A dual-time-scale state observation method and system for piezoelectric actuator

Abstract

The dual-time-scale state observation method and system for a piezoelectric actuator provided in the present application establish a hysteresis model of the piezoelectric actuator; design a state observer based on the hysteresis model; divide the state observer into time scales; design an adaptive parameter update law for the state observer after the time scale division; connect the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to achieve observation of the output state of the piezoelectric actuator. The dual-time-scale state observation method and system for a piezoelectric actuator provided in the present application overcome the problem that traditional models and state observation methods for piezoelectric actuators are mostly performed on one time scale, and there is an avoidable time scale problem in terms of state observation accuracy and acquisition of model parameters, so that the state observer parameters of the piezoelectric actuator are more accurate and the actuator state is accurately applied in the feedback controller.

Description

Technical Field

[0001] The present application relates to the technical field of modeling of micro-nano actuators, and in particular to a dual-time-scale state observation method and system for a piezoelectric actuator. Background Art

[0002] Piezoelectric actuators are widely used in the fields of high-precision drive positioning and processing. However, since some states of piezoelectric actuators are unmeasurable, high-precision feedback compensation of their states cannot be achieved, resulting in a decrease in their control accuracy, which limits their scope of application and hinders their further promotion.

[0003] At present, the models and state observation methods for piezoelectric actuators are mostly carried out on a time scale. There are unavoidable time scale problems in the state observation accuracy and the acquisition of model parameters, which leads to inaccurate state observer parameters of piezoelectric actuators, and the actuator state cannot be accurately applied in the feedback controller. Therefore, the existing technology has shortcomings and needs further research. Summary of the invention

[0004] In view of this, it is necessary to provide a dual-time scale state observation method and system in which the intermediate state of a piezoelectric actuator can be measured and the parameters of a state observer can be accurately estimated to address the defects in the prior art.

[0005] To solve the above problems, this application adopts the following technical solutions:

[0006] One of the purposes of this application is to provide a dual-time scale state observation method for a piezoelectric actuator, comprising the following steps:

[0007] Build a hysteresis model for piezoelectric actuators;

[0008] Designing a state observer based on the hysteresis model;

[0009] Performing time scale division on the state observer;

[0010] Designing an adaptive parameter update law for the state observer after time scale division;

[0011] The input and output ends of the state observer after the adaptive parameter update law are connected to the input and output ends of the piezoelectric actuator to achieve observation of the output state of the piezoelectric actuator.

[0012] In some embodiments, the step of establishing a hysteresis model of a piezoelectric actuator specifically includes the following steps:

[0013] The hysteresis model of piezoelectric actuator is established in the form of Bouc-Wen model.

[0014] In some embodiments, the Bouc-Wen model is constructed as follows:

[0015]

[0016] Among them, x 1 、x 2 and x 3 Respectively represent the position, velocity, and hysteresis output state of the piezoelectric actuator hysteresis model; a i (1,2,3) represent the nominal parameters of the model, which have no actual physical meaning and can be obtained through adaptive algorithms; α, β, γ represent the parameters of the model, which can affect the shape of the hysteresis loop output in the hysteresis state of the model; Represents the variable x 1 represents the derivative operation; |·| represents the absolute value operation.

[0017] In some embodiments, the step of designing a state observer based on the hysteresis model specifically includes:

[0018]

[0019] in, and denote the estimated values ​​of the position, velocity, and hysteresis output state of the estimated piezoelectric actuator, respectively; represents the estimated value of the nominal parameter; represents the estimated value of the model parameters, which determines the shape of the piezoelectric actuator output hysteresis loop; 1 , l 2 and l 3 are the gains of the designed state observer respectively.

[0020] In some of the embodiments, in the step of dividing the state observer into time scales, specifically: using a dual time scale module with time delay to divide the state observer into time scales.

[0021] In some embodiments, the step of designing an adaptive parameter update law for the state observer after dividing the time scale specifically includes the following steps: designing an adaptive parameter update law for the state observer after dividing the time scale by the following formula:

[0022]

[0023]

[0024] Among them, λ 1 and λ 2 are the parameters of the adaptive update law, and k is the parameter value measuring the time scale; is the fast time scale parameter update error,

[0025] Φ fast is the identification state of the fast time scale

[0026] is the parameter estimate of the fast state

[0027] is the parameter estimate of the slow state

[0028] is the slow time scale parameter update error

[0029]

[0030] Φ low is the slow time scale input state

[0031] In some embodiments, in the step of connecting the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to observe the output state of the piezoelectric actuator, specifically:

[0032] A driving signal is given to the piezoelectric actuator using a driving power supply, and then the input voltage data and the output data of the piezoelectric actuator are recorded; at the same time, the driving signal is input to the state observer after time scale division, and it is divided into two scales, and the parameters of the dual-time scale state observer are calculated by the adaptive parameter update law to obtain the output state at this time.

[0033] In addition, the present application also provides a dual-time scale state observation system for a piezoelectric actuator, comprising:

[0034] A hysteresis model building unit, used for building a hysteresis model of a piezoelectric actuator;

[0035] A state observer design unit, used for designing a state observer based on the hysteresis model;

[0036] A time scale division unit, used for performing time scale division on the state observer;

[0037] An adaptive parameter unit, used for designing an adaptive parameter update law for the state observer after time scale division;

[0038] The output unit is used to connect the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to achieve the observation of the output state of the piezoelectric actuator.

[0039] This application adopts the above technical solution, and its beneficial effects are as follows:

[0040] The dual-time-scale state observation method and system for a piezoelectric actuator provided in the present application establish a hysteresis model of the piezoelectric actuator; design a state observer based on the hysteresis model; divide the state observer into time scales; design an adaptive parameter update law for the state observer after the time scale division; connect the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to achieve observation of the output state of the piezoelectric actuator. The dual-time-scale state observation method and system for a piezoelectric actuator provided in the present application overcome the problem that traditional models and state observation methods for piezoelectric actuators are mostly performed on one time scale, and there is an avoidable time scale problem in terms of state observation accuracy and acquisition of model parameters, so that the state observer parameters of the piezoelectric actuator are more accurate and the actuator state is accurately applied in the feedback controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0042] Figure 1 A flowchart of the steps of the dual-time-scale state observation method for a piezoelectric actuator provided in Example 1 of the present application.

[0043] Figure 2 A structural diagram of the dual-time-scale state observation method for a piezoelectric actuator provided in Application Example 1.

[0044] Figure 3 This is a structural diagram of the state observer after time scale division provided in Application Example 1.

[0045] Figure 4 A schematic diagram of the structure of a dual-time-scale state observation system for a piezoelectric actuator provided in Example 2 of the present application. DETAILED DESCRIPTION

[0046] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0047] In the description of the present application, it should be understood that the terms "upper", "lower", "horizontal", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0048] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0049] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0050] Example 1

[0051] See also Figure 1 , is a flowchart of a dual-time-scale state observation method for a piezoelectric actuator provided in this embodiment 1, comprising the following steps:

[0052] Step S110: establishing a hysteresis model of the piezoelectric actuator.

[0053] In some of the embodiments, the step of establishing the hysteresis model of the piezoelectric actuator specifically includes the following steps: establishing the hysteresis model of the piezoelectric actuator in the form of a Bouc-Wen model.

[0054] Specifically, the construction formula of the Bouc-Wen model is as follows:

[0055]

[0056] Among them, x 1 、x 2 and x 3 Respectively represent the position, velocity, and hysteresis output state of the piezoelectric actuator hysteresis model; a i (1,2,3) represent the nominal parameters of the model, which have no actual physical meaning and can be obtained through adaptive algorithms; α, β, γ represent the parameters of the model, which can affect the shape of the hysteresis loop output in the hysteresis state of the model; Represents the variable x 1 represents the derivative operation; |·| represents the absolute value operation.

[0057] Step S120: designing a state observer based on the hysteresis model.

[0058] In this embodiment, the step of designing a state observer based on the hysteresis model specifically includes:

[0059]

[0060] in, and denote the estimated values ​​of the position, velocity, and hysteresis output state of the estimated piezoelectric actuator, respectively; represents the estimated value of the nominal parameter; represents the estimated value of the model parameters, which determines the shape of the piezoelectric actuator output hysteresis loop; 1 , l 2 and l 3 are the gains of the designed state observer respectively.

[0061] Step S130: dividing the state observer into time scales.

[0062] Specifically, in the step of dividing the state observer into time scales, specifically: using a dual time scale module with time delay to divide the state observer into time scales.

[0063] Since the linear dynamic part of the piezoelectric actuator responds quickly and the hysteresis state responds slowly, a dual time scale module with time delay is used to divide the time scale of the state observer.

[0064] Step S140: designing an adaptive parameter update law for the state observer after time scale division.

[0065] In some embodiments, the step of designing an adaptive parameter update law for the state observer after dividing the time scale specifically includes the following steps: designing an adaptive parameter update law for the state observer after dividing the time scale by the following formula:

[0066]

[0067]

[0068] Among them, λ 1 and λ 2 are the parameters of the adaptive update law, and k is the parameter value measuring the time scale; is the fast time scale parameter update error,

[0069] Φ fast is the identification state of the fast time scale

[0070] is the parameter estimate of the fast state

[0071] is the parameter estimate of the slow state

[0072] is the slow time scale parameter update error

[0073]

[0074] Φ low is the slow time scale input state

[0075] Step S150: connecting the input and output terminals of the state observer after the adaptive parameter update law to the input and output terminals of the piezoelectric actuator to achieve observation of the output state of the piezoelectric actuator.

[0076] In some embodiments, in the step of connecting the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to observe the output state of the piezoelectric actuator, specifically:

[0077] A driving signal is given to the piezoelectric actuator using a driving power supply, and then the input voltage data and the output data of the piezoelectric actuator are recorded; at the same time, the driving signal is input to the state observer after time scale division, and it is divided into two scales, and the parameters of the dual-time scale state observer are calculated by the adaptive parameter update law to obtain the output state at this time.

[0078] See also Figure 2 , which is a structural diagram of the dual-time-scale state observation method for a piezoelectric actuator provided in this embodiment, firstly, an excitation signal is given to the state observer, and is input to the power drive amplifier through the DAC conversion module, and then the output of the power drive drives the piezoelectric actuator; then, according to Figure 3As shown in the structure diagram of the state observer after time scale division, a dual-time scale state observation method is designed. Then, according to the fast response speed of the linear dynamic part and the slow response speed of the hysteresis state in the piezoelectric actuator, a dual-time scale module with time delay is used, that is, the update speed of the linear dynamic part is faster than the hysteresis state response by a sampling time, and parameter update calculation is performed. The ADC conversion module is used to output to the STM32 embedded system. At the same time, the output data of the state observer is collected and compared with the displacement data output by the ADC conversion module, and is brought into formulas (3) and (4); finally, the input and output data of the piezoelectric actuator are saved by the host computer, and at the same time, the output state data of the designed dual-time scale state observer is saved through the STM32 embedded system to obtain the estimated curves of the position, speed and hysteresis state of the piezoelectric actuator.

[0079] The dual-time-scale state observation method for piezoelectric actuators provided in Example 1 of the present application overcomes the problem that traditional models and state observation methods for piezoelectric actuators are mostly performed on one time scale, and there are avoidable time scale problems in state observation accuracy and acquisition of model parameters. This makes the state observer parameters of the piezoelectric actuator more accurate and enables the actuator state to be accurately applied in the feedback controller.

[0080] Example 2

[0081] See also Figure 4 Embodiment 2 of the present application provides a dual-time-scale state observation system for a piezoelectric actuator, including: a hysteresis model building unit 110, used to establish a hysteresis model of the piezoelectric actuator; a state observer design unit 120, used to design a state observer based on the hysteresis model; a time scale division unit 130, used to divide the state observer into time scales; an adaptive parameter unit 140, used to design an adaptive parameter update law for the state observer after the time scale division; an output unit 150, used to connect the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator, so as to realize the observation of the output state of the piezoelectric actuator.

[0082] The dual-time-scale state observation system for the piezoelectric actuator provided in Example 2 of the present application can be implemented in detail by referring to Example 1, which will not be described in detail here.

[0083] The dual-time-scale state observation system for piezoelectric actuators provided in Example 2 of the present application overcomes the problem that traditional models and state observation methods for piezoelectric actuators are mostly performed on one time scale, and there are avoidable time scale problems in state observation accuracy and acquisition of model parameters. This makes the state observer parameters of the piezoelectric actuator more accurate and enables the actuator state to be accurately applied in the feedback controller.

[0084] It can be understood that the technical features of the above-described embodiments can be arbitrarily combined. In order to make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0085] The above are only preferred embodiments of the present application, and only specifically describe the technical principles of the present application. These descriptions are only for explaining the principles of the present application and cannot be interpreted as limiting the scope of protection of the present application in any way. Based on the explanation here, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application, and other specific implementation methods of the present application that can be associated with the technicians in this field without creative work, should be included in the scope of protection of the present application.

Claims

1. A dual-time-scale state observation method for a piezoelectric actuator, characterized in that: The steps include: Build a hysteresis model for piezoelectric actuators; Designing a state observer based on the hysteresis model; Performing time scale division on the state observer; Designing an adaptive parameter update law for the state observer after time scale division; The input and output ends of the state observer after the adaptive parameter update law are connected to the input and output ends of the piezoelectric actuator to achieve observation of the output state of the piezoelectric actuator.

2. The dual-time-scale state observation method for a piezoelectric actuator according to claim 1, characterized in that: The steps of establishing the hysteresis model of the piezoelectric actuator specifically include the following steps: The hysteresis model of piezoelectric actuator is established in the form of Bouc-Wen model.

3. The dual-time-scale state observation method for a piezoelectric actuator according to claim 2, characterized in that: The construction formula of the Bouc-Wen model is as follows: Where x1, x2 and x3 represent the position, velocity and hysteresis output state of the piezoelectric actuator hysteresis model respectively; a i (1,2,3) represent the nominal parameters of the model, which have no actual physical meaning and can be obtained through adaptive algorithms; α, β, γ represent the parameters of the model, which can affect the shape of the hysteresis loop output in the hysteresis state of the model; represents the derivative operation of variable x1; |·| represents the absolute value operation.

4. The dual-time-scale state observation method for a piezoelectric actuator according to claim 1, characterized in that: The step of designing a state observer based on the hysteresis model specifically includes: in, and denote the estimated values ​​of the position, velocity, and hysteresis output state of the estimated piezoelectric actuator, respectively; represents the estimated value of the nominal parameter; represents the estimated value of the model parameters, which can determine the shape of the piezoelectric actuator output hysteresis loop; l1, l2 and l3 are the gains of the designed state observer.

5. The dual-time-scale state observation method for a piezoelectric actuator according to claim 1, characterized in that: In the step of dividing the state observer into time scales, specifically: using a dual time scale module with time delay to divide the state observer into time scales.

6. The dual-time-scale state observation method for a piezoelectric actuator according to claim 1, characterized in that: The step of designing an adaptive parameter update law for the state observer after dividing the time scale specifically includes the following steps: designing an adaptive parameter update law for the state observer after dividing the time scale by the following formula: Among them, λ1 and λ2 are the parameters of the adaptive update law, and k is the parameter value that measures the time scale; is the fast time scale parameter update error, Φ fast is the identification state of the fast time scale is the parameter estimate of the fast state is the parameter estimate of the slow state is the slow time scale parameter update error Φ low is the slow time scale input state 7. The dual-time-scale state observation method for a piezoelectric actuator according to claim 1, characterized in that: The step of connecting the input and output terminals of the state observer after the adaptive parameter update law to the input and output terminals of the piezoelectric actuator to realize the observation of the output state of the piezoelectric actuator is specifically as follows: A driving signal is given to the piezoelectric actuator using a driving power supply, and then the input voltage data and the output data of the piezoelectric actuator are recorded; at the same time, the driving signal is input to the state observer after time scale division, and it is divided into two scales, and the parameters of the dual-time scale state observer are calculated by the adaptive parameter update law to obtain the output state at this time.

8. A dual-time-scale state observation system for a piezoelectric actuator, characterized in that: include: A hysteresis model building unit, used for building a hysteresis model of a piezoelectric actuator; A state observer design unit, used for designing a state observer based on the hysteresis model; A time scale division unit, used for performing time scale division on the state observer; An adaptive parameter unit, used for designing an adaptive parameter update law for the state observer after time scale division; The output unit is used to connect the input and output ends of the state observer after the adaptive parameter update law to the input and output ends of the piezoelectric actuator to achieve the observation of the output state of the piezoelectric actuator.

Images