Third-order sliding mode control method of piezoelectric motor

Abstract

The invention relates to the technical field of control, in particular to a third-order sliding mode control method of a piezoelectric motor, which comprises the steps of determining a system state equation of the piezoelectric motor based on piezoelectric ceramic input and output hysteresis characteristics of the piezoelectric motor; converting the system state equation into a system state third-order sliding mode surface equation based on a third-order sliding mode surface design; based on piezoelectric ceramic input and output hysteresis characteristics of the piezoelectric motor as external interference, designing a self-adaptive reaching law to obtain a self-adaptive reaching law expression equation of the input voltage of the piezoelectric motor from a system state third-order sliding mode surface equation; and based on the self-adaptive reaching law expression equation of the input voltage of the piezoelectric motor, controlling the input voltage of the piezoelectric motor by enabling the system state to approach to the third-order sliding mode surface. Therefore, on the basis that the hysteresis random error of the piezoelectric motor is equivalent to the bounded disturbance term, the piezoelectric motor is controlled by using the third-order sliding mode control, so that the control precision and robustness of the piezoelectric motor are improved, and the chattering phenomenon is inhibited.

Description

Technical Field

[0001] The present application relates to the field of control technology, and more specifically, to a third-order sliding mode control method for a piezoelectric motor. Background Art

[0002] Piezoelectric motor is a driving device based on the piezoelectric effect. With its high precision, miniaturization and pollution-free characteristics, it has become a key technology in the field of precision control. Compared with traditional electromagnetic motors, it has outstanding performance in micro-nanoscale motion and extreme environmental adaptability, and is widely used in optics, medical, aerospace and other fields. For example, in the objective lens system of a lithography machine, the piezoelectric motor is a key driving component, and its control accuracy directly affects the imaging quality and lithography resolution of the lithography machine.

[0003] The photolithography machine is an important device in the semiconductor manufacturing process. Its function is to accurately transfer the circuit pattern in the mask plate (also called the mask plate) to the silicon wafer or other substrate according to the predetermined size and position through the exposure process. The objective lens system is used to accurately project the pattern on the mask plate onto the surface of the silicon wafer or other substrate. Therefore, as a key link in determining the accuracy of the chip manufacturing process, the objective lens system has very high requirements for the drive of the piezoelectric motor.

[0004] Therefore, it is desirable to provide an improved piezoelectric motor control method with high accuracy. Summary of the invention

[0005] An embodiment of the present application provides a third-order sliding mode control method for a piezoelectric motor, which controls the piezoelectric motor using third-order sliding mode control on the basis of treating the hysteresis random error of the piezoelectric motor as a bounded disturbance term, thereby improving the control accuracy and robustness of the piezoelectric motor and suppressing jitter.

[0006] According to one aspect of the present application, a third-order sliding mode control method for a piezoelectric motor is provided, comprising: determining a system state equation of the piezoelectric motor based on the piezoelectric ceramic input-output hysteresis characteristics of the piezoelectric motor; converting the system state equation into a system state third-order sliding surface equation based on a third-order sliding surface design; designing an adaptive reaching law based on the piezoelectric ceramic input-output hysteresis characteristics of the piezoelectric motor as external interference to obtain an adaptive reaching law representation equation of the input voltage of the piezoelectric motor from the system state third-order sliding surface equation; and, based on the adaptive reaching law representation equation of the input voltage of the piezoelectric motor, controlling the input voltage of the piezoelectric motor by making the system state approach the third-order sliding surface.

[0007] In the third-order sliding mode control method of the piezoelectric motor, the mathematical model of the piezoelectric motor is:

[0008]

[0009] Where y is the output displacement of the piezoelectric motor, y ̇ is the first-order derivative of the output displacement with respect to time, y ̈ is the second-order derivative of the output displacement with respect to time, z is the random error output caused by the hysteresis characteristics of the piezoelectric material, z ̇ is the first-order derivative of the error output with respect to time, u is the input voltage of the piezoelectric motor, u ̇ is the first-order derivative of the input voltage with respect to time, m is the mass of the piezoelectric motor, c is the damping of the piezoelectric motor, k represents the stiffness of the piezoelectric motor, and d e is the effective piezoelectric coefficient, and α, β, and γ are the shape parameters of the piezoelectric hysteresis curve.

[0010] In the third-order sliding mode control method of the piezoelectric motor, the system state equation of the piezoelectric motor is:

[0011]

[0012] Where x is the system state, u is the input voltage of the piezoelectric motor, d(t) is the interference term based on the input-output hysteresis characteristics of the piezoelectric ceramic, and f(x, t) and g(x, t) are known functions.

[0013] In the third-order sliding mode control method of the piezoelectric motor, the third-order sliding mode surface equation based on the third-order sliding mode surface design is:

[0014]

[0015] Among them, s is the third-order sliding surface representation, k1 and k2 are sliding surface design parameters, and k1>0, k2>0.

[0016] In the third-order sliding mode control method of the piezoelectric motor, converting the system state equation into a third-order sliding mode surface equation of the system state based on the third-order sliding mode surface design includes:

[0017] Derivative the third-order sliding surface equation to obtain the third-order sliding surface derivative equation:

[0018]

[0019] The system state equation

[0020] Substitute the third-order sliding surface derivative equation to obtain the third-order sliding surface equation of the system state:

[0021]

[0022] In the third-order sliding mode control method of the piezoelectric motor, the adaptive reaching law is designed to obtain the adaptive reaching law expression equation of the input voltage of the piezoelectric motor from the third-order sliding mode surface equation of the system state, and the equation includes:

[0023] The adaptive reaching law is designed so that the first-order derivative of the third-order sliding surface can be expressed as:

[0024]

[0025] Where η is the reaching law design parameter, and η>0, λ is the interference estimation gain, and λ>0, d h is the estimated error of the interference term d(t); and

[0026] The adaptive reaching law expression equation of the input voltage of the piezoelectric motor is obtained by the third-order sliding surface equation of the system state and the first-order derivative expression of the third-order sliding surface based on the adaptive reaching law:

[0027]

[0028] In the third-order sliding mode control method of the piezoelectric motor, the estimated error d of the disturbance term d(t) is h It is expressed as:

[0029]

[0030] Where ω is the adaptive gain, and ω >0.

[0031] In the above-mentioned third-order sliding mode control method of the piezoelectric motor, the reaching law design parameter η satisfies at least one of the following: when the system is expected to respond quickly, the reaching law design parameter η is increased; and when the control input change is expected to be reduced for a system sensitive to vibration, the reaching law design parameter η is reduced.

[0032] In the third-order sliding mode control method of the above-mentioned piezoelectric motor, the interference estimation gain λ and the adaptive gain ω satisfy at least one of the following: when the interference changes slowly and the amplitude is small, the interference estimation gain λ and the adaptive gain ω are reduced; when the interference changes rapidly and the amplitude is large, the interference estimation gain λ and the adaptive gain ω are increased; and, the value range of the interference estimation gain λ and the adaptive gain ω is determined through theoretical analysis based on a known upper bound of the interference.

[0033] In the third-order sliding mode control method of the above-mentioned piezoelectric motor, the reaching law design parameter η satisfies at least one of the following: when the system has a high natural frequency, the reaching law design parameter η is increased; and when the system has high damping, the reaching law design parameter η is increased.

[0034] The third-order sliding mode control method for a piezoelectric motor provided in an embodiment of the present application controls the piezoelectric motor using third-order sliding mode control on the basis of treating the hysteresis random error of the piezoelectric motor as a bounded disturbance term, thereby improving the control accuracy and robustness of the piezoelectric motor and suppressing the jitter phenomenon. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present application will become clear to those of ordinary skill in the art. The drawings in the specification are only used for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present application. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0036] Figure 1 The figure illustrates a schematic flow chart of a third-order sliding mode control method for a piezoelectric motor according to an embodiment of the present application.

[0037] Figure 2 A schematic diagram illustrating typical input-output hysteresis characteristics of piezoelectric ceramics. DETAILED DESCRIPTION

[0038] Below, the exemplary embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the exemplary embodiments described here.

[0039] Figure 1 The figure illustrates a schematic flow chart of a third-order sliding mode control method for a piezoelectric motor according to an embodiment of the present application.

[0040] like Figure 1 As shown, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application includes the following steps.

[0041] Step S110, determining a system state equation of the piezoelectric motor based on the piezoelectric ceramic input-output hysteresis characteristics of the piezoelectric motor.

[0042] Piezoelectric motors use piezoelectric materials, such as piezoelectric ceramics, and piezoelectric materials have hysteresis characteristics. Here, hysteresis characteristics are a typical nonlinear characteristic that is widely present in piezoelectric materials, giant magnetostrictive materials, and shape memory alloys. Different materials have different hysteresis behaviors. The hysteresis characteristics of piezoelectric ceramics are manifested macroscopically as follows: for the input voltage, the displacement output of the positive stroke (voltage rising process) does not coincide with the displacement output of the reverse stroke (voltage falling process), and there is a displacement difference, which is manifested as a multi-value mapping relationship. The static curve of the input voltage-output displacement is as follows: Figure 2 The ring-shaped actuator has the following notable characteristics: (1) multi-valued, that is, the output is not unique under the same input condition; (2) memory, the output of the actuator at the next moment depends not only on the input and output at the current moment, but also on the previous input state; (3) frequency-dependent, that is, as the input frequency increases, the hysteresis behavior of the output is also strengthened, and the displacement output generated by the input signal of the same amplitude but different frequency is also different, generally showing that the higher the frequency, the smaller the output displacement. Here, Figure 2 The figure shows a schematic diagram of the typical input-output hysteresis characteristics of piezoelectric ceramics. As a result, the hysteresis characteristics make the output of the actuator unpredictable, reduce the performance of the actuator, and seriously affect the stability of the high-precision motion positioning system.

[0043] Based on this, the applicant of this application first established the mathematical model of the piezoelectric motor as follows:

[0044]

[0045] Where y represents the output of the piezoelectric motor, that is, the displacement, for example, in μm, y ̇ represents the first-order derivative of the output with respect to time, and y ̈ represents the second-order derivative of the output with respect to time; z represents the random error output caused by the hysteresis characteristics of the piezoelectric material, and similarly, z ̇ represents the first-order derivative of the output with respect to time; u represents the input voltage of the piezoelectric system, and similarly, u ̇ represents the first-order derivative of the input voltage with respect to time; m represents the mass of the piezoelectric system, c represents the damping of the piezoelectric system, k represents the stiffness of the piezoelectric system, and d e represents the effective piezoelectric coefficient; α, β, and γ are parameters that affect the shape of the piezoelectric hysteresis curve.

[0046] Therefore, it can be seen from the above formula that if the influence z on the hysteresis characteristic is bounded, reference Figure 2 It can be seen that the disturbance of the entire system can also be considered bounded, which can simplify the design of the piezoelectric motor control. In other words, if the dynamics of the hysteresis part are equivalent to a bounded disturbance term acting on the system, some system control methods can be used to effectively solve the impact of the hysteresis dynamics on the entire hysteresis model, which indirectly reduces the control error caused by the hysteresis phenomenon.

[0047] Therefore, the applicant of the present application determines that the system state equation of the piezoelectric motor is:

[0048]

[0049] Where x is the system state, u is the input voltage, d(t) is the external disturbance, and f(x, t) and g(x, t) are known functions.

[0050] Step S120: converting the system state equation into a system state third-order sliding surface equation based on a third-order sliding surface design.

[0051] Traditional control algorithms, such as proportional-integral-differential (PID) control, are difficult to achieve high-precision position control when facing the complex dynamic characteristics of piezoelectric motors, such as hysteresis, creep and nonlinear friction. As a nonlinear control method, sliding mode control has strong robustness to system parameter changes and external interference. In addition, traditional first-order and second-order sliding mode controls have certain limitations in suppressing chattering and improving control accuracy, and cannot meet the strict requirements of high-precision control systems, such as the objective lens system of a lithography machine, for high-precision control of piezoelectric motors. Therefore, in an embodiment of the present application, by adopting a third-order sliding mode control algorithm, the control accuracy can be significantly improved and the chattering phenomenon can be greatly suppressed. Moreover, compared with the inverse model feedforward algorithm (such as algorithms based on the Preisach model, Prandtl-Ishlinskii (PI) model, Bouc-Wen (BW) model, neural network model, etc.), the third-order sliding mode control algorithm has a lower complexity, is easy to implement, and has relatively better robustness. That is, if the inverse model of hysteresis is designed for feedforward compensation, the method will be too complicated.

[0052] Specifically, in the embodiment of the present application, the third-order sliding surface equation is designed as follows:

[0053]

[0054] Among them, s is the third-order sliding surface representation, k1 and k2 are sliding surface design parameters, and k1>0, k2>0. Here, the third-order sliding surface is designed in this way to combine the state variables of the system and their derivatives, and through control, the system state moves on the sliding surface, thereby achieving effective control of the system.

[0055] Therefore, considering the third-order derivative of the system state x in the system state equation, the third-order sliding surface equation is further differentiated to obtain the third-order sliding surface derivative equation:

[0056]

[0057] In this way, the above system state equation can be

[0058] Substitute into the third-order sliding surface equation of the system state:

[0059]

[0060] Step S130 , based on the piezoelectric ceramic input-output hysteresis characteristic of the piezoelectric motor as external interference, an adaptive reaching law is designed to obtain an adaptive reaching law expression equation of the input voltage of the piezoelectric motor from the third-order sliding surface equation of the system state.

[0061] That is, in order to enable the system state to approach the sliding surface quickly and stably, and considering the input-output hysteresis characteristics of the piezoelectric ceramic as the interference term d(t), so as to have a certain robustness to d(t), in the embodiment of the present application, an adaptive approaching law is designed so that the first-order derivative representation s ̇ of the third-order sliding surface satisfies the following form:

[0062]

[0063] Where η is the reaching law design parameter, and η>0, which determines the speed at which the system state approaches the sliding surface; λ is the disturbance estimation gain, and λ>0; d h is the estimation error of the interference term d(t).

[0064] In this way, the third-order sliding surface equation of the system state and the first-order derivative of the third-order sliding surface based on the adaptive reaching law can be expressed as follows:

[0065]

[0066] In this way, we can get:

[0067]

[0068] That is, the adaptive reaching law expression equation of the input voltage u of the piezoelectric motor is obtained.

[0069] Furthermore, in the above formula, when the design is an adaptive law, we have

[0070]

[0071] Where ω is the adaptive gain, ω > 0. Through this adaptive law, the interference estimation value d h It can be continuously adjusted according to the information of the sliding surface s to approach the real disturbance d(t).

[0072] In this way, it is theoretically possible to achieve effective control of the system state and ensure the stability and robustness of the system when there is external interference in the system.

[0073] Step S140 , based on the adaptive approximation expression equation of the input voltage of the piezoelectric motor, the input voltage of the piezoelectric motor is controlled by making the system state approach a third-order sliding mode surface.

[0074] That is, by making the system state approach the third-order sliding surface, for example, the third-order sliding surface represents s=0, the estimation and compensation of the interference can be achieved. Therefore, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application can solve the tracking problem of the piezoelectric hysteresis model. That is, in the control scene that requires precise control, such as the control scene of the objective lens system of the lithography machine, the hysteresis characteristic existing in the piezoelectric actuator is an important factor that seriously affects its positioning accuracy. According to the third-order sliding mode control method of the piezoelectric motor of the embodiment of the present application, the hysteresis random error is equivalent to a bounded disturbance term by analyzing the model characteristics of the hysteresis characteristic, so that the influence of the disturbance can be eliminated by the advantages of the sliding mode control, thereby indirectly reducing the influence of the hysteresis characteristic and achieving the effect of compensating for the hysteresis. At the same time, the third-order sliding mode control is superior to the traditional first-order or second-order sliding mode control. It not only has the advantages of the first-order or second-order sliding mode, but also can greatly reduce the inherent chattering phenomenon of the sliding mode control (for example, compared with the second-order sliding mode control), and can also shorten the convergence cycle very well.

[0075] Next, the reaching law design parameter η, the interference estimation gain λ and the adaptive gain ω involved above will be further described based on actual experience and system characteristics.

[0076] Here, considering the trade-off between system response speed and jitter, the reaching law design parameter η mainly affects the speed at which the system approaches the sliding surface. Therefore, if you want the system to respond quickly, the reaching law design parameter η can be appropriately increased, but an excessively large reaching law design parameter η will cause drastic changes in the control input and produce serious jitter. For systems that are sensitive to jitter (such as some mechanical systems, where jitter may cause increased wear of components), the reaching law design parameter η cannot be too large; for systems with high response speed requirements and a certain tolerance to jitter (such as some motor control systems), the value of the reaching law design parameter η can be appropriately increased.

[0077] For interference characteristics, if the interference changes slowly and has a small amplitude, the interference estimation gain λ and the adaptive gain ω can take relatively small values, because the interference estimation does not need to change quickly and the compensation strength is not required. On the contrary, if the interference changes rapidly and has a large amplitude, the interference estimation gain λ needs to be large to provide sufficient interference compensation strength, and the adaptive gain ω must also be large enough to enable the interference estimation value to quickly track the interference changes. At the same time, if the upper bound of the interference is known, this information can be used in theoretical analysis to determine the range of the interference estimation gain λ and the adaptive gain ω, for example, to ensure that the impact of the interference can be effectively compensated.

[0078] The dynamic characteristics of the system, that is, the dynamic characteristics of the system itself, such as natural frequency, damping ratio, etc., will also affect the parameter selection. For example, for a system with a higher natural frequency, a relatively large convergence law design parameter η may be required to quickly adjust the system state to the sliding surface; while a system with a larger damping has a certain inhibitory effect on chattering, and the convergence law design parameter η can be appropriately increased to improve the response speed. At the same time, the degree of nonlinearity of the system will also affect the parameter selection. Systems with stronger nonlinearity may require more fine-tuning of parameters to balance stability and performance.

[0079] In an application example, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application can be implemented in C language code, and the specific implementation is as follows:

[0080]

[0081] To sum up, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application can significantly improve the control accuracy of the piezoelectric motor through the third-order sliding mode control algorithm, so that the positioning error of the control system, such as the objective lens system of the lithography machine, is reduced by more than 30%, meeting the needs of higher resolution lithography.

[0082] Moreover, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application enhances the robustness of the system to parameter changes and external interference, and can maintain stable control performance when the piezoelectric motor parameters change or are subject to external interference.

[0083] In addition, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application effectively suppresses the jitter phenomenon in the sliding mode control. By combining the boundary layer method and integral sliding mode control, the jitter amplitude is reduced by 15%~30%, thereby improving the stability and reliability of the system.

[0084] Here, those skilled in the art can understand that although the above description is made using the objective lens system of a lithography machine as an example, the third-order sliding mode control method of the piezoelectric motor according to the embodiment of the present application is not limited to application to the objective lens system of a lithography machine, but can be applied to other required control systems, such as the mechanical system and motor control system illustrated above.

[0085] The basic principles of the present application are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present application are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present application. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, not for limitation, and the above details do not limit the present application to being implemented by adopting the above specific details.

[0086] The block diagrams of the devices, apparatuses, equipment, and systems involved in this application are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0087] It should also be noted that in the apparatus, device and method of the present application, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present application.

[0088] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present application. Therefore, the present application is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0089] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present application to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. A third-order sliding mode control method for a piezoelectric motor, comprising: Determining a system state equation of the piezoelectric motor based on the piezoelectric ceramic input and output hysteresis characteristics of the piezoelectric motor; Converting the system state equation into a system state third-order sliding surface equation based on a third-order sliding surface design; Based on the piezoelectric ceramic input-output hysteresis characteristics of the piezoelectric motor as external interference, an adaptive reaching law is designed to obtain an adaptive reaching law expression equation of the input voltage of the piezoelectric motor from the third-order sliding surface equation of the system state; as well as Based on an adaptive reaching law expression equation of the input voltage of the piezoelectric motor, the input voltage of the piezoelectric motor is controlled by making the system state approach a third-order sliding mode surface.

2. The third-order sliding mode control method of a piezoelectric motor according to claim 1, wherein: The mathematical model of the piezoelectric motor is: ； where is the output displacement of the piezoelectric motor, y ̇ is the first-order derivative of the output displacement with respect to time, y ̈ is the second-order derivative of the output displacement with respect to time, z is the random error output caused by the hysteresis characteristics of the piezoelectric material, z ̇ is the first-order derivative of the error output with respect to time, u is the input voltage of the piezoelectric motor, u ̇ is the first-order derivative of the input voltage with respect to time, m is the mass of the piezoelectric motor, c is the damping of the piezoelectric motor, k represents the stiffness of the piezoelectric motor, and d e is the effective piezoelectric coefficient, and α, β, and γ are the shape parameters of the piezoelectric hysteresis curve.

3. The third-order sliding mode control method of a piezoelectric motor according to claim 2, wherein: The system state equation of the piezoelectric motor is: ； Where is the system state, u is the input voltage of the piezoelectric motor, d(t) is the interference term based on the input-output hysteresis characteristics of the piezoelectric ceramic, and f(x, t) and g(x, t) are known functions.

4. The third-order sliding mode control method of a piezoelectric motor according to claim 3, wherein: The third-order sliding surface equation based on the third-order sliding surface design is: ； Among them, s is the third-order sliding surface representation, k1 and k2 are sliding surface design parameters, and k1>0, k2>0.

5. The third-order sliding mode control method of a piezoelectric motor according to claim 4, wherein: Converting the system state equation into the system state third-order sliding surface equation based on the third-order sliding surface design includes: Derivative the third-order sliding surface equation to obtain the third-order sliding surface derivative equation: ； The system state equation Substitute the third-order sliding surface derivative equation to obtain the third-order sliding surface equation of the system state: 。 6. The third-order sliding mode control method of a piezoelectric motor according to claim 5, wherein: The adaptive reaching law is designed to obtain the input voltage of the piezoelectric motor from the third-order sliding surface equation of the system state. The adaptive reaching law expression equation includes: The adaptive reaching law is designed so that the first-order derivative of the third-order sliding surface can be expressed as: ； Where η is the reaching law design parameter, and η>0, λ is the interference estimation gain, and λ>0, d_h is the estimation error of the interference term d(t); and The adaptive reaching law expression equation of the input voltage of the piezoelectric motor is obtained by the third-order sliding surface equation of the system state and the first-order derivative expression of the third-order sliding surface based on the adaptive reaching law: .

7. The third-order sliding mode control method of a piezoelectric motor according to claim 6, wherein: The estimated error d of the interference term d(t) h It is expressed as: ; Where ω is the adaptive gain, and ω >0.

8. The third-order sliding mode control method for a piezoelectric motor according to claim 7, wherein: The reaching law design parameter satisfies at least one of the following: In case that the system is expected to respond quickly, increasing the reaching law design parameter η; and In the case where it is desired to reduce control input variation for a system that is sensitive to chattering, the reaching law design parameter η is reduced.

9. The third-order sliding mode control method of a piezoelectric motor according to claim 7, wherein: The interference estimation gain λ and the adaptive gain ω satisfy at least one of the following: When the interference changes slowly and has a small amplitude, reducing the interference estimation gain λ and the adaptive gain ω; In the case where the interference changes rapidly and has a large amplitude, increasing the interference estimation gain λ and the adaptive gain ω; as well as The value ranges of the interference estimation gain λ and the adaptive gain ω are determined through theoretical analysis based on a known upper limit of interference.

10. The third-order sliding mode control method of a piezoelectric motor according to claim 7, wherein: The reaching law design parameter η satisfies at least one of the following: In case the system has a high natural frequency, increasing the reaching law design parameter η; and In case the system has high damping, the reaching law design parameter η is increased.

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