Nonlinear dynamic compensation adjustment method for piezoelectric ceramic actuator

Abstract

The invention relates to the technical field of piezoelectric ceramic actuators, and discloses a piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method which comprises the steps of model establishment, parameter identification, feed-forward compensation, feedback control, dynamic adjustment and the like. Positioning errors and vibration caused by hysteresis nonlinearity of piezoelectric ceramics are reduced, so that the stability and the reliability of the system are improved; the method also has the advantages of being simple and easy to implement, and is particularly suitable for a high-precision control piezoelectric ceramic actuator using system required during three-dimensional surface profile testing.

Description

Technical Field

[0001] The invention relates to the technical field of piezoelectric ceramic actuators, and in particular to a nonlinear dynamic compensation adjustment method for piezoelectric ceramic actuators. Background Art

[0002] Piezoelectric ceramic actuators are based on the piezoelectric effect of piezoelectric ceramic sheets, that is, piezoelectric ceramic sheets will deform under the action of an external electric field, converting electrical energy into mechanical energy, achieving precise micro-displacement adjustment to drive the machine. This effect of piezoelectric ceramic sheets enables piezoelectric ceramic actuators to produce large displacements under tiny voltages, making them also have the advantages of small size, fast response, low heat generation, and high resolution, making them particularly suitable for occasions that require high-precision control. However, under the action of the electric field, the displacement output of piezoelectric ceramics and the applied voltage input will show a non-one-to-one correspondence, that is, the same voltage will cause different displacements during loading and unloading, thus forming a hysteresis loop, which will seriously affect its control effect. When the control system using piezoelectric ceramic actuators adopts a two-stage XY mobile scanning design, it will bring more nonlinearity caused by scanning, and ultimately cause a hysteresis effect caused by the nonlinearity of the piezoelectric ceramic actuator, making it difficult for the designed control system to provide distortion-free scanning images within a certain range. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a nonlinear dynamic compensation adjustment method for a piezoelectric ceramic actuator which can reduce positioning errors and vibrations caused by hysteresis nonlinearity and improve control accuracy, response speed, stability and reliability.

[0004] To solve the above technical problems, the technical solution of the present invention is: a piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method, comprising the following steps: SP 1 , build the model According to the characteristics of piezoelectric ceramic materials, its nonlinear dynamic model is established; SP 2 , parameter identification Using experimental data, the model parameters are identified through genetic algorithms to ensure that the model can accurately reflect the actual working characteristics of the piezoelectric ceramic actuator; SP 3 , feedforward compensation Based on the identified model parameters, a feedforward compensator is designed, and the input signal is preprocessed by the feedforward compensator to offset the hysteresis nonlinear characteristics of the piezoelectric ceramic, and the feedforward compensator can calculate the input voltage to be applied according to the desired output displacement and the known model parameters; SP 4 , Feedback Control A PID controller is used to perform closed-loop control on the actual output displacement of the piezoelectric ceramic actuator; SP 5 , Dynamic Adjustment According to the actual working state of the piezoelectric ceramic actuator and the changes in external conditions, the parameters of the feedforward compensator and the PID controller are dynamically adjusted to make the piezoelectric ceramic actuator adapt to different working environments.

[0005] As a preferred technical solution, in step SP 1 In the process, the established nonlinear dynamic model needs to consider the influence of hysteresis nonlinear factors, creep nonlinear factors, temperature factors and external load factors of piezoelectric ceramic materials on model parameters.

[0006] As a preferred technical solution, based on the hysteresis nonlinear factors of piezoelectric ceramic materials, the dynamic hysteresis model of the piezoelectric ceramic actuator is established using Bouc-Wen: Among them, x is the displacement, u is the input voltage, α, β, γ are model parameters, n is an integer greater than 1, and the specific values ​​of α, β, γ and n are identified and determined through experimental data.

[0007] As a preferred technical solution, based on the creep nonlinear factor of piezoelectric ceramic materials, an empirical formula is used to describe this characteristic: Among them, x 0 is the initial displacement, i.e., the displacement corresponding to the instant when the voltage is just applied, λ is the creep coefficient corresponding to the piezoelectric ceramic material, τ is the time constant, and t is the time variable.

[0008] As a preferred technical solution, based on the temperature factor of the piezoelectric ceramic material, the parameters in the Bouc-Wen model are expressed as functions related to the temperature T through experimental data, and are recorded as α(T), β(T), and γ(T).

[0009] As a preferred technical solution, based on the external load factor of the piezoelectric ceramic material, when the external load acts on the piezoelectric ceramic material, it will change its internal stress to form an external load force F. Considering the coupling of Hooke's law and the piezoelectric effect, the established relationship is: Where k is the equivalent elastic coefficient, x is the displacement, and d 33 is the piezoelectric constant and E is the electric field strength, which is related to the input voltage.

[0010] As a preferred technical solution, in step SP 1 In the above example, the nonlinear dynamic model is constructed as follows: In the above dynamic model, x is the output variable, voltage u, temperature T, and external load force F are input variables; ξ(t) and η(t) are random noise terms, which are used to describe some unpredictable small fluctuations or measurement errors in the actual system; the function E(u) is the conversion relationship between electric field strength and input voltage.

[0011] As a preferred technical solution, in step SP 2 In the above example, the fitness function of the dynamic model is defined as: Among them, θ is a parameter combination, and the goal is to find the parameter combination with the largest fitness(θ); In order to determine the parameters in the model, it is necessary to apply voltage signals of different frequencies and amplitudes to the piezoelectric ceramics at different temperatures and different external loads, and record the displacement output and actual temperature of the piezoelectric ceramic actuator at the same time. The data are collected to form a data set, which contains n groups of data, each of which includes the input voltage u i , the corresponding output displacement x i , the temperature at that time T i and external load force F i ; Preprocess the data, including removing outliers and normalizing the data; The genetic algorithm includes the following steps: SP 2-1 , Initialize parameter population Set the parameters to be identified to m 1 The population size is N 1 ; Randomly generate N 2 Group parameter vectors, each of length m 2 , and m 1 =m 2 , N 1 =N 2 ; SP 2-2 , calculate the fitness value of each individual For each individual parameter combination θ, substitute it into the nonlinear dynamic model to calculate the predicted output, then compare it with the actual experimental data, and calculate the fitness value according to the fitness function fitness(θ); SP 2-3 , make a selection According to the calculated fitness value, excellent individuals are selected to enter the next generation population; SP 2-4 , perform crossover and mutation operations Randomly select two individuals and exchange them at a certain parameter position to complete the crossover operation; Select a probability value to randomly perturb a parameter and complete the mutation operation; SP 2-5 , identification parameter estimates Repeat step SP 2-2 To SP 2-4 , the evolution of the set number of generations is completed, and the parameter combination corresponding to the optimal individual in the population is the identified parameter estimate; SP 2-6 , prediction and verification Substituting the identified parameter estimates into the nonlinear dynamic model to generate a prediction output; The predicted output is compared with the actual experimental data to verify the parameter identification results.

[0012] As a preferred technical solution, in step SP 3 In the figure, an approximate functional relationship under specific conditions can be obtained based on the model parameters: output = f(input, temperature, load), where output is the output of the piezoelectric ceramic actuator, input is the input voltage, temperature is the temperature, and load is the external load. According to the above approximate functional relationship, the model of the feedforward compensator is designed, that is, a specific output desired_output is set, and the required input voltage compensated_input is calculated by the inverse function, that is, compensated_input = f_inv(desired_output, temperature, load), wherein f_inv is the inverse function of f, the system temperature current_temperature and the external load current_load are measured and obtained, and the feedforward compensation amount is calculated using the model of the feedforward compensator.

[0013] As an improvement to the above technical solution, the step SP 4 include, SP 4-1 , collect actual output data Real-time detection and acquisition of the displacement of the piezoelectric ceramic actuator, and using the detected displacement value as actual output data; SP 4-2 , calculate the error signal Subtract the expected output displacement from the actual output data to obtain the error signal, which serves as the basis for feedback control; SP 4-3 , calculate PID control output Based on the PID control principle of proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd, the outputs of proportional, integral, and differential control items are calculated respectively, and then they are added together to obtain the total output of PID control; SP 4-4 , combined with the feedforward compensation The total output of the PID control is combined with the feedforward compensation to form the final control input.

[0014] Due to the adoption of the above technical scheme, the present invention has the following beneficial effects: the method can significantly improve the control accuracy and response speed of the piezoelectric ceramic actuator, and reduce the positioning error and vibration caused by the hysteresis nonlinearity of the piezoelectric ceramic, thereby improving the stability and reliability of the system; the method also has the advantages of being simple and easy to implement, and is particularly suitable for high-precision control piezoelectric ceramic actuator use systems required for three-dimensional surface profile testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The following drawings are intended only to illustrate and explain the present invention, and are not intended to limit the scope of the present invention. Figure 1 It is a simplified flow chart of an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The present invention is further described below in conjunction with the accompanying drawings and examples. In the following detailed description, certain exemplary embodiments of the present invention are described only by way of illustration. Needless to say, those of ordinary skill in the art will recognize that the described embodiments may be modified in various ways without departing from the spirit and scope of the present invention. Therefore, the drawings and description are illustrative in nature and are not intended to limit the scope of protection of the claims.

[0017] like Figure 1 As shown, a nonlinear dynamic compensation adjustment method for a piezoelectric ceramic actuator is intended to improve the control accuracy and response speed of the piezoelectric ceramic actuator, and specifically includes the following steps: SP 1 , build the model According to the characteristics of the piezoelectric ceramic material, a nonlinear dynamic model is established. In this step, the nonlinear dynamic model established needs to consider the influence of the hysteresis nonlinear factor, creep nonlinear factor, temperature factor and external load factor of the piezoelectric ceramic material on the model parameters.

[0018] This embodiment uses Bouc-Wen to establish a dynamic hysteresis model of a piezoelectric ceramic actuator based on the hysteresis nonlinearity of the piezoelectric ceramic material: Among them, x is the displacement, u is the input voltage, α, β, γ are model parameters, n is an integer greater than 1, and the specific values ​​of α, β, γ and n are identified and determined through experimental data.

[0019] Under the action of constant voltage, the displacement of piezoelectric ceramic materials will change slowly over time, which is the creep phenomenon. Based on the nonlinear factors of creep of piezoelectric ceramic materials, an empirical formula is used to describe this characteristic: Among them, x 0 is the initial displacement, i.e., the displacement corresponding to the instant when the voltage is just applied, λ is the creep coefficient corresponding to the piezoelectric ceramic material, τ is the time constant, and t is the time variable.

[0020] Based on the temperature factor of piezoelectric ceramic materials, the parameters in the Bouc-Wen model are expressed as functions related to the temperature T through experimental data, recorded as α(T), β(T) and γ(T), that is, the model parameters α, β, γ are obtained. Specifically, by measuring the experimental data at different temperatures, a function related to each model parameter and temperature is formed, which is often expressed as a polynomial relationship, a linear relationship, etc., which is well known to technicians in this technical field and will not be described in detail here.

[0021] Based on the external load factor of piezoelectric ceramic materials, when the external load acts on the piezoelectric ceramic material, it will change its internal stress to form an external load force F, thereby affecting its electric field-mechanical displacement conversion characteristics, causing the displacement output to change. Under the action of the external load force F, considering the coupling of Hooke's law and the piezoelectric effect, the established relationship is: , where k is the known equivalent elastic coefficient, which is specific to the piezoelectric ceramic material, x is the displacement, and d 33 is the piezoelectric constant, and E is the electric field strength, which is related to the input voltage. This equation is used to reflect the effect of external load on the displacement of piezoelectric ceramics and then integrate it into the overall nonlinear dynamic model.

[0022] This embodiment takes the above factors into consideration and constructs a relatively complete nonlinear dynamic model as follows: In the above dynamic model equation, x is the output variable, voltage u, temperature T, and external load force F are input variables; ξ(t) and η(t) are random noise terms, which are used to describe some unpredictable small fluctuations or measurement errors in actual systems; the function E(u) is the conversion relationship between electric field intensity and input voltage (for example, for a uniform electric field, E(u)=u / h, where h is the thickness of the piezoelectric ceramic along the electric field direction).

[0023] In the above model, the functional construction of the output variable x takes into account the influence of the hysteresis nonlinear factor and temperature factor of the piezoelectric ceramic material; the functional construction of x(t) takes into account the influence of the creep nonlinear factor and temperature factor of the piezoelectric ceramic material; and the functional construction of the external load force F takes into account the influence of the external load factor. Therefore, the comprehensive consideration of the hysteresis nonlinear factor, creep nonlinear factor, temperature factor and external load factor on the model parameters is achieved.

[0024] SP 2 , parameter identification Using the experimental data, the parameters of the model are identified through a genetic algorithm to ensure that the model can accurately reflect the actual working characteristics of the piezoelectric ceramic actuator. The specific principles and processes of the genetic algorithm are well known to ordinary technicians in this technical field and will not be described in detail here. The experimental data are the input conditions and environmental conditions designed in the nonlinear dynamic model, specifically voltage u, temperature T, external load force F, etc., which are used to obtain the corresponding output data and collect them, and the parameters are identified through the collected output data to obtain α, β, γ and n, etc.

[0025] In this embodiment, at step SP 2 In the above example, the fitness function of the dynamic model is defined as: Among them, θ is a parameter combination, and the goal is to find the parameter combination with the largest fitness(θ); In order to determine the parameters in the model, it is necessary to apply voltage signals of different frequencies (such as 1Hz, 10Hz, 100Hz) and amplitudes (such as 1V, 2V, 5V) to the piezoelectric ceramics at different temperatures (such as 20℃, 40℃, 60℃) and different external loads (such as 0N, 1N, 2N) to conduct experiments. At the same time, sensors are used to record the displacement output and actual temperature of the piezoelectric ceramic actuator. The data are collected to form a data set, which contains n groups of data, each of which includes the input voltage u i , the corresponding output displacement x i , the temperature at that time T i and external load force F i .

[0026] Preprocess the data, including but not limited to removing outliers and normalizing the data. Outliers may be caused by data points that are obviously inconsistent with other data due to experimental equipment failure or interference; data normalization is to map variables of different ranges to a standard range, such as the [0,1] interval, to facilitate subsequent calculations and processing.

[0027] Then the genetic algorithm is performed, including the following steps, SP 2-1, Initialize parameter population Set the parameters to be identified to m 1 The population size is N 1 ; Randomly generate N 2 Group parameter vectors, each vector is of length m 2 , and m 1 =m 2 , N 1 =N 2 For example, when the parameter range is within a certain interval (such as α∈[0,10], β∈[0,5], etc.), the parameters of each individual are initialized by randomly generating values ​​within this interval.

[0028] In this embodiment, the identification parameter m 1 The number of is determined by the previously collected data set. For example, assuming the model parameter functions α(T)=a+bT, β(T)=c+dT, γ(T)=e+fT, then m 1 =6 (i.e. a, b, c, d, e, f).

[0029] In the genetic algorithm, the population size N 1 It is self-determined. In this embodiment, since it includes multiple parameters related to temperature, external load, amplitude, etc., N is usually selected. 1 The number of populations is about 50. The advantage of a small population is that it can find the general solution quickly, while the disadvantage of a large population is that the calculation speed is slow. Therefore, we can start with N 1 Start from the above range and observe the convergence of the genetic algorithm and the quality of the results. If the results are not satisfactory, you can try to adjust N 1 The value of is determined through experiments. For details, please refer to the general practice of genetic algorithms.

[0030] SP 2-2 , calculate the fitness value of each individual For each individual parameter combination θ, it is substituted into the nonlinear dynamic model to calculate the predicted output, which is then compared with the actual experimental data, and the fitness value is calculated according to the fitness function fitness(θ).

[0031] SP 2-3 , make a selection According to the calculated fitness value, excellent individuals are selected to enter the next generation population. A common selection method is roulette selection, that is, the probability of an individual being selected is proportional to its fitness value.

[0032] SP 2-4 , perform crossover and mutation operations The crossover operation is to exchange some parameter genes of the selected individuals with each other to generate new individuals. In this embodiment, two individuals are randomly selected and exchanged at a certain parameter position to complete the crossover operation.

[0033] Select a probability value (such as 0.01) to randomly perturb a parameter (such as adding a small random number to its current value) to complete the mutation operation to increase the diversity of the population.

[0034] SP 2-5 , identification parameter estimates Repeat step SP 2-2 To SP 2-4 , after completing the set number of generations (such as 100 generations or more, determined according to the convergence situation), the parameter combination corresponding to the optimal individual in the population is the identified parameter estimate.

[0035] SP 2-6 , prediction and verification The identified parameter estimates are substituted into the nonlinear dynamic model to generate a predicted output.

[0036] The predicted output is compared with the actual experimental data to verify the parameter identification results.

[0037] SP 3 , feedforward compensation Based on the identified model parameters, a feedforward compensator is designed, and the input signal is preprocessed by the feedforward compensator to offset the hysteresis nonlinear characteristics of the piezoelectric ceramic. The feedforward compensator can calculate the input voltage to be applied according to the desired output displacement and the known model parameters.

[0038] In this embodiment, at step SP 3 According to the model parameters, an approximate functional relationship under specific conditions can be obtained: output = f(input, temperature, load), where output is the output of the piezoelectric ceramic actuator, input is the input voltage, temperature is the temperature, and load is the external load; According to the above approximate functional relationship, the model of the feedforward compensator is designed, that is, a specific output desired_output is set, and the required input voltage compensated_input is calculated by the inverse function, that is, compensated_input = f_inv(desired_output, temperature, load), wherein f_inv is the inverse function of f, the system temperature current_temperature and the external load current_load are measured and obtained, and the feedforward compensation amount is calculated using the model of the feedforward compensator.

[0039] SP 4 , Feedback Control A PID controller is used to perform closed-loop control of the actual output displacement of the piezoelectric ceramic actuator to further improve the control accuracy and stability of the system.

[0040] Specifically, the step SP 4 include, SP 4-1 , collect actual output data Real-time detection obtains the displacement of the piezoelectric ceramic actuator, such as real-time measurement through a sensor, and uses the detected displacement value as the actual output data. This data acquisition process needs to ensure sufficient accuracy and appropriate sampling frequency to accurately reflect the dynamic characteristics of the system.

[0041] SP 4-2 , calculate the error signal Subtract the expected output displacement from the actual output data to obtain an error signal, which serves as the basis for feedback control; subsequent PID control calculations are all based on this error signal.

[0042] SP 4-3 , calculate PID control output Based on the PID control principle of proportional coefficient Kp, integral coefficient Ki and differential coefficient Kd, the outputs of proportional, integral and differential control items are calculated respectively, and then they are added together to obtain the total output of PID control.

[0043] SP 4-4 , combined with the feedforward compensation The total output of PID control is combined with the feedforward compensation to form the final control input. Feedforward compensation is mainly used to pre-compensate for known nonlinearities and disturbances in the system, while feedback control is used to handle the remaining errors and dynamic changes.

[0044] The specific process of feedback control is as follows. In the following content, / / and the corresponding text after it are explanatory notes, and the actual running code does not contain / / and the corresponding text after it: / / PID control function based on feedforward compensation float pid_with_feedforward(float setpoint, float actual_value, floatKp, float Ki, float Kd, float feedforward) { / / Integral term, initialized to 0, used to accumulate past deviations. Static variables can maintain values ​​between multiple function calls static float integral = 0; / / The last deviation is used to calculate the differential term. Static variables can maintain values ​​between multiple function calls. static float last_error = 0; / / Calculate the current deviation, that is, the difference between the expected output displacement and the actual output data float error = setpoint - actual_value; / / Accumulate deviation to integral term integral += error; / / Calculate the rate of change of the deviation, that is, the difference between the current deviation and the last deviation float derivative = error - last_error; / / Update the last deviation value last_error = error; / / PID calculation: proportional term + integral term + differential term + feedforward compensation / / Kp * error: proportional term, respond quickly based on current deviation / / Ki * integral: integral term, accumulates deviation to eliminate steady-state error / / Kd * derivative: differential term, adjusted according to the rate of change of deviation to reduce oscillation / / feedforward: feedforward compensation, pre-compensation for known disturbances or expected input changes float output = Kp * error + Ki * integral + Kd * derivative +feedforward; return output; } Among them, the functions of variables and static variables are: error: Calculate the current deviation, that is, the difference between the expected output displacement and the actual output data.

[0045] Integral: The integral term is used to accumulate past deviations to eliminate steady-state errors. Since its value needs to be maintained in multiple function calls, it is declared as a static variable.

[0046] last_error: used to calculate the differential term, that is, the difference between the current deviation and the previous deviation. It is also declared as a static variable to save the last value.

[0047] Kp * error: Proportional term, which responds quickly based on the current deviation.

[0048] Ki * integral: The integral term accumulates deviations over time and helps eliminate steady-state errors, but may cause overshoot, requiring appropriate adjustment of the Ki parameter.

[0049] Kd * derivative: The differential term is adjusted according to the rate of change of the deviation, which helps to reduce the oscillation of the system and improve stability.

[0050] feedforward: Feedforward compensation is added directly to the output of the PID calculation to compensate for known disturbances or expected input changes in the system in advance, thereby improving the response speed and accuracy of the system.

[0051] The parameters of the PID controller can be optimized by genetic algorithms or other optimization methods, such as using the following steps: SP 4-5 , parameter optimization Set the integral coefficient Ki and the differential coefficient Kd to 0, and only adjust the proportional coefficient Kp, gradually increasing the value of Kp until the system shows continuous oscillation. At this time, record the corresponding Kp value and set it as Kpc; According to the Ziegler-Nichols setting formula, preliminarily determine the values ​​of the proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd; Through further experiments, the proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd are fine-tuned, and the response curve of the system (such as overshoot, rise time, steady-state error, etc.) is observed to achieve the desired control effect. In the specific fine-tuning process, for example, if the system overshoot is too large, Kp can be appropriately reduced or Kd can be increased; if the steady-state error is large, Ki can be appropriately increased.

[0052] SP5 , Dynamic Adjustment According to the actual working state of the piezoelectric ceramic actuator and the changes in external conditions, the parameters of the feedforward compensator and the PID controller are dynamically adjusted to make the piezoelectric ceramic actuator adapt to different working environments.

[0053] The overall specific process of feedforward compensation, feedback control, and dynamic adjustment of this embodiment is as follows, wherein the approximate function relationship needs to be determined by a specific system in actual application. In order to simplify the description, this embodiment only uses a simple linear plus nonlinear test function as an example. #include<stdio.h> #include<math.h> / / Simulation system input and output relationship function / / Assume that the output displacement has the following relationship with the input voltage, temperature, and load (only for testing, not the actual situation) / / output = (input * 0.5) + (temperature * 0.1) + (load * 0.2) + 0.1* input * input float system_model(float input, float temperature, float load) { return (input * 0.5) + (temperature * 0.1) + (load * 0.2) + 0.1 *input * input; } / / Calculate the input of the feedforward compensator float feedforward_compensator(float desired_output, floattemperature, float load) { / / Here we use the iteration method to approximate the inverse function float input_guess = desired_output / 0.5; / / Make a simple initial guess float tolerance = 0.001; / / Accuracy tolerance float error = fabs(system_model(input_guess, temperature, load) -desired_output); while (error>tolerance) { / / Adjust the guess value based on the error if (system_model(input_guess, temperature, load)>desired_output) { input_guess -= 0.01; } else { input_guess += 0.01; } error = fabs(system_model(input_guess, temperature, load) -desired_output); } return input_guess; } / / Simple PID control function float pid_control(float setpoint, float process_variable, float Kp, float Ki, float Kd) { static float integral = 0; static float last_error = 0; float error = setpoint - process_variable; integral += error; float derivative = error - last_error; last_error = error; return Kp * error + Ki * integral + Kd * derivative; } int main() { / / Expected piezoelectric ceramic displacement output value float desired_displacement = 10.0; / / Simulated real-time temperature and load (here we simply give the initial value, which is actually obtained from the sensor) float current_temperature = 20.0; float current_load = 5.0; / / PID control parameters (example values, actual values ​​will be determined based on debugging) float Kp = 0.5; float Ki = 0.1; float Kd = 0.2; / / Calculate the feedforward compensation float feedforward_voltage = feedforward_compensator(desired_displacement, current_temperature,current_load); / / Current output after applying feedforward compensation first (analog system output) float current_output = system_model(feedforward_voltage, current_temperature, current_load); / / PID control further correction float pid_correction = pid_control(desired_displacement, current_output, Kp, Ki, Kd); / / Final control input (combination of feedforward compensation and PID correction) float final_control_input = feedforward_voltage + pid_correction; / / Output relevant results printf("Expected displacement: %.2f\n", desired_displacement); printf("Feedforward compensation voltage: %.2f\n", feedforward_voltage); printf("Current output after feedforward compensation: %.2f\n", current_output); printf("PID correction: %.2f\n", pid_correction); printf("Final control input: %.2f\n", final_control_input); return 0; } in, system_model function The relationship between the input voltage, temperature, external load and output displacement of the piezoelectric ceramic system is simulated. This embodiment is only a simple example relationship, which should be accurately constructed according to the characteristics of the real system in practice.

[0054] feedforward_compensator function Try to calculate the input of the feedforward compensator, that is, according to the expected output displacement, current temperature and load, obtain the corresponding compensation voltage by approximately solving the inverse function of the system model. Here, you can also use methods such as lookup tables to obtain more accurate compensation values.

[0055] pid_control Function A basic PID control logic is implemented to further correct the deviation that still exists after feedforward compensation, and the correction amount is obtained by calculating the proportional, integral and differential terms.

[0056] main function The desired piezoelectric ceramic displacement, simulated real-time temperature and load, and PID control parameters are set.

[0057] In the above process, the feedforward compensation voltage is calculated first, and then the current output of the system after feedforward compensation is obtained, and then the correction amount is calculated through PID control. Finally, the feedforward compensation amount and the PID correction amount are combined as the final control input, and the relevant results of each stage are output, which shows the whole process of combining feedforward compensation with PID control, improves the response speed and accuracy of the system, and is especially suitable for the high-precision control piezoelectric ceramic actuator system required for three-dimensional surface contour testing.

[0058] The description of the present invention is given for the purpose of illustration and description, and is not intended to be exhaustive or to limit the invention to the disclosed form. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for particular uses.

Claims

1. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method, characterized in that: The following steps are included: SP1. Model building According to the characteristics of piezoelectric ceramic materials, its nonlinear dynamic model is established; SP2, parameter identification Using experimental data, the model parameters are identified through genetic algorithms to ensure that the model can accurately reflect the actual working characteristics of the piezoelectric ceramic actuator; SP3, feedforward compensation Based on the identified model parameters, a feedforward compensator is designed, and the input signal is preprocessed by the feedforward compensator to offset the hysteresis nonlinear characteristics of the piezoelectric ceramic, and the feedforward compensator can calculate the input voltage to be applied according to the desired output displacement and the known model parameters; SP4, Feedback Control A PID controller is used to perform closed-loop control on the actual output displacement of the piezoelectric ceramic actuator; SP5, Dynamic Adjustment According to the actual working state of the piezoelectric ceramic actuator and the changes in external conditions, the parameters of the feedforward compensator and the PID controller are dynamically adjusted to make the piezoelectric ceramic actuator adapt to different working environments.

2. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 1, characterized in that: In step SP1, the nonlinear dynamic model established needs to consider the influence of the hysteresis nonlinear factor, creep nonlinear factor, temperature factor and external load factor of the piezoelectric ceramic material on the model parameters.

3. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 2, characterized in that: Based on the hysteresis nonlinear factors of piezoelectric ceramic materials, the dynamic hysteresis model of piezoelectric ceramic actuator is established using Bouc-Wen: Among them, x is the displacement, u is the input voltage, α, β, γ are model parameters, n is an integer greater than 1, and the specific values ​​of α, β, γ and n are identified and determined through experimental data.

4. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 3, characterized in that: Based on the creep nonlinearity of piezoelectric ceramic materials, an empirical formula is used to describe this characteristic: Among them, x0 is the initial displacement, that is, the displacement corresponding to the moment the voltage is just applied, λ is the creep coefficient corresponding to the piezoelectric ceramic material, τ is the time constant, and t is the time variable.

5. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 4, characterized in that: Based on the temperature factor of piezoelectric ceramic materials, the parameters in the Bouc-Wen model are expressed as functions related to temperature T through experimental data, and are recorded as α(T), β(T), and γ(T).

6. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 5, characterized in that: Based on the external load factor of piezoelectric ceramic materials, when the external load acts on the piezoelectric ceramic material, it will change its internal stress to form an external load force F. Considering the coupling of Hooke's law and piezoelectric effect, the established relationship is: Where k is the equivalent elastic coefficient, x is the displacement, and d 33 is the piezoelectric constant and E is the electric field strength, which is related to the input voltage.

7. A piezoelectric ceramic actuator nonlinear dynamic compensation adjustment method as claimed in claim 6, characterized in that: In step SP1, the nonlinear dynamic model constructed is: In the above dynamic model, x is the output variable, voltage u, temperature T, and external load force F are input variables; ξ(t) and η(t) are random noise terms, which are used to describe some unpredictable small fluctuations or measurement errors in the actual system; the function E(u) is the conversion relationship between electric field strength and input voltage.

8. The nonlinear dynamic compensation adjustment method of a piezoelectric ceramic actuator according to claim 1, characterized in that: In step SP2, the fitness function of the dynamic model is defined as, Among them, θ is a parameter combination, and the goal is to find the parameter combination with the largest fitness(θ); In order to determine the parameters in the model, it is necessary to apply voltage signals of different frequencies and amplitudes to the piezoelectric ceramics at different temperatures and different external loads, and record the displacement output and actual temperature of the piezoelectric ceramic actuator at the same time. The data are collected to form a data set, which contains n groups of data, each of which includes the input voltage u i , the corresponding output displacement x i , the temperature at that time T i and external load force F i ; Preprocess the data, including removing outliers and normalizing the data; The genetic algorithm includes the following steps: SP 2-1 , Initialize parameter population Set the number of parameters to be identified to be m1 and the population size to be N1; randomly generate N2 groups of parameter vectors, each of which has a length of m2, and m1=m2, N1=N2; SP 2-2 , calculate the fitness value of each individual For each individual parameter combination θ, substitute it into the nonlinear dynamic model to calculate the predicted output, then compare it with the actual experimental data, and calculate the fitness value according to the fitness function fitness(θ); SP 2-3 , make a selection According to the calculated fitness value, excellent individuals are selected to enter the next generation population; SP 2-4 , perform crossover and mutation operations Randomly select two individuals and exchange them at a certain parameter position to complete the crossover operation; Select a probability value to randomly perturb a parameter and complete the mutation operation; SP 2-5 , identification parameter estimates Repeat step SP 2-2 To SP 2-4 , the evolution of the set number of generations is completed, and the parameter combination corresponding to the optimal individual in the population is the identified parameter estimate; SP 2-6 , prediction and verification Substituting the identified parameter estimates into the nonlinear dynamic model to generate a prediction output; The predicted output is compared with the actual experimental data to verify the parameter identification results.

9. The nonlinear dynamic compensation adjustment method of a piezoelectric ceramic actuator according to claim 1, characterized in that: In step SP3, an approximate functional relationship under specific conditions can be obtained according to the model parameters, output = f(input, temperature, load), where output is the output of the piezoelectric ceramic actuator, input is the input voltage, temperature is the temperature, and load is the external load; According to the above approximate functional relationship, the model of the feedforward compensator is designed, that is, a specific output desired_output is set, and the required input voltage compensated_input is calculated by the inverse function, that is, compensated_input =f_inv(desired_output, temperature, load), wherein f_inv is the inverse function of f, the system temperature current_temperature and the external load current_load are measured and obtained, and the feedforward compensation amount is calculated using the model of the feedforward compensator.

10. The nonlinear dynamic compensation adjustment method of a piezoelectric ceramic actuator according to claim 9, characterized in that: The step SP4 comprises: SP 4-1 , collect actual output data Real-time detection and acquisition of the displacement of the piezoelectric ceramic actuator, and using the detected displacement value as actual output data; SP 4-2 , calculate the error signal Subtract the expected output displacement from the actual output data to obtain the error signal, which serves as the basis for feedback control; SP 4-3 , calculate PID control output Based on the PID control principle of proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd, the outputs of proportional, integral, and differential control items are calculated respectively, and then they are added together to obtain the total output of PID control; SP 4-4 , combined with the feedforward compensation The total output of the PID control is combined with the feedforward compensation to form the final control input.

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