A piezoelectric ceramic actuator driven by asymmetric voltage

Abstract

The invention discloses an asymmetric voltage-driven piezoelectric ceramic driver, which relates to the technical field of piezoelectric ceramic drivers. The invention comprises the following steps: step one, establishing a hysteresis model; step two, identifying model parameters; step three, designing a linearization controller; and step four, designing an active vibration suppression controller. The invention solves the influence of nonlinear characteristics such as hysteresis and creep existing in piezoelectric ceramic materials on system performance, selects an appropriate hysteresis model, and selects a corresponding control method according to the model to realize the linearization of the piezoelectric ceramic driver. The linearized piezoelectric ceramic driver is used as a microcontroller, and a corresponding vibration control algorithm is selected to perform double-degree-of-freedom decoupling and control of vibration.

Description

Technical Field

[0001] The invention belongs to the technical field of piezoelectric ceramic driving, and in particular relates to a piezoelectric ceramic driver driven by an asymmetric voltage. Background Art

[0002] Piezoelectric ceramic actuators are a type of intelligent material with excellent performance. They have outstanding advantages such as large force, high stiffness, high control accuracy, low power consumption, and fast response speed. Therefore, they have been widely used in applications such as micro-manipulation, micro-robotic arms, active optical components, active vibration control, and biomedical engineering. In applications where piezoelectric ceramic actuators are used for active vibration control, low-frequency vibrations below 100 Hz are mainly targeted. At this time, traditional passive vibration isolation methods are difficult to work. Piezoelectric ceramic actuators are used to generate motion that is equal to the magnitude of the vibration wave and opposite to the direction, thereby weakening the vibration amplitude. In this process, the piezoelectric ceramic actuator is required to accurately track the reference signal whose amplitude and frequency change randomly and continuously. Therefore, the nonlinearities such as its hysteresis characteristics and creep characteristics, as well as the modeling accuracy of these nonlinear characteristics following the change of the motion frequency, will significantly affect the performance of the active vibration isolation control method. Its creep characteristics and rate-dependent hysteresis characteristics such as Figure 1 and Figure 2 In the existing literature, although some research results are given for the modeling and control methods of the rate-dependent nonlinear characteristics of piezoelectric ceramic actuators at different frequency points, the existing modeling methods still have great deficiencies in describing the nonlinear characteristics of the continuous random change of tracking frequency. Summary of the invention

[0003] To solve the problems in the background technology, the present invention aims to provide a piezoelectric ceramic driver driven by an asymmetric voltage.

[0004] The present invention provides an asymmetric voltage driven piezoelectric ceramic driver, comprising the following steps:

[0005] Step 1: Establish hysteresis model:

[0006] A rate-dependent hysteresis nonlinear model based on the improved Bouc-Wen model and the fractional-order model is adopted; the static nonlinear part of the Hammerstein model is described by the improved Bouc-Wen model, and the linear dynamic part is described by the fractional-order model;

[0007] 1.1. Improved Bouc-Wen hysteresis model:

[0008] The classic Bouc-Wen model was introduced by Bouc and expanded by Wen. The improved Bouc-Wen model is used to describe the asymmetric nature of the piezoelectric actuator input and output, which is asymmetric about the origin, by defining l(t)=l(u(t)) as a generalized input function, i.e., a function of the input voltage u(t).

[0009] 1.2. Fractional order dynamics model:

[0010] When the ARX model is used to describe the dynamic characteristics, the output at the current moment is determined not only by the input at the current moment, but also by the input and output at all previous moments; when the integer-order model is used to describe the dynamic characteristics, it is necessary to analyze the dynamic characteristics of the piezoelectric actuator and estimate the redundant parameters that affect the robustness in the control application; while the fractional-order system is considered to have improved robustness in the control design, and only needs input and output data to model without dynamic analysis; fractional-order calculus is a generalization of integer-order integration and differentiation to all real numbers;

[0011] Step 2: Model parameter identification:

[0012] The calculation process of the artificial bee colony algorithm mainly includes three stages: leading bees, following bees and scout bees. When using the artificial bee colony algorithm to identify model parameters, each food source represents a feasible solution to the model parameters, the amount of nectar (fitness) represents the quality of the solution, and the number of solutions is equal to the number of leading bees. The root mean square error (RMSE) is introduced as the fitness function of DE-ABC to reflect the modeling error.

[0013] Step 3: Linear controller design:

[0014] 3.1. Composite controller:

[0015] According to the improved Bouw-Wen model mentioned above, the inverse model is solved. When the expected trajectory is y r (t), design a compensator based on the inverse model to determine the input voltage of the piezoelectric actuator as u(t); so that the desired displacement y of the piezoelectric micro-positioning platform r (t) and the actual output displacement y(t) are linearized to eliminate the hysteresis nonlinearity; the sliding mode feedback control is combined with it to design a composite closed-loop controller.

[0016] 3.2 Sliding mode controller:

[0017] In order to design a sliding mode controller, it is necessary to design a fractional-order sliding surface and a suitable control signal so that the state trajectory reaches the sliding surface and remains on the sliding surface;

[0018] 3.2.1. Design the sliding surface according to the determined piezoelectric actuator system model;

[0019] 3.2.2. The design of the sliding mode reaching law usually adopts the sign function sgn(x). Due to the discontinuity of the sign function, the control input will oscillate. Selecting a suitable reaching law can eliminate the oscillation.

[0020] 3.2.3. Obtain the control input u(t) and perform stability analysis and proof on the obtained controller;

[0021] Step 4: Active vibration suppression controller:

[0022] The system has coupling in the X and Y directions, so the motion variables need to be converted into generalized variables, and the vibration control system is designed based on the generalized system. Finally, the calculated control force is converted into the generalized control force. The Jacobian matrix is ​​used to convert the generalized control force into the desired control force of the actuator, and the piezoelectric actuator hysteresis linearization controller proposed above is used to solve the piezoelectric driver that feeds back the driving voltage to the vibration isolation platform. In the decoupling control of the active vibration suppression system, the overall MISO system is decoupled into two SISO vibration isolation systems for independent control.

[0023] As a preferred embodiment, the improved Bouc-Wen model expression is:

[0024] x(t)=l[u(t)]-z(t)=[xu 2 (t)+yu(t)]-z(t)

[0025]

[0026] Where x(t) is the output displacement of the actuator; l[u(t)] is the non-singular input function; z(t) is the hysteresis displacement component; is the time derivative of z(t); u(t) represents the input voltage; is the time derivative of u(t); x and y control the asymmetry of the input signal; α controls the size of the hysteresis loop; β and γ control the shape of the hysteresis loop respectively; n represents the smoothness of the transition from the elastic part to the plastic part; by properly selecting the model parameters, it can represent various hysteresis phenomena in various shapes.

[0027] Preferably, the basic operator of the fractional calculus is is defined as:

[0028]

[0029] Where t0 and t are the lower and upper boundaries of the integral respectively, α is the fractional order, which can be a complex number, and Re(α) is the real part of α;

[0030] There are many definitions of fractional calculus, the most commonly used of which are the Grunwald–Letnikov (GL) definition and the Riemann–Liouville (RL) definition. The approximate calculation of the GL definition is used to perform numerical simulation of fractional operators. The GL definition is given as:

[0031]

[0032] Fractional-order systems can be represented by fractional-order linear differential equations in the form of:

[0033]

[0034] Where u(t) and x(t) are the system input and output respectively. α x(t) is the αth time derivative of x(t); if the initial condition is zero, then D α The Laplace transform of x(t) is:

[0035] L{D α x(t)}=s α X

[0036] Take the Laplace transform of both ends of the above equation; the fractional-order linear time-invariant system can be rewritten as the following transfer function form:

[0037]

[0038] Where α0<α1<…<α n , and β0<β1<…<β m .

[0039] Preferably, the fitness function formula of DE-ABC is as follows:

[0040]

[0041] where y exp is the sampling value of the experimental data, y is the sampling value of the model data, N is the number of sampling points, and each solution x i (i=1,2,…) with a D-dimensional vector x i =(x i1 , x i2 , …, x iD ) T To represent, D is the number of model parameters to be identified.

[0042] The specific process of DE-ABC identification is as follows:

[0043] (1) Obtaining experimental input and output data;

[0044] (2) Setting initial conditions and number of parameters;

[0045] (3) Parameter identification based on DE-ABC;

[0046] (4) Verification: If the fitness does not meet the requirements, return to (2) and continue identification.

[0047] DE-ABC introduces the mutation strategy of the differential evolution algorithm into the artificial bee colony algorithm. In the search of the leading bee, the search of the leading bee is carried out according to the following formula:

[0048] x ij ′=x best,j +F i ×(x ij -x kj )

[0049] Here, x best,j is the best individual of the previous generation, j∈{1,2,…,D}, k∈{1,2,…,N}, j and k are randomly selected, but j≠k, F i It is no longer a constant used in traditional ABC, but an adaptive and dynamically adjusted variable as shown in the following formula; where Iter is the maximum number of iterations and iter is the current number of iterations;

[0050]

[0051] In the early stages of algorithm evolution, iter is small and F i The larger the algorithm mutation intensity, the more effective and rapid the evolution to the optimal value. As the evolution continues, in the later stage of algorithm evolution, iter becomes larger, and F i becomes smaller, and as the individual evolves towards the optimal value, the function can converge to the optimal value quickly and stably;

[0052] In traditional ABC, if a solution x i If there is still no improvement after L cycles, the solution will be abandoned by the leading bee, and the leading bee will become a scout bee to randomly generate a new solution to replace it; in the DE-ABC used, chaotic search is introduced into the identification algorithm.

[0053] Chaotic search uses the chaotic sequence generated by Logistic chaotic mapping to replace the random numbers in the traditional ABC formula;

[0054] The Logistic chaos mapping equation is as follows:

[0055] C n+1 =4C n (1-C n )

[0056] Among them, 0<C n<1; let the solution where the search stops be x i =(x i1 , x i2 , …, x iD ), the main steps of the chaotic search of the scout bee are as follows:

[0057] (1) The initial value of the chaotic sequence is generated according to the following formula;

[0058]

[0059] (2) Generate chaotic sequence according to the chaotic mapping equation;

[0060] (3) Generate a new solution as follows, calculate its fitness value, compare it with the original solution, and retain the best solution;

[0061] x ij ′=x i,j +C ij ×(x max,j -x min,j )

[0062] (4) If the maximum number of chaotic iterations is reached, the search ends, otherwise go to step (2);

[0063] Among them, x min,j is the minimum value of the jth dimension obtained so far, x max,j is the maximum value of the j-th dimension obtained so far;

[0064] When the input signal frequency is lower than 5Hz, the hysteresis loop of the piezoelectric ceramic driver hardly changes. Therefore, the input and output data of the piezoelectric driver at an input frequency of 1Hz are used to establish a static Bouc-Wen model, which reflects the static hysteresis characteristics of the piezoelectric driver. A sine sweep signal with a frequency range of 0-100Hz is generated by Matlab as the input of the Bouc-Wen model. The output data of the Bouc-Wen model is used as the input of the fractional-order model, and the output data of the experimental equipment of the collected sweep signal is used as the output of the fractional-order model. The DE-ABC algorithm is used to identify the parameters of the fractional-order model through the input and output data of the above-mentioned fractional-order model.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. Solve the impact of nonlinear characteristics such as hysteresis and creep of piezoelectric ceramic materials on system performance, select an appropriate hysteresis model, and select the corresponding control method based on the model to achieve linearization of the piezoelectric ceramic driver.

[0067] Second, use the linearized piezoelectric ceramic driver as a microcontroller, select the corresponding vibration control algorithm, and decouple and control the vibration in two degrees of freedom. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] For ease of explanation, the present invention is described in detail with reference to the following specific implementations and the accompanying drawings.

[0069] Figure 1 It is a structural schematic diagram of a creep characteristic curve in the background technology;

[0070] Figure 2 It is a schematic diagram of a rate-dependent hysteresis characteristic curve in the background technology;

[0071] Figure 3 It is a schematic diagram of the Hammerstein model structure of the piezoelectric actuator in the present invention;

[0072] Figure 4 This is a flow chart of the artificial bee colony algorithm in the present invention;

[0073] Figure 5 This is a principle block diagram of the composite controller in the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is described below by the specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. The structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions that the present invention can be implemented, so they have no technical substantive significance. Any structural modification, change in proportional relationship or adjustment of size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope of the technical content disclosed by the present invention. In addition, in the following description, the description of known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0075] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, only structures and / or processing steps closely related to the solutions according to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0076] This specific implementation adopts the following technical solutions:

[0077] 1. Establish hysteresis model:

[0078] Currently, there is no unified mathematical model for nonlinear systems. The Hammerstein model, as a nonlinear model based on module connection, can more accurately describe the rate-dependent characteristics of the piezoelectric actuator. In this specific implementation, a rate-dependent hysteresis nonlinear model based on an improved Bouc-Wen model and a fractional-order model is used. The static nonlinear part of the Hammerstein model is described by the improved Bouc-Wen model, and the linear dynamic part is described by the fractional-order model. The structure is as follows: Figure 3 shown.

[0079] 1.1. Improved Bouc-Wen hysteresis model:

[0080] The classic Bouc-Wen model was introduced by Bouc and expanded by Wen. Compared with other models describing hysteresis characteristics, the Bouc-Wen model contains fewer parameters and can be identified with less data. However, in actual situations, the piezoelectric driver input has an inherent asymmetric nature of a multi-valued memory-dependent hysteresis loop. Therefore, an improved Bouc-Wen model is used to describe the asymmetric nature of the piezoelectric driver input and output, which is concerned with the asymmetry of the origin, by defining l(t) = l(u(t)) as a generalized input function, that is, a function of the input voltage u(t). The improved Bouc-Wen model is expressed as:

[0081] x(t)=l[u(t)]-z(t)=[xu 2 (t)+yu(t)]-z(t)

[0082]

[0083] Where x(t) is the output displacement of the actuator; l[u(t)] is the non-singular input function; z(t) is the hysteresis displacement component; is the time derivative of z(t); u(t) represents the input voltage; is the time derivative of u(t); x and y control the asymmetry of the input signal; α controls the size of the hysteresis loop; β and γ control the shape of the hysteresis loop respectively; n represents the smoothness of the transition from the elastic part to the plastic part. By properly selecting the model parameters, it can represent a variety of hysteresis phenomena with various shapes.

[0084] 1.2. Fractional order dynamics model:

[0085] Most Hammerstein models use integer-order calculus models or autoregressive (ARX) models to describe the dynamic characteristics of piezoelectric actuators, which often ignores some real phenomena and properties with fractional-order characteristics. When the ARX model is used to describe the dynamic characteristics, the output at the current moment is determined not only by the input at the current moment, but also by the input and output at all previous moments. The fractional-order model can be a good substitute for the ARX model due to its long memory characteristics. When the integer-order model is used to describe the dynamic characteristics, it is necessary to analyze the dynamic characteristics of the piezoelectric actuator and estimate the redundant parameters that affect the robustness of the control application. The fractional-order system is considered to have improved robustness in control design, and only input and output data are needed to model without dynamic analysis. Due to the mathematical characteristics of fractional globality and long memory, it has the advantages of the ARX model and can use fewer parameters to model complex systems. It has been widely used in physics and control. The fractional-order Hammerstein model avoids complex internal mechanism analysis on the basis of obtaining good modeling accuracy.

[0086] Fractional calculus is a generalization of integer-order integrals and differentials to all real numbers. is defined as:

[0087]

[0088] where t0 and t are the lower and upper bounds of the integral, α is the fractional order, which can be a complex number, and Re(α) is the real part of α.

[0089] There are many definitions of fractional calculus, the most commonly used of which are the Grunwald–Letnikov (GL) definition and the Riemann–Liouville (RL) definition. The approximate calculation of the GL definition is used to perform numerical simulation of fractional operators. The GL definition is given as:

[0090]

[0091] Fractional-order systems can be represented by fractional-order linear differential equations in the form of:

[0092]

[0093] Where u(t) and x(t) are the system input and output respectively. α x(t) is the αth time derivative of x(t). If the initial condition is zero, then D α The Laplace transform of x(t) is:

[0094] L{D α x(t)}=s α X

[0095] Take the Laplace transform of both ends of the above equation. The fractional-order linear time-invariant system can be rewritten as the following transfer function form:

[0096]

[0097] Where α0<α1<…<α n , and β0<β1<…<β m .

[0098] 2. Model parameter identification:

[0099] Compared with other algorithms, the artificial bee colony algorithm has an obvious feature that it requires fewer parameters to be set, is simple to operate, and has higher search efficiency. Figure 4 shown.

[0100] The calculation process of the artificial bee colony algorithm mainly includes three stages: leading bees, following bees, and scout bees. When using the artificial bee colony algorithm to identify model parameters, each food source represents a feasible solution to the model parameters, the amount of nectar (fitness) represents the quality of the solution, and the number of solutions is equal to the number of leading bees. The root mean square error (RMSE) is introduced as the fitness function of DE-ABC to reflect the modeling error. The formula is as follows:

[0101]

[0102] where y exp is the sampling value of the experimental data, y is the sampling value of the model data, N is the number of sampling points, and each solution x i (i=1,2,…) with a D-dimensional vector x i =(x i1 , x i2 , …, x iD ) T To represent, D is the number of model parameters to be identified.

[0103] The specific process of DE-ABC identification is as follows:

[0104] (5) Obtain the input and output data of the experiment.

[0105] (6) Set the initial conditions and number of parameters.

[0106] (7) Parameter identification based on DE-ABC.

[0107] (8) Verification. If the fitness does not meet the requirements, return to (2) to continue identification.

[0108] DE-ABC introduces the mutation strategy of the differential evolution algorithm into the artificial bee colony algorithm. In the search of the leading bee, the search of the leading bee is carried out according to the following formula.

[0109] x ij ′=x best,j +F i ×(x ij -x kj )

[0110] Here, x best,j is the best individual of the previous generation, j∈{1,2,…,D}, k∈{1,2,…,N}, j and k are randomly selected, but j≠k, F i It is no longer a constant used in traditional ABC, but an adaptive and dynamically adjusted variable as shown in the following formula: Iter is the maximum number of iterations, and iter is the current number of iterations.

[0111]

[0112] In the early stages of algorithm evolution, iter is small and F i The larger the algorithm mutation intensity, the more effective and rapid the evolution to the optimal value. As the evolution continues, in the later stage of algorithm evolution, iter becomes larger, and F i becomes smaller, and as the individual evolves towards the optimal value, the function can converge to the optimal value quickly and stably.

[0113] In traditional ABC, if a solution x i After L cycles, if there is still no improvement, the solution will be abandoned by the leading bee, and the leading bee will become a scout bee to randomly generate a new solution to replace it. In the DE-ABC used, chaotic search is introduced into the identification algorithm.

[0114] When a solution is not improved after L cycles, it may be trapped in a local optimum. The scout bee will perform a chaotic search to jump out of the local optimum. The chaotic search here uses the chaotic sequence generated by the Logistic chaotic map to replace the random number in the traditional ABC formula. The Logistic chaotic map equation is as follows:

[0115] C n+1 =4C n (1-C n )

[0116] Among them, 0<C n <1. Let the solution where the search is stagnant be x i =(x i1 , x i2 , …, x iD ), the main steps of the chaotic search of the scout bee are as follows:

[0117] (1) The initial value of the chaotic sequence is generated according to the following formula;

[0118]

[0119] (2) Generate chaotic sequence according to the chaotic mapping equation;

[0120] (3) Generate a new solution as follows, calculate its fitness value, compare it with the original solution, and retain the best solution;

[0121] x ij ′=x i,j +C ij ×(x max,j -x min,j )

[0122] (4) If the maximum number of chaotic iterations is reached, the search ends; otherwise, go to step (2).

[0123] Among them, x min,j is the minimum value of the jth dimension obtained so far, x max,j is the maximum value of the j-th dimension obtained so far.

[0124] When the input signal frequency is lower than 5Hz, the hysteresis loop of the piezoelectric ceramic driver hardly changes. Therefore, the input and output data of the piezoelectric driver at an input frequency of 1Hz are used to establish a static Bouc-Wen model, which reflects the static hysteresis characteristics of the piezoelectric driver. A sinusoidal sweep signal with a frequency range of 0-100Hz is generated by Matlab as the input of the Bouc-Wen model. The output data of the Bouc-Wen model is used as the input of the fractional-order model, and the output data of the experimental equipment of the collected sweep signal is used as the output of the fractional-order model. The DE-ABC algorithm is used to identify the parameters of the fractional-order model through the input and output data of the above-mentioned fractional-order model.

[0125] 3. Linear controller design:

[0126] 3.1. Composite controller:

[0127] According to the improved Bouw-Wen model mentioned above, the inverse model is solved. When the expected trajectory is y r (t), and design a compensator based on the inverse model to determine the input voltage of the piezoelectric actuator as u(t). r (t) and the actual output displacement y(t) are linearized to eliminate hysteresis nonlinearity. Since the open-loop control system cannot provide feedback to correct the error, the control effect depends to a large extent on the accuracy of the mathematical model of the piezoelectric ceramic driver, and requires the performance of the controller to be highly stable and have poor anti-interference ability. Therefore, the sliding mode feedback control is combined with it to design a composite closed-loop controller; such as Figure 5 shown.

[0128] 3.2 Sliding mode controller:

[0129] In order to design a sliding mode controller, it is necessary to design a fractional-order sliding surface and a suitable control signal so that the state trajectory reaches the sliding surface and remains on the sliding surface.

[0130] 3.2.1. Design the sliding surface according to the determined piezoelectric actuator system model. (Ensure the existence of the sliding mode and make the sliding surface s=0 within a finite time, i.e., s→0 when t→∞)

[0131] 3.2.2. The design of the sliding mode reaching law usually adopts the sign function sgn(x). Due to the discontinuity of the sign function, the control input will oscillate. Selecting a suitable reaching law can eliminate the oscillation.

[0132] 3.2.3. Obtain the control input u(t) and perform stability analysis and proof on the obtained controller.

[0133] 4. Active Vibration Suppression Controller:

[0134] The system has coupling in the X and Y directions. The motion variables need to be converted into generalized variables, and the vibration control system is designed based on the generalized system. Finally, the calculated control force is converted into the generalized control force. The Jacobian matrix is ​​used to convert the generalized control force into the desired control force of the actuator, and the piezoelectric actuator hysteresis linearization controller proposed above solves the piezoelectric drive that feeds the driving voltage back to the vibration isolation platform. In the decoupling control of the active vibration suppression system, the overall MISO system is decoupled into two SISO vibration isolation systems for independent control.

[0135] In this specific implementation, an appropriate hysteresis model is selected, and a corresponding control method is selected according to the model to realize the linearization of the piezoelectric ceramic driver. Secondly, the linearized piezoelectric ceramic driver is used as a microcontroller, and a corresponding vibration control algorithm is selected to perform double-degree-of-freedom decoupling and control of the vibration.

[0136] (1) Based on the basic principles of piezoelectric ceramics, the effects of the temperature characteristics, hysteresis characteristics, creep characteristics, vibration characteristics, etc. of piezoelectric ceramics on the performance of the actuator are studied to provide a basis for subsequent nonlinear modeling and control.

[0137] (2) The hysteresis characteristics of piezoelectric ceramics are modeled respectively, and the Hammerstein hysteresis model is studied and improved so that the improved model can accurately describe the hysteresis characteristics and the constructed model can describe the hysteresis effect at different frequencies.

[0138] (3) According to the properties of the nonlinear model established above, the model parameters are analyzed and summarized, and the parameters are identified online using an artificial bee colony algorithm based on a differential evolution strategy, and the accuracy of the model is tested under driving voltage signals at different frequencies.

[0139] (4) After obtaining a relatively accurate model, an open-loop feedforward compensation controller is designed based on the accurate model. Since the anti-interference ability of the feedforward model is poor, a feedback control system is designed based on the feedforward control compensation and combined with a sliding mode controller.

[0140] (5) After obtaining a better linear piezoelectric ceramic driver, it is used as a controller to design a dual-degree-of-freedom active vibration control platform.

[0141] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered exemplary and non-restrictive in all respects, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present invention.

[0142] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A piezoelectric ceramic driver driven by an asymmetric voltage, characterized in that: The steps include: Step 1: Establish hysteresis model: A rate-dependent hysteresis nonlinear model based on the improved Bouc-Wen model and the fractional-order model is adopted; the static nonlinear part of the Hammerstein model is described by the improved Bouc-Wen model, and the linear dynamic part is described by the fractional-order model; 1.

1. Improved Bouc-Wen hysteresis model: The classic Bouc-Wen model was introduced by Bouc and expanded by Wen. The improved Bouc-Wen model is used to describe the asymmetric nature of the piezoelectric actuator input and output, which is asymmetric about the origin, by defining l(t)=l(u(t)) as a generalized input function, i.e., a function of the input voltage u(t). 1.2, Fractional Order Model: When the ARX model is used to describe the dynamic characteristics, the output at the current moment is determined not only by the input at the current moment, but also by the input and output at all previous moments; when the integer-order model is used to describe the dynamic characteristics, it is necessary to analyze the dynamic characteristics of the piezoelectric actuator and estimate the redundant parameters that affect the robustness in the control application; while the fractional-order system is considered to have improved robustness in the control design, and only needs input and output data to model without dynamic analysis; fractional-order calculus is a generalization of integer-order integration and differentiation to all real numbers; Step 2: Model parameter identification: The calculation process of the artificial bee colony algorithm mainly includes three stages: leading bees, following bees and scout bees. When using the artificial bee colony algorithm to identify model parameters, each food source represents a feasible solution to the model parameters, the amount of nectar represents the quality of the solution, and the number of solutions is equal to the number of leading bees. The root mean square error (RMSE) is introduced as the fitness function of DE-ABC to reflect the modeling error. Step 3: Linear controller design: 3.

1. Composite controller: According to the improved Bouw-Wen model mentioned above, the inverse model is solved. When the expected trajectory is y r (t), design a compensator based on the inverse model to determine the input voltage of the piezoelectric actuator as u(t); The desired displacement y of the piezoelectric micropositioning platform is r (t) and the actual output displacement y(t) are linearized to eliminate the hysteresis nonlinearity; the sliding mode feedback control is combined with it to design a composite closed-loop controller; 3.2 Sliding mode controller: In order to design a sliding mode controller, it is necessary to design a fractional-order sliding surface and a suitable control signal so that the state trajectory reaches the sliding surface and remains on the sliding surface; 3.2.

1. Design the sliding surface according to the determined piezoelectric actuator system model; 3.2.

2. The sliding mode reaching law is usually designed by using the sign function sgn(x). Due to the discontinuity of the sign function, the control input will oscillate. Selecting a suitable reaching law can eliminate the oscillation. 3.2.

3. Obtain the control input u(t) and perform stability analysis and proof on the obtained controller; Step 4: Active vibration suppression controller: The system has coupling in the X and Y directions, so the motion variables need to be converted into generalized variables, and the vibration control system is designed based on the generalized system. Finally, the calculated control force is converted into the generalized control force. The Jacobian matrix is ​​used to convert the generalized control force into the desired control force of the actuator, and the linearized controller proposed above is used to solve the piezoelectric driver that feeds the driving voltage back to the vibration isolation platform. In the decoupling control of the active vibration suppression system, the overall MISO system is decoupled into two SISO vibration isolation systems for independent control. The improved Bouc-Wen model expression is: x(t)=l[u(t)]-z(t)=[xu 2 (t)+yu(t)]-z(t) Where x(t) is the output displacement of the actuator; l[u(t)] is the non-singular input function; z(t) is the hysteresis displacement component; is the time derivative of z(t); u(t) represents the input voltage; is the time derivative of u(t); x and y control the asymmetry of the input signal; α controls the size of the hysteresis loop; β and γ control the shape of the hysteresis loop respectively; n represents the smoothness of the transition from the elastic part to the plastic part; by properly selecting the model parameters, it can represent various hysteresis phenomena in various shapes.

2. The asymmetric voltage-driven piezoelectric ceramic driver according to claim 1, characterized in that: The basic operators of fractional calculus is defined as: Where t0 and t are the lower and upper boundaries of the integral respectively, α is the fractional order, which can be a complex number, and Re(α) is the real part of α; There are many definitions of fractional calculus, the most commonly used of which are the Grunwald–Letnikov definition and the Riemann–Liouville definition. The approximate calculation of the Grunwald–Letnikov definition is used to perform numerical simulations of fractional operators. The Grunwald–Letnikov definition is given as: Fractional-order systems can be represented by fractional-order linear differential equations in the form of: Where u(t) and x(t) are the system input and output respectively; D α x(t) is the αth time derivative of x(t); if the initial condition is zero, then D α The Laplace transform of x(t) is: L{D α x(t)}=s α X Take the Laplace transform of both ends of the above equation; the fractional-order linear time-invariant system can be rewritten as the following transfer function form: Where α0<α1<…<α n , and β0<β1<…<β m ; The fitness function formula of DE-ABC is as follows: where y exp is the sampling value of the experimental data, y is the sampling value of the model data, N is the number of sampling points, and each solution xi (i = 1, 2, ...) is represented by a D-dimensional vector x i =(x i1 , x i2 , …, x iD ) T To represent, D is the number of model parameters to be identified; The specific process of DE-ABC identification is as follows: (1) Obtain the input and output data of the experiment; (2) Set the initial conditions and number of parameters; (3) Parameter identification based on DE-ABC; (4) Verification: If the fitness does not meet the requirements, return to (2) to continue identification; DE-ABC introduces the mutation strategy of the differential evolution algorithm into the artificial bee colony algorithm. In the search of the leading bee, the search of the leading bee is carried out according to the following formula: x ij ′=x best,j +F i ×(x ij -x kj ) Here, x best,j is the best individual of the previous generation, j∈{1,2,…,D}, k∈{1,2,…,N}, j and k are randomly selected, but j≠k, F i It is no longer a constant used in traditional ABC, but an adaptive and dynamically adjusted variable as shown in the following formula; where Iter is the maximum number of iterations and iter is the current number of iterations; In the early stages of algorithm evolution, iter is small and F i The larger the algorithm mutation intensity, the more effective and rapid the evolution to the optimal value. As the evolution continues, in the later stage of algorithm evolution, iter becomes larger, and F i becomes smaller, and as the individual evolves towards the optimal value, the function can converge to the optimal value quickly and stably; In traditional ABC, if a solution x i After L cycles, if there is still no improvement, the solution will be abandoned by the leading bee, and the leading bee will become a scout bee to randomly generate a new solution to replace it. In the DE-ABC used, chaotic search is introduced into the identification algorithm. Chaotic search uses the chaotic sequence generated by Logistic chaotic mapping to replace the random numbers in the traditional ABC formula; The Logistic chaos mapping equation is as follows: C n+1 =4C n (1-C n ) Among them, 0<C n <1; let the solution where the search is stagnant be x i =(x i1 , x i2 , …, x iD ), the main steps of the chaotic search of the scout bee are as follows: (1) The initial value of the chaotic sequence is generated according to the following formula; (2) Generate chaotic sequence according to the chaotic mapping equation; (3) Generate a new solution as follows, calculate its fitness value, compare it with the original solution, and retain the best solution; x ij ′=x i,j +C ij ×(x max,j -x min,j ) (4) If the maximum number of chaotic iterations is reached, the search ends, otherwise go to step (2); Among them, x min,j is the minimum value of the jth dimension obtained so far, x max,j is the maximum value of the j-th dimension obtained so far; When the input signal frequency is lower than 5Hz, the hysteresis loop of the piezoelectric ceramic driver hardly changes. Therefore, the input and output data of the piezoelectric driver at an input frequency of 1Hz are used to establish a static improved Bouc-Wen model, which reflects the static hysteresis characteristics of the piezoelectric driver. A sinusoidal sweep signal with a frequency range of 0-100Hz is generated by Matlab as the input of the improved Bouc-Wen model. The output data of the improved Bouc-Wen model is used as the input of the fractional-order model, and the output data of the experimental equipment of the collected sweep signal is used as the output of the fractional-order model. The DE-ABC algorithm is used to identify the parameters of the fractional-order model through the input and output data of the above-mentioned fractional-order model.

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