-order creep hysteresis model, comprising: A building block for constructing a fractional-order creep hysteresis model based on the GL fractional-order integral operator and the KP hysteresis model; the KP hysteresis model is used to describe the hysteresis behavior of a dielectric elastomer actuator under input action; and the GL fractional-order integral operator is used to describe the creep characteristics of the dielectric elastomer actuator. An inverse compensation module is used to perform creep inverse compensation on the fractional-order creep hysteresis model through an inverse compensator; the inverse compensator is used to reconstruct and offset the creep nonlinear term in the fractional-order creep hysteresis model; A definition module is used to construct a second-order system state equation of the dielectric elastomer actuator based on a fractional-order creep hysteresis model after creep inverse compensation, and to define a tracking error of the dielectric elastomer actuator based on the second-order system state equation and a desired trajectory of the dielectric elastomer actuator; the second-order system state equation is used to describe the state behavior of the dielectric elastomer actuator; A design module for approximating the nonlinear function in the second-order system state equation of the dielectric elastomer actuator using a radial basis function neural network, with the tracking error of the dielectric elastomer actuator converging within a preset performance boundary as a constraint, and recursively designing a temporary control law and an adaptive law through a backstepping method; The extraction module is used to extract the actual control signal of the dielectric elastomer actuator through the hysteresis implicit inverse algorithm by designing the temporary control law and adaptive law based on the backstepping method.

[0014] The present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the control method of the dielectric elastomer actuator based on the fractional-order creep hysteresis model is implemented.

[0015] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the control method of the dielectric elastomer actuator based on the fractional-order creep hysteresis model is implemented.

[0016] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects: based on the output of the GL fractional-order integral operator and the KP hysteresis model, this method constructs a fractional-order creep hysteresis model, designs a negative fractional-order inverse compensator, and performs creep inverse compensation on the initial fractional-order creep hysteresis model through the inverse compensator, significantly reducing the interference of the creep effect on the control accuracy; based on the state equation of the dielectric elastomer actuator and the expected trajectory of the dielectric elastomer actuator, the tracking error of the dielectric elastomer actuator is defined; the temporary control law and the adaptive law are recursively designed by the backstepping method, and the nonlinear terms in the state equation of the second-order system are approximated by the radial basis function neural network, so that the tracking error of the dielectric elastomer actuator converges within the preset performance boundary to ensure system stability; the control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm, avoiding the cumulative error problem of traditional feedforward compensation. This method can improve the control accuracy of the dielectric elastomer actuator. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0018] Figure 1 A schematic flow chart of a control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model provided by the present invention; Figure 2 Schematic diagram of fractional creep hysteresis models of different orders provided by the present invention; Figure 3 A schematic diagram of fractional-order identification of creep characteristics of a dielectric elastomer actuator provided by the present invention; Figure 4 Comparison of the control performance of the control scheme provided by the present invention with other control schemes for single signal tracking control; Figure 5 Comparison of the control scheme provided by the present invention with other control schemes for single signal tracking control error; Figure 6 Comparison of the control performance of the control scheme provided by the present invention with other control schemes for composite signal tracking control; Figure 7 Comparison of the control scheme provided by the present invention with other control schemes for composite signal tracking control errors; Figure 8A schematic diagram of the control flow provided by the present invention; Figure 9 A schematic diagram of a dielectric elastomer actuator control device based on a fractional-order creep hysteresis model provided by the present invention; Figure 10 A schematic diagram of a computer device for implementing a control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model provided by the present invention. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0020] Devices such as desktop computers, servers, and laptop computers that can execute the solution of the present invention are described below with the server as the execution subject for the sake of convenience.

[0021] The dynamic response of smart material-driven systems is affected by multiple factors, including material properties, excitation conditions, and environmental factors, which increases the complexity of controller design.

[0022] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0023] Figure 1 The figure is a flow chart of a control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model in the present invention, which specifically includes the following steps: S101: Based on the GL fractional-order integral operator and the KP hysteresis model, a fractional-order creep hysteresis model is constructed; the KP hysteresis model is used to describe the hysteresis behavior of the dielectric elastomer actuator under input action; the GL fractional-order integral operator is used to describe the creep characteristics of the dielectric elastomer actuator.

[0024] A fractional-order integral operator is used to describe the creep characteristics of smart materials. This operator is combined with the KP hysteresis model to form an initial fractional-order creep hysteresis model. The parameters of the initial fractional-order creep hysteresis model are obtained through experimental data identification, enabling it to accurately characterize the dynamic hysteresis nonlinear characteristics of smart materials.

[0025] The initial fractional-order creep hysteresis model is shown in formula (1): (1) in, is the fractional-order creep hysteresis model, is the GL fractional-order operator, is the output of the KP hysteresis model.

[0026] In an exemplary embodiment, a fractional-order creep hysteresis model is constructed based on the GL fractional-order integral operator and the KP hysteresis model, specifically including: The output of the KP hysteresis model Convert to , and substitute into the initial fractional-order creep hysteresis model , we get formula (2) as follows: (2) in, is the density function, is the kernel function under different parameters, is a fractional order operator.

[0027] Will After transformation, the fractional-order creep hysteresis model is obtained as shown in formula (3): (3) in, is the number of combinations, For the distance walk length, Indicates the segmented rounding of the time interval. Represents the cumulative effect of a function delayed over time.

[0028] Specifically, the GL (Grünwald-Letnikov) fractional-order calculus definition is widely used in engineering calculations due to its discretization characteristics, and is particularly suitable for constructing numerical algorithms. In the study of the hysteresis and creep characteristics of smart material actuators, in order to accurately calculate the fractional-order calculus value and design the MATLAB algorithm calculation, the Grünwald-Letnikov fractional-order integral is introduced as shown in formula (4):

[0029] (4) in, For the distance walk length, Indicates the segmented rounding of the time interval. is the number of combinations, reflecting the coefficient characteristics of fractional-order operations, It characterizes the cumulative effect of the function over time and provides a numerical calculation basis for subsequent model construction.

[0030] This definition transforms fractional calculus into a numerically computable discrete form through limit and summation forms.

[0031] This paper combines the GL fractional-order integral operator with the KP (Krasnoselskii-Pokrovskii) model for the first time, proposing a fractional-order creep hysteresis model. The KP hysteresis model is a classic model for describing hysteresis characteristics, and its kernel function can effectively characterize the hysteresis behavior of smart material actuators under input. By introducing a fractional-order integral operator, the model can further incorporate creep characteristics. The specific derivation is shown in Equation (5):

[0032] (5) in, Is the density function, used to characterize the kernel function under different parameters The contribution of the fractional order operator is realized by double integration to achieve a multi-dimensional description of the hysteresis characteristics. The introduction of enables the model to capture the creep nonlinearity of smart materials, breaking through the limitation of traditional models that only describe hysteresis. The characteristics exhibited by the power function (constant) are consistent with the creep nonlinearity exhibited by smart material actuators under DC voltage drive. It can ideally describe the creep degree parameter of smart material actuators. This is the output of the KP hysteresis model, accurately describing the hysteresis characteristics of smart material actuators. This model can simultaneously quantify both hysteresis and creep nonlinear behaviors, providing a more precise theoretical model for the control and application of smart material actuators.

[0033] During the implementation process, the parameters of the fractional-order creep hysteresis model must first be identified using experimental data. Systematic experiments were conducted on a dielectric elastomer actuator. Sinusoidal voltage excitation experiments were performed with amplitudes ranging from 1.5 kV to 3 kV and frequencies ranging from 0.5 to 5 Hz. Constant voltage hold experiments were performed to obtain displacement response data under different voltage conditions. The least-squares method was used to fit the parameters α of the GL fractional-order integral operator and the parameters of the KP kernel function. The specific process involved inputting the experimentally acquired displacement-voltage data into the fitting algorithm. The α value and kernel function parameters were iteratively adjusted, with the mean squared error between the model output and the measured displacement as the optimization objective. By comparing the model output for different values ​​of α (e.g., α∈[-0.5, 0]), the parameter combination was determined that resulted in a less than 5% error between the model output and the measured data within the 0.5-5 Hz frequency band. This process not only validated the model's ability to describe the coupled creep and hysteresis characteristics but also provided an accurate model foundation for subsequent compensation control.

[0034] S102: Performing creep inverse compensation on the fractional-order creep hysteresis model through an inverse compensator; the inverse compensator is used to reconstruct and offset the creep nonlinear term in the fractional-order creep hysteresis model.

[0035] Since some smart materials have obvious creep phenomena, fractional-order inverse operations are used to perform creep compensation after identifying the fractional order of the smart material. Dielectric elastomer brakes are a representative category of smart materials.

[0036] In an exemplary embodiment, creep inverse compensation is performed on the fractional-order creep hysteresis model through an inverse compensator, specifically including: obtaining an inverse compensator of negative fractional order; the inverse compensator is shown in formula (6): (6) in, and is the discretization step size, and Indicates time The piecewise rounding operation, Indicates input voltage The influence of time-varying creep characteristics; Formula (6) transforms the fractional-order operation into a discretized numerical calculation process through the double limit summation form.

[0037] The coefficients of the fractional-order operation of -α order are integrated through the quadratic coefficient relationship, which is shown in formula (7): (7) This combinatorial mathematics plays a key role in coefficient integration in fractional-order operations. By combining the coefficients in the double summation, the derivation of fractional-order integral operations is simplified, providing theoretical support for the subsequent cancellation of creep nonlinearity.

[0038] when hour, ; when When α is used, the -α-order fractional-order inverse compensation reconstructs and offsets the nonlinear terms in the initial fractional-order creep hysteresis model through integral calculation, achieving creep inverse compensation for the initial fractional-order creep hysteresis model. Essentially, this method leverages the integral properties of fractional-order operations to inversely compensate for the creep effect, eliminating creep interference from the output. Ultimately, it effectively suppresses creep nonlinearities in the fractional-order creep hysteresis model, laying the foundation for subsequent system control, such as high-precision trajectory tracking.

[0039] S103: Based on the fractional-order creep hysteresis model after creep inverse compensation, a second-order system state equation of the dielectric elastomer actuator is constructed, and based on the second-order system state equation and the expected trajectory of the dielectric elastomer actuator, the tracking error of the dielectric elastomer actuator is defined; the second-order system state equation is used to describe the state behavior of the dielectric elastomer actuator.

[0040] As a type of smart material actuator, the dynamic behavior of the dielectric elastomer actuator is described by the second-order system state equation, as shown in formula (8): (8) in, Characterize the output of fractional-order creep hysteresis nonlinearity, the response actuator under the input voltage The complex nonlinear behavior caused by creep and hysteresis effect of the material under the action of is a bounded perturbation, is the actuator displacement, For speed, Represents the unknown continuous nonlinear mapping of coupled electromechanical effects, characterizing the conversion relationship from voltage input to mechanical motion, A smooth unknown function describing hyperelastic properties, reflecting the elastic properties of the material.

[0041] S104: With the tracking error of the dielectric elastomer actuator converging within the preset performance boundary as a constraint, a radial basis function neural network is used to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, and the temporary control law and adaptive law are recursively designed through the backstepping method.

[0042] An error transformation function is designed to converge the tracking error of the smart material actuator within a preset performance boundary, improving the control performance of the control system. Backstepping is used in a recursive design to gradually eliminate errors and ensure the stability of the closed-loop system. A radial basis function neural network is used to approximate the unknown nonlinear terms of the system, improving the controller's adaptability.

[0043] In an exemplary embodiment, the tracking error of the dielectric elastomer actuator converges within a preset performance boundary as a constraint condition, and a radial basis function neural network is used to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer driver, and a temporary control law and an adaptive law are recursively designed by backstepping. Specifically, the method includes: for the second-order system state equation, combining the preset performance control and the backstepping method, introducing the preset performance function into the first Lyapunov function of the backstepping method, and designing a virtual control law to make the first Lyapunov function positive definite and the derivative negative definite; using the radial basis function neural network to approximate the nonlinear term in the second-order system state equation, introducing the radial basis function neural network and the adaptive law of the density function into the second Lyapunov function, and designing a temporary control law and an adaptive law to make the second Lyapunov function positive definite and the derivative negative definite; the second Lyapunov function is composed of a polynomial; the polynomial includes an error, a weight estimation error and a density function estimation error; based on the stability analysis of the first Lyapunov function, the virtual control law is derived by controlling the derivative of the first Lyapunov function to be negative definite. To ensure the convergence of the first-order error; use the radial basis neural network to solve the nonlinear function in the state equation of the second-order system and Design a temporary control law based on the virtual control law The weight estimation is adjusted online through the adaptive law, and through parameter adjustment and adaptive law design, the derivative of the second Lyapunov function is made less than zero, satisfying the Lyapunov stability, achieving global stability and tracking error convergence.

[0044] Specifically, to ensure the feasibility and stability of the controller design, the following assumptions are made: Assumption 1: External disturbance satisfies , represents an unknown bounded constant. This assumption limits the range of disturbances and ensures that the controller can handle disturbances robustly during design, thus avoiding system runaway due to unbounded disturbances.

[0045] Assumption 2: Reference trajectory and its derivatives are all located in the compact set The compact set assumption guarantees the continuity and boundedness of the reference trajectory, which is the premise for designing the tracking controller and ensures that the system state will not be untrackable due to sudden changes in the reference trajectory.

[0046] Assumption 3: Without loss of generality, assume , and is a positive constant, so that , there is a constant , making This assumption is for nonlinear mappings It is defined to facilitate the processing of nonlinear terms in subsequent controller design.

[0047] Since its introduction, preset performance control has been recognized for its ability to effectively improve transient system performance (such as overshoot and convergence speed), breaking the limitations of traditional theory that focuses on steady-state performance. Its core concept is to design a boundary function as a constraint envelope, converging the tracking error within the boundary. By adjusting the boundary shape, the convergence speed and overshoot can be controlled.

[0048] definition , Is a performance function that satisfies positive definite and strictly monotonically decreasing conditions, and is continuously differentiable. In order to achieve the specified performance control of the tracking error, the performance function is defined as shown in formula (9):

[0049] (9) in, , is the initial error bound, is the allowable steady-state error boundary, represents the performance function attenuation rate, determines the attenuation speed, and is a predefined positive constant. The convergence region is selected as shown in formula (10):

[0050] (10) In the process of designing the system control law, the convergence region cannot be directly brought into the calculation, so it needs to be converted into an equation for calculation. The function after this conversion is the error conversion function. The error conversion function is now defined as shown in formula (11): (11) according to Formula (12) can be obtained: (12) Define a new variable as shown in formula (13): (13) Backstepping control designs a virtual control law by selecting the Lyapunov function, which obtains the mathematical relationship between the virtual control variable and the state variable. To meet the stability criterion, the Lyapunov function is guaranteed to be positive definite and its derivative is negative definite.

[0051] Define the first Lyapunov function As shown in formula (14): (14) Taking the derivative of formula (14), we get formula (15) (15) in, , To ensure system stability, ,set up , From this we can get formula (16): (16) Multiply both sides of the equation (16) by , we get formula (17): (17) choose ,make sure , the virtual control law is obtained as shown in formula (18): (18) definition , and then take the derivative to get formula (19): (19) Approximating unknown nonlinear functions using radial basis neural networks ,in and is the approximation error, and is the optimal weight, and is the basis function, and the basis function is shown in formula (20): (20) From this we can get formula (21): (twenty one) The designed temporary control law is shown in formula (22): (twenty two) Substituting formula (22) into formula (21), we obtain formula (23): (twenty three) in, is a positive design parameter, , , there exists a constant such that , the system reconstruction error is shown in formula (24): (twenty four) Define the second Lyapunov function As shown in formula (25): (25) Taking the derivative of formula (25), we get formula (26): (26) The adaptive update law is selected as shown in formula (27): (27) By adjusting the parameters are all positive numbers, ensuring , ultimately achieving system stability and ensuring that the tracking error converges according to the preset performance.

[0052] The controller design uses a preset performance backstepping method, combined with a radial basis neural network to online approximate unknown nonlinear terms. First, a performance function including the maximum steady-state error and convergence speed is defined, and the tracking error is mapped to the allowable range through the error transformation function. During the backstepping recursive process, the virtual control law is designed through the Lyapunov function to ensure stability, and the neural network weights are updated in real time by the adaptive law to compensate for the system modeling error. In the experiment, the neural network uses 5 Gaussian basis functions, and the center values ​​are evenly distributed in the input space. The learning rate is set to 0.1 to ensure that the approximation error is less than 0.01mm within 50ms. The hysteresis implicit inverse algorithm determines the actual control input through iterative search, and the single-cycle iteration time is controlled within 0.2ms to ensure real-time performance.

[0053] S105: Based on the temporary control law and adaptive law designed by backstepping method, the actual control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm.

[0054] The final control input signal is extracted by optimizing the search algorithm, avoiding the construction of complex direct inverse models and improving the feasibility and adaptability of control.

[0055] In an exemplary embodiment, a temporary control law and an adaptive law are recursively designed based on the backstepping method, and the actual control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm. Specifically, the controller is constructed; the controller integrates the kernel function of the fractional-order creep hysteresis model with the parameter estimation value, and associates the adaptive law, the state behavior of the dielectric elastomer actuator, and the tracking error of the dielectric elastomer actuator; the parameter estimation value is updated through the adaptive law; the controller is as shown in formula (28): (28) in, is the neural network weight estimate, is the systematic error, is the control parameter; Obtain the adaptive law of density function, which is shown in formula (29): (29) Obtain the constraints that the controller satisfies at all times; the constraints (30) are as follows: (30) in, for The maximum value of for The minimum value of is the actual input range of the hysteresis operator, for KP Kernel function, is the estimated value of the density function.

[0056] Specifically, considering the actual input range of the fractional-order creep hysteresis model , assuming correspond , and the input signal is in the interval Keep monotonous. Constraints are satisfied. The constraints are satisfied at all times.

[0057] make Indicates the adjustment amount and defines the temporary control signal And the hysteresis response corresponding to the temporary control signal ; when When the control signal ; when When the control signal ; when When the initial value Start increasing the adjustment amount and generate a temporary control signal through iterative calculation and its corresponding hysteresis response , when the conditions are met The iteration stops when the condition is met. The value is set to , and define Corresponding control signal .

[0058] The final actual output control signal is ,This process achieves precise compensation control of the hysteresis nonlinear system through a search algorithm.

[0059] The dielectric elastomer film was equibiaxially pre-stretched and fixed to a polymethyl methacrylate (DEA) ring with an inner and outer diameter of 40 mm and 60 mm, respectively. Carbon conductive grease 864-80G was evenly applied to the annular areas on both sides of the DEA, and flexible electrodes were cut and attached. The ring was left to stand for 30 minutes. A 20g load weight was attached to the center of the dielectric elastomer film. The specific actuation process and signal transmission are as follows: First, according to the experimental requirements, a digital drive voltage was input through a MATLAB / Simulink model. The digital voltage signal was converted to an analog drive voltage signal via an NI card (PCIe-6361). At this point, the analog voltage was too small to drive the dielectric elastomer actuator. Therefore, the model drive voltage signal was transmitted to a voltage amplifier (TERK 10 / 40A-HS) and amplified at a fixed gain of 1000 V / V to a sufficient level to drive the dielectric elastomer actuator to produce output displacement. At this point, a laser displacement sensor measures the actuator's output displacement and transmits the resulting analog displacement to an NI card (PCIe-6361), which converts it into a digital displacement signal (i.e., displacement data) and stores it in a computer. Experimental results show that when tracking a composite sinusoidal signal, the maximum tracking error is less than 0.13mm, and the root mean square error is 0.028mm, representing an improvement of over 60% compared to traditional PID control, validating the engineering practicality of this solution.

[0060] This invention effectively overcomes the challenging coupling of dynamic hysteresis and creep nonlinearity faced by intelligent material drive systems in high-precision control by constructing a fractional-order creep hysteresis model and combining it with a preset performance backstepping control strategy. The synergistic effect of fractional-order inverse compensation and an implicit inverse algorithm significantly improves the system's tracking accuracy and dynamic response, enabling engineering applications of the drive system in areas such as micro-nano manipulation and flexible robotics, thus opening up new technical paths for the practical application of intelligent material drive technology.

[0061] Figure 2 is a schematic diagram of the fractional creep KP model of different orders, Figure 2 It can be seen that the fractional-order creep hysteresis model describes the creep and hysteresis nonlinear phenomena very well, and the order of the fractional order represents different creep degrees.

[0062] Figure 3 Schematic diagram of fitting the experimental data of the open-loop DC dielectric elastomer actuator with the fractional creep order identification results. Figure 3 It can be seen that the identified fractional order can well describe the creep phenomenon of the dielectric elastomer brake.

[0063] Figure 4 For a single frequency A tracking control experiment is carried out for the desired trajectory. The proposed preset performance backstepping control scheme can realize that the actual output of the dielectric elastomer actuator accurately tracks the desired trajectory. The proposed preset performance backstepping control scheme is compared with the classic PID control scheme and the backstepping control scheme. From the tracking of the desired trajectory, it can be seen that the proposed control scheme has a better tracking effect on the single frequency signal.

[0064] Figure 5 In the figure, it can be seen from the tracking errors of different tracking strategies that the proposed preset performance backstepping control scheme has a smaller tracking error in the tracking control of a single frequency signal compared with the classic PID control scheme and the backstepping control scheme.

[0065] Figure 6 In the composite frequency A tracking control experiment is carried out to obtain the desired trajectory. The proposed preset performance backstepping control method enables the actual output of the dielectric elastomer actuator to accurately track the desired trajectory. The proposed preset performance backstepping control scheme is compared with the PID control scheme and the backstepping control scheme. From the tracking of the desired trajectory, it can be seen that the proposed control scheme has a better tracking effect.

[0066] Figure 7 In the figure, it can be seen from the tracking errors of different tracking strategies that the proposed preset performance backstepping control scheme has a smaller tracking error in the tracking control of composite frequency signals compared with the classic PID control scheme and the backstepping control scheme.

[0067] In an exemplary embodiment, the present invention provides Figure 8 The control flow chart shown in the figure begins with the desired trajectory input. In the second step, the desired trajectory is compared with the actual output feedback value, and the difference is calculated. In the third step, the difference is input into the preset performance backstepping controller for processing. In the fourth step, the processed result enters the creep inverse model to compensate for creep nonlinearity. In the fifth step, the data calculated by the creep inverse model enters the implicit inverse algorithm for calculation to compensate for hysteresis nonlinearity. In the sixth step, the calculated result is fed back to the comparison stage with the desired trajectory as output and to the fractional-order KP model as input. In the seventh step, the fractional-order KP model data is input into the experimental platform. In the eighth step, the experimental platform generates the actual output and feeds it back to the comparison stage with the desired trajectory, forming a closed loop. The creep inverse model is an inverse compensator, and the fractional-order KP model is a fractional-order creep hysteresis model.

[0068] When applying the dielectric elastomer actuator control method based on the fractional-order creep hysteresis model provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0069] The above is a dielectric elastomer actuator control method based on a fractional-order creep hysteresis model provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding dielectric elastomer actuator control device based on a fractional-order creep hysteresis model, such as Figure 9 shown.

[0070] Figure 9 A schematic diagram of a dielectric elastomer actuator control device based on a fractional-order creep hysteresis model provided by the present invention includes: Construction module 901 is used to construct a fractional-order creep hysteresis model based on the GL fractional-order integral operator and the KP hysteresis model; the KP hysteresis model is used to describe the hysteresis behavior of the dielectric elastomer actuator under input action; the GL fractional-order integral operator is used to describe the creep characteristics of the dielectric elastomer actuator.

[0071] The inverse compensation module 902 is used to perform creep inverse compensation on the fractional-order creep hysteresis model through an inverse compensator; the inverse compensator is used to reconstruct and offset the creep nonlinear term in the fractional-order creep hysteresis model.

[0072] Definition module 903 is used to construct a second-order system state equation of the dielectric elastomer actuator based on the fractional-order creep hysteresis model after creep inverse compensation, and define the tracking error of the dielectric elastomer actuator based on the second-order system state equation and the expected trajectory of the dielectric elastomer actuator; the second-order system state equation is used to describe the state behavior of the dielectric elastomer actuator.

[0073] Design module 904 is used to use a radial basis function neural network to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, with the tracking error of the dielectric elastomer actuator converging within a preset performance boundary as a constraint condition, and to recursively design a temporary control law and an adaptive law through a backstepping method.

[0074] The extraction module 905 is used to extract the actual control signal of the dielectric elastomer actuator through the hysteresis implicit inverse algorithm based on the temporary control law and adaptive law designed by the backstepping method.

[0075] Regarding the specific limitations of the dielectric elastomer actuator control device based on the fractional-order creep hysteresis model, please refer to the limitations of the dielectric elastomer actuator control method based on the fractional-order creep hysteresis model above, which will not be repeated here. The various modules in the above-mentioned dielectric elastomer actuator control device based on the fractional-order creep hysteresis model can be fully or partially implemented by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0076] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 1 A control method for dielectric elastomer actuator based on fractional-order creep hysteresis model is provided.

[0077] The present invention also provides Figure 10 The structural diagram of the computer equipment shown in FIG. Figure 10 As shown in the figure, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1 A control method for dielectric elastomer actuator based on fractional-order creep hysteresis model is provided.

[0078] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware using a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes in the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0079] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A control method for a dielectric elastomer actuator based on a fractional-order creep hysteresis model, characterized in that: include: Based on the GL fractional-order integral operator and the KP hysteresis model, a fractional-order creep hysteresis model is constructed; the KP hysteresis model is used to describe the hysteresis behavior of the dielectric elastomer actuator under input action; the GL fractional-order integral operator is used to describe the creep characteristics of the dielectric elastomer actuator; Performing creep inverse compensation on the fractional-order creep hysteresis model through an inverse compensator; the inverse compensator is used to reconstruct and offset the creep nonlinear term in the fractional-order creep hysteresis model; A second-order system state equation of the dielectric elastomer actuator is constructed based on a fractional-order creep hysteresis model after creep inverse compensation, and a tracking error of the dielectric elastomer actuator is defined based on the second-order system state equation and a desired trajectory of the dielectric elastomer actuator; the second-order system state equation is used to describe the state behavior of the dielectric elastomer actuator; With the tracking error of the dielectric elastomer actuator converging within the preset performance boundary as the constraint, a radial basis function neural network is used to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, and the temporary control law and adaptive law are recursively designed through the backstepping method. Based on the temporary control law and adaptive law designed recursively by backstepping method, the actual control signal of the dielectric elastomer actuator is extracted through the hysteresis implicit inverse algorithm.

2. The method according to claim 1, wherein The fractional-order creep hysteresis model is constructed based on the GL fractional-order integral operator and the KP hysteresis model, including: The output of the KP hysteresis model Convert to , and substitute into the initial fractional-order creep hysteresis model ,get: ； in, is the density function, is the kernel function under different parameters, is a fractional-order operator, is the output of the KP hysteresis model; Will After transformation, the fractional-order creep hysteresis model is obtained as follows: ； in, is the number of combinations, For the distance walk length, Indicates the segmented rounding of the time interval. Represents the cumulative effect of a function delayed over time.

3. The method according to claim 2, wherein The inverse compensator is: ； in, and is the discretization step size, and Indicates time The piecewise rounding operation, Indicates input voltage The influence of time-varying creep properties, k =0,1,..., , j =0,1,..., , α is the fractional-order integral operator parameter.

4. The method according to claim 3, wherein The performing creep inverse compensation on the fractional-order creep hysteresis model by using an inverse compensator specifically includes: Get the negative fractional order inverse compensator; The coefficients of the fractional-order operation of -α order are integrated through the quadratic coefficient relationship; the quadratic coefficient relationship is: ； when hour, ; when When , the -α-order fractional-order inverse compensator reconstructs and offsets the creep nonlinear term in the fractional-order creep hysteresis model through integral calculation, so as to realize creep inverse compensation for the fractional-order creep hysteresis model.

5. The method according to claim 1, wherein The method uses the constraint condition that the tracking error of the dielectric elastomer actuator converges within a preset performance boundary, uses a radial basis function neural network to approximate the nonlinear function in the second-order system state equation of the dielectric elastomer actuator, and recursively designs the temporary control law and the adaptive law through the backstepping method, specifically including: For the second-order system state equation, the preset performance function is introduced into the first Lyapunov function of the backstepping method by combining the preset performance control and the backstepping method, and a virtual control law is designed to make the first Lyapunov function positive definite and the derivative negative definite; The radial basis function neural network is used to approximate the nonlinear terms in the state equation of the second-order system, the adaptive law of the radial basis function neural network and the density function is introduced into a second Lyapunov function, and a temporary control law and an adaptive law are designed to make the second Lyapunov function positive definite and the derivative negative definite; the second Lyapunov function is composed of a polynomial; the polynomial includes an error, a weight estimation error, and a density function estimation error; Based on the stability analysis of the first Lyapunov function, the virtual control law is derived by controlling the negative derivative of the first Lyapunov function. , to ensure the first-order error convergence; Using radial basis function neural network to analyze the nonlinear function in the state equation of the second order system and Make an approximation; Design a temporary control law based on the virtual control law The weight estimation is adjusted online through the adaptive law, and through parameter adjustment and adaptive law design, the derivative of the second Lyapunov function is made less than zero, satisfying the Lyapunov stability, achieving global stability and tracking error convergence.

6. The method according to claim 5, wherein The state equation of the second-order system is: ； in, is the output of the fractional-order creep hysteresis model, is the input voltage of the dielectric elastomer actuator, is a bounded perturbation, is the displacement of the dielectric elastomer actuator, is the velocity of the dielectric elastomer actuator, represents the unknown continuous nonlinear mapping of coupled electromechanical effects, Smooth unknown function describing the hyperelastic properties.

7. The method according to claim 6, wherein The temporary control law and adaptive law designed based on the backstepping method recursively extract the actual control signal of the dielectric elastomer actuator through the hysteresis implicit inverse algorithm, specifically including: A controller is constructed; the controller integrates the kernel function of the fractional-order creep hysteresis model with the parameter estimates, and relates the adaptive law, the state behavior of the dielectric elastomer actuator, and the tracking error of the dielectric elastomer actuator; the parameter estimates are updated through the adaptive law; the controller is: in, is the weight estimate of the neural network, , are the design parameters of the controller, is the virtual control law, is the velocity of the dielectric elastomer actuator, and is the basis function, is the KP kernel function, is the estimated value of the density function; Obtain an adaptive law of the density function; the adaptive law of the density function is: Obtain constraints that the controller satisfies at all times; the constraints are: in, for The maximum value of for The minimum value of is the actual input range of the hysteresis operator; Defining temporary control signals And the hysteresis response corresponding to the temporary control signal ,parameter represents the optimal step length adjustment; Taking the temporary control law as the basis of the hysteresis implicit inverse algorithm, when When the control signal of the dielectric elastomer actuator is ; when When the control signal of the dielectric elastomer actuator is ; when When the initial value Start increasing the adjustment amount and generate a temporary control signal through iterative calculation and its corresponding hysteresis response , when the conditions are met The iteration stops when the condition is met. The value is set to , and define Corresponding control signal of dielectric elastomer actuator .

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