A method for inverse control of a conical dielectric elastomer actuator with input quadratic state constraints

Abstract

The present application relates to a kind of cone-shaped dielectric elastomer actuator (Dielectric Elastomer Actuator, DEA) implicit inverse control method for input square state constraint, aims at effectively reducing the influence of hysteresis on system control performance, and solve the input square full state constraint problem in DEA control, including the following steps: based on traditional Preisach model, input square Preisach model is proposed, the hysteresis modeling when input is voltage square term in DEA system is realized.Combined with Fuzzy Logic System (FLS) and Barrier Lyapunov Function (BLF), a new adaptive fuzzy segmented implicit inverse controller is proposed for DEA system with input square state constraint.Based on the control platform built, compared with the controller without implicit inverse and the traditional Backstepping controller, the accuracy and effectiveness of the designed control strategy are verified, the proposed control algorithm has higher precision, and the high-precision control goal of dielectric elastomer actuator is realized.

Description

Technical Field

[0001] This invention relates to the design of adaptive control methods for precision intelligent material actuators, specifically to a hidden inverse control method for a tapered dielectric elastomer actuator with input square state constraints. Background Technology

[0002] Intelligent material actuators are mainly divided into two categories: rigid and flexible. Rigid intelligent material actuators, such as magnetostrictive actuators and piezoelectric actuators, are primarily used in robotic micro-assembly and optical component processing. Flexible intelligent material actuators, such as dielectric elastomer actuators, have attracted increasing attention due to their high flexibility and safety, playing a crucial role in mechatronics and soft robotics. However, hysteresis nonlinearity inevitably occurs between the input and output of intelligent material actuators, and after modeling, the input signal of intelligent material actuators such as dielectric elastomers is a square term. Studying, modeling, and compensating for the hysteresis characteristics of square-term inputs, and then designing adaptive controllers with square-term inputs, is key to the rational application of flexible intelligent material actuators.

[0003] Hysteresis modeling is currently divided into two main aspects. One is modeling based on differential equations, which is not suitable for controller design. The other is operator-based modeling, which is generally used in controller design. However, current focus is more on hysteresis modeling for inputs with first-order terms. Hysteresis inverse compensation is mainly divided into two schemes: robust adaptive control and adaptive inverse control. Robust adaptive control does not require an inverse model of hysteresis; instead, it treats the hysteresis nonlinearity as a bounded disturbance. While simple to implement, this method has lower accuracy and often suffers from algebraic loop problems. Adaptive inverse control can be divided into direct inverse compensation and implicit inverse compensation. Direct inverse compensation achieves hysteresis cancellation by constructing an inverse model of hysteresis, but accurate inverse models of hysteresis are difficult to construct and sometimes nonexistent. Implicit inverse compensation employs an algorithm that extracts the actual control signal coupled to the hysteresis control signal, avoiding complex inverse model construction and thus greatly eliminating the impact of hysteresis on the system. However, existing implicit inverse compensation schemes are designed for systems with first-order inputs, and the process of extracting the optimal value of the actual control signal usually incurs a heavy computational burden, which significantly impacts real-time control performance.

[0004] To simplify controller design, we often assume the control input is linear to the first power. However, in reality, system modeling, such as dielectric elastomer actuators and magnetic levitation systems, involves input signals that are quadratic terms. Currently, there are few published designs for controllers with quadratic inputs, and these designs suffer from limitations such as requiring all parameters to be known, excessive constraints, low flexibility, and a lack of consideration for system nonlinear hysteresis. Therefore, researching the design of adaptive hysteresis compensation controllers with quadratic inputs and hysteresis has become an important direction for the rational use of precision smart materials such as dielectric elastomers. Furthermore, the states of practical control systems are usually constrained. Barrier Lyapunov functions (BLFs) are widely used to handle state-constrained control problems, but many BLF-based control schemes do not consider the hysteresis nonlinearity in smart material actuators and are all designed for systems with linear inputs. Currently, there is no controller design that combines state constraints, quadratic input signals, and hysteresis in smart material actuators such as dielectric elastomer actuators (DEA). Summary of the Invention

[0005] The purpose of this invention is to provide a hidden inverse control method for a tapered dielectric elastomer actuator with input square state constraints, in order to address the problems raised in the background art.

[0006] The present invention provides a solution using the following technical method:

[0007] In a first aspect, the present invention provides a hidden inverse control method for a tapered dielectric elastomer actuator with input square state constraints, comprising:

[0008] Construct a DEA system model for a tapered dielectric elastomer actuator;

[0009] To address the hysteresis phenomenon in the DEA system model, a Preisach model with squared inputs is constructed.

[0010] Design a hysteresis temporary controller to determine the temporary control signals for the DEA system model;

[0011] Based on the hysteresis segmented implicit inverse compensation strategy, the actual control signal is determined according to the temporary control signal and the Preisach model.

[0012] As a preferred embodiment, the Preisach model is represented as follows:

[0013]

[0014]

[0015] Among them, u 2w(t) and w(t) are the input and output of the Preisach model, respectively, μ(t,α,β) is the weight function, T0=β≥α; α and β are the thresholds.

[0016] As a preferred embodiment, the temporary control signal w(u) of the DEA system model 2 It is determined to be:

[0017]

[0018] e1 = x1 - y r

[0019]

[0020] Where η is a positive design parameter greater than 1, and e1 represents the difference between the actual output x1 and the expected output y of the DEA system model. r The error, e2 represents the speed; For the design parameters, g(x) is a known function; F(x) is an unknown continuous function.

[0021] As a preferred embodiment, the temporary control signal w(u) of the DEA system model 2 The steps for determining ) include:

[0022] The actual output x1 and the expected output y of the system r The error e1 = x1 - y r and speed The DEA system model is transformed as a state variable.

[0023] Take the barrier Lyapunov function as Where log(χ) represents the natural logarithm of χ. γ W For design parameters, and Then the derivative of V(e) is

[0024] Using FLS to approximate the unknown continuous function F(x), let in The optimal weight W in the real-time updated FLS * The estimated value, according to the adaptive law renew And determine the temporary control signal w(u) 2 ), where γ M These are positive design parameters.

[0025] In a preferred embodiment, the step of determining the actual control signal includes:

[0026] According to the temporary control signal w(u) 2 ), to find the actual control signal u 2* (t), satisfying:

[0027]

[0028] in, This is an estimate of the unknown weight function μ(t,α,β);

[0029] Let the actual control signal u 2 The range of (t) is w(t) in The current is monotonically decreasing. Let w be the highest point of the single-loop hysteresis. max (t), the lowest point is w min (t); Definition:

[0030]

[0031] Furthermore,

[0032]

[0033] Define two new variables w l (t) and in It is a positive parameter;

[0034] If w(t) > w max (t), then

[0035] If w(t) < w min (t), then

[0036] If w min (t)≤w(t)≤w max (t), u 2* (t) is obtained by the following steps:

[0037] Step 1: Assume the input range It can be divided into N equal parts, defined and Where i = 1, ..., N-1.

[0038] Step 2: Calculation and if Next, define

[0039] Step 3: Increase l from zero to

[0040] Step 4: Calculation and w l The value of (t), if w l If (t) < w(t), then l continues to increase and returns to Step 4; otherwise, proceed to Step 5.

[0041] Step 5: Stop increasing l, and denote the current l as l0. Define

[0042] The final adaptive control law

[0043] As a preferred embodiment, The estimated value of the unknown weight function μ(t,α,β) is obtained in real time through the following adaptive law:

[0044]

[0045] Where γ μ γ δ These are positive design parameters.

[0046] Real-time acquisition is achieved through the following adaptive law;

[0047]

[0048] Where γ μ γ δ These are positive design parameters.

[0049] As a preferred embodiment, the dynamic model of the DEA system model is expressed as follows:

[0050]

[0051] Where m is the mass of the load (g), g is the acceleration due to gravity, and F s For linear spring force (N), F DEA Let θ be the total radial force of the DE film (N), θ be the angle between the DE film and the horizontal direction, d be the load displacement (mm), and ε be the total radial force of the DE film (N). e Let the elastic strain within the system be represented by the state variable x1 = d. x3=ε e The state-space equations of the DEA system model are as follows:

[0052]

[0053] Where r is the radius of the inner circular plate (mm), μ is the strain shear modulus, ε is the dielectric constant, and z pre The thickness (mm) of the pre-stretched film, l preλ is the radial length (mm) of the pre-stretched film. pre k is the pre-stretch ratio. e and η e K represents the system stiffness coefficient and damping coefficient, respectively. s η is the spring stiffness coefficient (N / mm), d0 is the initial pre-compression of the spring (mm), and η is the spring stiffness coefficient. s Let f(x) be the damping constant of the spring (N·s / mm), g(x) > 0, f(x) be an unknown continuous function, and F s Unknown elastic force given by the spring

[0054] In a preferred embodiment, all states in the DEA system are constrained, satisfying... The constant is a positive constant, and the state-space equations of the DEA system model satisfy the following assumptions:

[0055] Assumption 1: Reference trajectory y r It is known and smooth. Let be a known compact set on all t≥0.

[0056] Assumption 2: g(x) > 0 is known and a positive constant g exists. min and g max , such that 0 < g min <|g(x)|<g max .

[0057] Compared with existing technologies, this invention has the following advantages: Since the input signal of a dielectric elastomer actuator is a square term after modeling, and the system state is usually constrained in practice, there is currently no controller for DEA systems that can solve the above problems. This invention addresses the hysteresis phenomenon between the square input and the model output of a conical DEA model with a spring, which has a square input after modeling. Characteristic analysis was performed, and an input square Preisach model was proposed to model it, achieving good hysteresis fitting results. Furthermore, an adaptive fuzzy piecewise implicit inverse controller with input square hysteresis was designed and implemented. Instead of treating the input signal as a linear term, it treats it as a square term, solving the design problem of the DEA input square hysteresis controller. Experiments were conducted on the constructed conical dielectric elastomer control experimental platform. The experiments show that the proposed control algorithm can effectively alleviate the hysteresis phenomenon between the square input and output. Compared with the experimental results without implicit inverse compensation and the experimental results of the traditional backstepping control algorithm, the error is significantly reduced, proving the effectiveness and accuracy of the proposed control algorithm. Attached Figure Description

[0058] Figure 1The logic diagram of the implicit inverse control method of the tapered dielectric elastomer actuator for input square state constraints provided by the present invention;

[0059] Figure 2 Physical diagram of a conical DEA with a spring provided for this invention.

[0060] Figure 3 The DEA experimental platform and its signal transmission process provided by this invention

[0061] Figure 4 The hysteresis phenomenon in the input squared DEA and the output comparison diagram of the Preisach model provided by this invention.

[0062] Figure 5 The output displacement and single-frequency desired trajectory y under the control algorithm provided by this invention r1 (t)

[0063] Figure 6 The single-frequency expected trajectory y provided by this invention r1 Comparison of tracking errors under (t)

[0064] Figure 7 The output displacement and multi-frequency desired trajectory y under the control algorithm provided by this invention r2 (t)

[0065] Figure 8 The multi-frequency desired trajectory y provided by this invention r2 Comparison of tracking errors under (t) Detailed Implementation

[0066] It should be noted that the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features described herein are detailed descriptions of the technical solution of the present invention, not limitations thereof. Where there is no conflict, the embodiments and technical features described herein can be combined with each other. The term "and / or" merely describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0067] Example 1

[0068] To make the purpose, technical solution, and advantages of this invention patent clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0069] The implementation steps of the proposed method will be described in detail below.

[0070] like Figure 1 As shown, this invention provides a hidden inverse control method for a cone dielectric elastomer actuator with input square state constraints. The main innovative steps of this method are as follows:

[0071] Input squared hysteresis modeling: Using a conical dielectric elastomer actuator as the experimental prototype, and considering the hysteresis nonlinearity between the system's input and output, an input squared Preisach model is proposed to model the hysteresis phenomenon, thus solving the current limitation of modeling hysteresis with squared input terms.

[0072] Design of a DEA controller with input squared state constraints: An adaptive fuzzy piecewise implicit inverse control strategy is proposed, combining state constraints, the squared term of the input signal, and hysteresis in a dielectric elastic body, to achieve the goal of mitigating hysteresis and achieving precise control tracking. Here, implicit inverse compensation means that an exact inverse model of hysteresis is not required; instead, a novel search mechanism is developed to extract the optimal value of the actual squared control signal from the designed hysteresis temporary controller.

[0073] Physical experiment verification: A conical dielectric elastomer-driven motion control platform was built, and comparative experiments were conducted on the proposed control strategy, the control strategy without piecewise implicit inverse compensation, and the traditional backstepping control algorithm to verify the accuracy and effectiveness of the algorithm.

[0074] Through these three key steps, this invention aims to design a novel input-squared adaptive fuzzy piecewise implicit inverse control strategy under the condition of constrained DEA system state, achieving good modeling and control performance, and providing an innovative and comprehensive solution for high-precision DEA operation. The invention is mainly divided into several parts:

[0075] Step 1: Modeling the Conical DEA System. After constructing the DEA system with springs, a dynamic model is established by incorporating factors such as load, inertia, spring force, dielectric elastomer driving force, and damping force. Through the interaction of these factors, the motion characteristics and behavior of the actuator can be accurately described. To further analyze the system's behavior, the state-space equations of the system are established. These equations include multiple system parameters, enabling the simulation of the system's dynamic response and providing the necessary theoretical foundation for subsequent controller design.

[0076] Specifically, in combination Figures 2-3 In this embodiment, a conical dielectric elastomer model with a spring was designed and constructed. The upper part is the load weight, and the lower part is the bias spring. The dielectric elastomer film is a DE film of model VBH4910 produced by 3M. Carbon conductive grease is applied to the upper and lower surfaces of the DE film to provide charge stimulation and attach the electrodes. The support frame is made of acrylic plate and provides pre-stretching of the DE film.

[0077] To achieve precise control of the dielectric elastomer actuator (DEA), a dynamic model of the system is needed to describe the dynamic relationship between the input voltage and the output displacement. In the constructed DEA system, the load is considered as the object of force analysis. The system maintains dynamic equilibrium under the combined action of load gravity, inertial force, spring force, the reaction force of the dielectric elastomer's driving force, and damping force. Taking the horizontal position of the dielectric elastomer when it is not energized as the initial displacement point, and assuming its acceleration is upward, considering actuator dynamics, electromechanical dynamics, and viscoelastic dynamics, based on the driving principle and process of the DEA drive system, its dynamic model can be expressed as follows:

[0078]

[0079] Where m is the mass of the load (g), g is the acceleration due to gravity, and F s For linear spring force (N), F DEA Let θ be the total radial force of the DE film (N), θ be the angle between the DE film and the horizontal direction, d be the load displacement (mm), and ε be the total radial force of the DE film (N). e Let the elastic strain within the system be represented by the state variable x1 = d. x3=ε e Therefore, the state-space equation of the DEA system is obtained as follows:

[0080]

[0081] Where r is the radius of the inner circular plate (mm), μ is the strain shear modulus, ε is the dielectric constant, and z pre The thickness (mm) of the pre-stretched film, l pre λ is the radial length (mm) of the pre-stretched film. pre k is the pre-stretch ratio. e and η e K represents the system stiffness coefficient and damping coefficient, respectively. s η is the spring stiffness coefficient (N / mm), d0 is the initial pre-compression of the spring (mm), and η is the spring stiffness coefficient. s Let be the damping constant of the spring (N·s / mm).

[0082] also, Given that the motion characteristics of DEA satisfy g(x) > 0, f(x) is an unknown continuous function, and F s Given an unknown elastic force from a spring, and considering that all states in the DEA system are constrained, satisfying... It is a positive number. Meanwhile, to continue the controller design, the following assumptions need to be made about system (2):

[0083] Assumption 1: Reference trajectory y r It is known and smooth. Let be a known compact set on all t≥0.

[0084] Assumption 2: g(x) > 0 is known and a positive constant g exists. min and g max , such that 0 < g min <|g(x)|<g max .

[0085] Step 2: Input-squared Preisach Hysteresis Modeling. When the input is a squared term, an input-squared Preisach model is proposed to describe the nonlinear hysteresis characteristics of the system. This model defines the relationship between the squared input and the output and introduces a weighting function to capture the hysteresis effect of the system. This modeling method can effectively reflect the dynamic response of the DEA system under squared inputs, overcoming the limitations of current hysteresis modeling methods. Figure 3 The figure shown is a comparison of the hysteresis phenomenon in the input squared DEA provided by this invention and the output of the Preisach model.

[0086] When the system input is a squared term, the Preisach model for the squared input is defined as follows:

[0087]

[0088] Where u 2 w(t) and w(t) are the input and output of the above equation, respectively, μ(t,α,β) is the weight function, T0=β≥α, and relay operator γ α,β [u 2 ](t) is defined as:

[0089]

[0090] Where α and β are threshold values.

[0091] Step 3: Hysteresis Temporary Controller Design. In designing the hysteresis temporary controller, to handle the hysteresis characteristics of the unknown continuous function, an FLS (Fuzzy Logic System) was introduced to approximate the function. Combined with a barrier Lyapunov function, an adaptive law was designed to update the optimal weights in real time, thereby dynamically adjusting the controller's output and providing an input squared control strategy for the DEA system.

[0092] (3) Hysteresis Temporary Controller Design

[0093] Consider polynomial systems

[0094]

[0095] For positive definite functions definition

[0096]

[0097] If for all x≠0, we have

[0098] b(x) 2 -4a(x)c(x)>0, a(x)≠0 (7)

[0099] Then system (5) can remain stable under the following control law.

[0100]

[0101] Where, w(x) is

[0102]

[0103] Based on the above derivation, the actual system output x1 and the expected output y r The error e1 = x1 - y r and speed As state variables, system (2) is transformed into the following form

[0104]

[0105] in Take the barrier Lyapunov function as

[0106]

[0107] Where log(χ) represents the natural logarithm of χ. γ W For design parameters, and Then the derivative of V(e) is

[0108]

[0109] The calculated values ​​of a(e), b(e), and c(e) are:

[0110]

[0111] Furthermore, in order to satisfy condition, take in η is a positive design parameter greater than 1.

[0112] Using FLS to approximate the unknown continuous function F(x), let in The optimal weight W in the real-time updated FLS * The estimated value is obtained, and the following adaptive law update is designed.

[0113]

[0114] Where γ M For positive design parameters, the temporary control signal w(u) is then used. 2 It can be designed as

[0115]

[0116] in,

[0117] Step 4: Design of Hysteresis Piecewise Implicit Inverse Compensation Algorithm. The design of the hysteresis piecewise implicit inverse compensation algorithm aims to search for the optimal control signal to improve system stability and controller performance. The core idea of ​​this algorithm is to find an optimal virtual control signal based on the temporary control signal and estimate the unknown weight function in real time using an adaptive law. During the design process, the range of the actual control signal is divided into multiple equal parts, and the optimal control signal is gradually approximated through incremental and stepwise search methods, ensuring that the system can effectively cope with hysteresis characteristics and providing an efficient solution for hysteresis compensation of the input squared DEA.

[0118] The designed control signal is coupled to the hysteresis temporary controller w(u) 2 In order to extract from w(u) 2 To extract the actual control signal from the integral expression, we designed a hysteresis segmented implicit inverse compensation strategy. The design idea and steps are as follows:

[0119] According to the temporary control signal w(u) 2 To find an optimal virtual control signal that satisfies...

[0120]

[0121] in, The estimated value of the unknown weight function μ(t,α,β) is obtained in real time through the following adaptive law.

[0122]

[0123] Where γ μ γ δ Let u be the positive design parameter. 2 The range of (t) is w(t) in The current is monotonically decreasing. Let w be the highest point of the single-loop hysteresis. max (t), the lowest point is w min (t), defined

[0124]

[0125] Furthermore,

[0126]

[0127] Next, define two new variables w. l (t) and in Let be a positive parameter. Then there is

[0128]

[0129] If w(t) > w max (t), then

[0130] If w(t) < w min (t), then

[0131] If w min (t)≤w(t)≤w max (t), u 2* (t) is obtained by the following steps:

[0132] Step 1: Assume the input range It can be divided into N equal parts, defined and Where i = 1, ..., N-1.

[0133] Step 2: Calculation and if Next, we define

[0134] Step 3: Increase l from zero to

[0135] Step 4: Calculation and w l The value of (t), if w l If (t) < w(t), then l continues to increase and returns to Step 4; otherwise, proceed to Step 5.

[0136] Step 5: Stop increasing l, and denote the current l as l0. Define

[0137] Using the above piecewise implicit inverse compensation search method, the final adaptive control law should be selected as:

[0138]

[0139] Since the input signal of a dielectric elastomer actuator (DEA) is a square term after modeling, and the system state is usually constrained in practice, there is currently no controller for DEA systems that can solve the above problems. This invention addresses the hysteresis phenomenon between the squared input and the model output of a conical DEA model with a spring, which has a squared input after modeling. Characteristic analysis was performed, and an input squared Preisach model was proposed to model it, achieving good hysteresis fitting results. Furthermore, an adaptive fuzzy piecewise implicit inverse controller with input squared hysteresis was designed and implemented. Instead of treating the input signal as a linear term, it treats it as a squared term, solving the design problem of the DEA input squared hysteresis controller. Experiments were conducted on the constructed conical dielectric elastomer control experimental platform. The experiments show that the proposed control algorithm can effectively alleviate the hysteresis phenomenon between the squared input and output. Compared with the experimental results without implicit inverse compensation and the experimental results of the traditional backstepping control algorithm, the error is significantly reduced, proving the effectiveness and accuracy of the proposed control algorithm.

[0140] Example 2

[0141] Based on specific experimental data, this invention proposes an adaptive piecewise implicit inverse compensation control strategy for a state-constrained dielectric elastomer system with input square. Building upon the constructed conical DEA system, an input square Preisach model is proposed to describe the hysteresis phenomenon between the DEA system's input and output. Furthermore, an adaptive piecewise implicit inverse compensation control is designed by combining a fuzzy logic system (FLS) and a barrier Lyapunov function. Experiments verify the effectiveness and accuracy of the proposed hysteresis modeling and control algorithm.

[0142] To demonstrate the effectiveness and accuracy of the proposed input-squared adaptive piecewise implicit inverse control algorithm, a closed-loop control experiment was conducted on the constructed DEA control experimental platform. In the controller design, the initial values ​​of the parameters to be updated in the adaptive law were set to... The initial values ​​of the system state vector, as measured, are x1(0) = 0 and x2(0) = 0. The fuzzy basis function vector is h(ζ) = [h 1 (ζ),h 2 (ζ),h 3 (ζ),h 4 (ζ),h 5 (ζ)] T Choose b in the fuzzy membership function i =5, center point Where i = 2, j = 5. Under the same conditions, comparative experiments will be conducted with a control strategy without implicit inverse compensation and a traditional backstepping control strategy. The reference trajectory for Experiment 1 is y. r1(t)=0.25sin(0.4πt)+0.8, the controller design parameters are selected as k1=3.5, k2=0.01, η=0.01, γ W =1.5, γ μ =0.001;

[0143] The reference trajectory for Experiment 2 is y r2 (t) = 0.1sin(0.2πt) + 0.2sin(0.1πt) + 0.1sin(0.3πt) + 1.5, and the controller design parameters are selected as follows: η = 2, γ W =0.05, γ M =0.01γ μ =0.001,γ δ =0.001.

[0144] Combination Figures 5-8 ,like Figure 5 The figure shows the output displacement and single-frequency desired trajectory y under the control algorithm provided by this invention. r1 (t), such as Figure 6 The single-frequency expected trajectory y provided by this invention r1 The tracking error comparison chart under (t) is shown below. Figure 7 The figure shows the output displacement and multi-frequency desired trajectory y under the control algorithm proposed in this invention. r2 (t), such as Figure 8 The figure shows the multi-frequency desired trajectory y provided by the present invention. r2 Comparison of tracking errors under (t)

[0145] To further illustrate the effectiveness of the proposed control scheme, three methods will be used to describe the tracking error: maximum absolute error (MAE), standard root mean square error (NRMSE), and the second norm of the tracking error (2NTE), which are defined as follows:

[0146]

[0147] Further analysis reveals that the proposed control scheme exhibits lower MAE, NRMSE, and 2NTE compared to the control scheme without piecewise implicit inversion and the traditional backstepping scheme. In Experiment 1, compared to the scheme without implicit inversion compensation, MAE, NRMSE, and 2NTE are reduced by nearly 4 times; compared to the traditional backstepping control algorithm, MAE is reduced by nearly 10 times, NRMSE by nearly 4 times, and 2NTE by nearly 5.5 times. In Experiment 2, compared to the control scheme without piecewise implicit inversion, MAE is reduced by nearly 1.5 times, NRMSE by nearly 7 times, and 2NTE by nearly 3.6 times; compared to the traditional backstepping control algorithm, MAE is reduced by nearly 7 times, NRMSE by nearly 2.5 times, and 2NTE by nearly 2.7 times. These experimental results demonstrate that the proposed control algorithm possesses strong robustness and adaptability, and can meet the high-precision control performance requirements of dielectric elastomer systems.

[0148] This invention solves the problems of hysteresis and controller design in dielectric elastic systems under input square state constraints. Compared with control algorithms without implicit inverses and traditional backstepping algorithms, the experimental results show a significant reduction in error.

[0149] The achievement of higher precision and stability demonstrates the effectiveness and accuracy of the proposed control algorithm, providing a new high-precision control strategy for precision smart material DEA.

[0150] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0151] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0152] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0154] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for implicit inverse control of a cone dielectric elastomer actuator with input square state constraints, characterized in that, Comprising: constructing a DEA system model of a conical dielectric elastomer actuator; constructing an input-squared Preisach model for hysteresis phenomena of the DEA system model; designing a hysteresis provisional controller to determine a provisional control signal of the DEA system model; determining an actual control signal based on a hysteresis piecewise inverse compensation strategy according to the provisional control signal and the Preisach model; the Preisach model is expressed as: wherein, and are the input and output of the Preisach model, respectively, is a weight function, ; and is a threshold value; The temporary control signal of the DEA system model It is determined that: wherein, is a positive design parameter greater than 1, denotes the error of the actual output of the DEA system model from the desired output , denotes the velocity error; , is a design parameter, is a known function; is an unknown continuous function; The temporary control signal of the DEA system model The determining step comprises: with the system actual output and the desired output error and velocity as state variables into ; is the linear spring force; is the mass of the load weight; The Lyapunov function is taken as ; wherein, represents the natural logarithm of , , is a design parameter, and , then the derivative of ; Approximating unknown continuous functions using FLS , let where is an estimate of the optimal weight in the FLS updated in real time according to the adaptive law update and determine the temporary control signal where is a positive design parameter; the step of determining the actual control signal comprises: According to the provisional control signal , find the actual control signal , satisfy: wherein is an estimate of the unknown weight function w(x). Assume the actual control signal The range is , exist The current is monotonically decreasing. Let the highest point of the single-loop hysteresis be... The lowest point is ;definition further comprising Define two new variables and where is a positive parameter; If , then ; If , then ; If , then by the following steps: Step 1: Assume the range of input Can be divided into N equal parts, define And Where ; Step 2: Calculate and ; if , then define , ; Step 3: Let increase from zero to ; Step 4: Calculate and If then Continue to increase and go back to Step 4; otherwise go to Step 5; Step 5: Let the increase stop and record the time as , define ; Final adaptive control law .

2. The inverse control method of the conical dielectric elastomer driver according to claim 1, wherein unknown weight function is estimated by the following adaptive law in real time: is obtained in real time by the following adaptation law; wherein , is a positive design parameter.

3. The inverse control method of the conical dielectric elastomer driver according to claim 1, wherein a dynamic model of the DEA system model is expressed as: wherein, is the mass of the load (g), is the acceleration of gravity, is the linear spring force (N), is the total radial force of the DE film (N), is the angle of the DE film with the horizontal direction, is the load displacement (mm), is the internal elastic strain of the system, assuming the state variable , , ; the state space equation of the DEA system model is: in, The radius (mm) of the inner circular plate. For strain shear modulus, Where is the dielectric constant. The thickness (mm) of the pre-stretched film. The radial length (mm) of the pre-stretched film. This is the pre-stretch ratio. and These represent the system stiffness coefficient and damping coefficient, respectively. is the stiffness coefficient of the spring (N / mm). The initial pre-compression of the spring is (mm). Let be the damping constant of the spring (N·s / mm). , For an unknown continuous function, It is a linear spring force.

4. The inverse control method of the conical dielectric elastomer driver according to claim 1, wherein, All states in the DEA system are constrained, satisfying , are real numbers, and the state space equation of the DEA system model satisfies the following assumptions: Assumption 1: The reference trajectory is known and smooth, is a known compact set in all ; Assumption 2: known and there exists a positive number and such that .

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