Single-degree-of-freedom compliant precision positioning platform control method and system, medium and equipment

Abstract

The invention discloses a single-degree-of-freedom compliant precision positioning platform control method and system, a medium and equipment, and relates to the technical field of robot driving control, and the single-degree-of-freedom compliant precision positioning platform control method mainly comprises the steps: building a kinetic model according to a to-be-controlled piezoelectric driving system, constructing a proportional differential sliding mode surface, and then constructing a controller, and controlling the piezoelectric driving system to be controlled by using the controller. By implementing the single-degree-of-freedom compliant precision positioning platform control method, system, medium and equipment provided by the invention, micron-level movement of the single-degree-of-freedom compliant precision positioning platform at low frequency, high frequency and composite frequency can be realized, and very low error is kept.

Description

Technical Field

[0001] The present invention relates to the field of robot drive control technology, and more specifically, to a control method, system, medium and equipment for a single-degree-of-freedom compliant precision positioning platform. Background Art

[0002] With the rapid development of science and technology, people's requirements for exploration and operation in the microscopic field are getting higher and higher. Not only do they require micro-nano positioning and ultra-high precision, but they also need to adapt to a variety of extreme working scenarios. Traditional rigid machinery is often difficult to meet these requirements due to its large size and friction loss. Therefore, compliant mechanisms are widely used because of their advantages such as no friction, no gap, lightweight and high precision. For example, they are used in biomedicine, genetic engineering, aerospace and other fields. Compliant mechanisms often rely on piezoelectric ceramics as drivers. Piezoelectric drivers are one of the most widely used ones. Because piezoelectric drivers themselves have the characteristics of high temperature resistance, strong anti-interference ability and stable output, they are favored by many researchers. However, due to the shortcomings of the piezoelectric driver itself, such as the hysteresis effect, the output and input of the piezoelectric driver show a nonlinear effect. At the same time, the output amplitude of the piezoelectric driver will also change with the change of the input signal frequency, which aggravates the nonlinearity of the piezoelectric drive system. Therefore, it is necessary to design a control algorithm for the piezoelectric drive system to suppress its hysteresis effect and the nonlinearity of input and output, and at the same time, it is necessary to improve the anti-interference ability of the system.

[0003] There are many control strategies for mechanical systems. Among them, sliding mode control has been widely used due to its excellent performance. However, sliding mode control also has problems such as controller output jitter and system output not being smooth enough. Therefore, it needs to be optimized and improved according to the system. Summary of the invention

[0004] The object of the present invention is to provide a control method, system, medium and equipment for a single-degree-of-freedom flexible precision positioning platform, which can realize micron-level motion of the single-degree-of-freedom flexible precision positioning platform at low frequency, high frequency and composite frequency, and maintain very low error.

[0005] The present invention provides a single-degree-of-freedom compliant precision positioning platform control method, comprising the following steps: S1: establishing a dynamic model according to a piezoelectric drive system to be controlled; S2: constructing a proportional differential sliding surface, and obtaining a controller according to the dynamic model and the proportional differential sliding surface; S3: using the controller to control the piezoelectric drive system to be controlled.

[0006] Furthermore, the above step S1 specifically includes: establishing a dynamic model according to the piezoelectric drive system to be controlled, such as the formula: , in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value.

[0007] Furthermore, the above step S2 specifically includes: S21: Construct proportional differential sliding surface, such as formula: , , , , , , , , , in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; S22: According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as formula: , , , , , , , in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter.

[0008] The present invention also provides a single-degree-of-freedom compliant precision positioning platform control system, comprising the following modules: a dynamic model building module, configured to establish a dynamic model according to the piezoelectric drive system to be controlled; a controller building module, configured to construct a proportional differential sliding surface, and obtain a controller according to the dynamic model and the proportional differential sliding surface; a control module, configured to control the piezoelectric drive system to be controlled using the controller.

[0009] Furthermore, the above-mentioned dynamic model building module is specifically configured as follows: according to the piezoelectric drive system to be controlled, a dynamic model is established, such as the formula: , in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value.

[0010] Furthermore, the controller construction module is specifically configured to construct a proportional differential sliding surface, such as the formula: , , , , , , , , , in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as the formula: , , , , , , , in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter.

[0011] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method are implemented.

[0012] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method are implemented.

[0013] The present invention also provides a computer program product, including a computer program, which implements the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method when executed by a processor.

[0014] The single-degree-of-freedom compliant precision positioning platform control method, system, medium and device provided by the present invention have the following beneficial effects: The present invention makes an innovative structural design for an adaptive control algorithm based on a smoothing function for a compliant precision positioning platform based on piezoelectric drive, designs an adaptive sliding mode control strategy, not only designs the adaptive parameters of the sliding mode surface, but also proposes a set of adaptive convergence laws combined with smoothing functions; compared with traditional sliding mode control, the adaptive sliding mode controller designed by the present invention introduces an adaptive sliding mode surface gain and an adaptive convergence law in the control strategy, and uses a smoothing function instead of a sign function; by selecting a suitable Lyapunov equation, the present invention theoretically proves the stability of the system through the Lyapunov second method, and also proves the effectiveness of the algorithm through experiments; the present invention realizes the micrometer-level motion of the platform at low frequency, high frequency and composite frequency, and maintains a very low error. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which: Figure 1It is a flow chart of the control method of the single-degree-of-freedom compliant precision positioning platform provided by the present invention; Figure 2 It is a schematic diagram of the physical arrangement of the experiment provided by the present invention; Figure 3 This is a graph of experimental results provided by the present invention when the input signal is 1 Hz; Figure 4 This is a graph of experimental results provided by the present invention when the input signal is 20 Hz; Figure 5 This is a graph of experimental results provided by the present invention when the input signal is 50 Hz; Figure 6 This is a graph of experimental results provided by the present invention when the input signal is 80 Hz; Figure 7 This is a graph of experimental results provided by the present invention when the input signal is 100 Hz; Figure 8 It is a graph of experimental results provided by the present invention when the input signal is a composite frequency of 1 Hz; Fig. 9 It is a structural block diagram of the computer device provided by the present invention. DETAILED DESCRIPTION

[0016] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0017] Figure 1 A schematic diagram of a single-degree-of-freedom compliant precision positioning platform control method of this embodiment is shown. In this embodiment, the single-degree-of-freedom compliant precision positioning platform control method includes the following steps: S1: Establish a dynamic model according to the piezoelectric drive system to be controlled; In one embodiment, step S1 specifically includes: establishing a dynamic model according to the piezoelectric drive system to be controlled, such as the formula: , in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value; As an embodiment, in step S1, a piezoelectric drive system dynamics model is constructed to establish a second-order dynamic equation of the platform, specifically including: Based on the Bouc-Wen model, the dynamic hysteresis model of the piezoelectric actuator is established. The relationship between the input voltage and output displacement of the piezoelectric actuator system can be expressed as follows: (1) (2) Among them, the above formulas represent the steady-state gain, damping coefficient and natural frequency of the system respectively. Represents the overall disturbance of the system caused by external load disturbances as well as unmodeled dynamics and other unknowns; For the disturbance part of the dynamic model, consider estimating the hysteresis term , there is an error between the actual hysteresis term h, so the dynamic model (1) and the hysteresis term (2) are converted into: (3) (4) definition The actual hysteresis of the system and calculation hysteresis Then considering the uncertainty between system parameters, the system can be expressed as follows: (5) in , , , Represent the errors of model parameters respectively, and all unknown terms include unknown disturbances , hysteresis error And the above parameter error terms can be summarized as the following perturbation estimation equation: (6) The estimated value of the perturbation estimation equation can be expressed as: (7) Then the system dynamic model can be expressed as: (8) in Represents the error between the actual disturbance value and its estimated value. The subsequent adaptive sliding mode control will be based on this dynamic model; S2: constructing a proportional differential sliding surface, and obtaining a controller according to the dynamic model and the proportional differential sliding surface; In one embodiment, step S2 specifically includes: S21: Construct proportional differential sliding surface, such as formula: , , , , , , , , , in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; S22: According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as formula: , , , , , , , in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter; It should be noted that the above parameters can be obtained through multiple trial and error experiments; As an embodiment, in step S2, a controller is designed based on sliding mode control, the second-order dynamic equation of the platform is substituted into it, a PD-type adaptive sliding surface and an adaptive reaching law are designed, and a smooth function is selected to replace the sign function therein, wherein the adaptive sliding mode control algorithm design process is as follows: The system state can be defined as and , so the system displacement tracking error can be defined as and ,here is the expected displacement of the system, and the integral of the error with respect to time can be expressed as: (twenty three) (twenty four) Then a proportional differential sliding surface based on adaptive gain is designed: (25) Here the adaptive gain Can be defined as: ,in is a constant parameter and , s and They are sliding surface and tracking error respectively; according to the dynamic model and sliding surface, the controller of the system can be designed as: (26) in is an equivalent control term, are the switching rate control terms, which are expressed as: , (27) Smt(s) is a smooth function, expressed as , is a positive parameter, The variable parameters are all positive values. It can be expressed as: (28) (29) in , , , and are all positive parameters, It is also a smooth function, defined as ,in is a positive parameter; S3: Using the controller to control the piezoelectric drive system to be controlled.

[0018] The present embodiment provides a single-degree-of-freedom compliant precision positioning platform control system, comprising the following modules: a dynamic model building module, configured to establish a dynamic model according to the piezoelectric drive system to be controlled; a controller building module, configured to build a proportional differential sliding surface, and obtain a controller according to the dynamic model and the proportional differential sliding surface; a control module, configured to control the piezoelectric drive system to be controlled using the controller.

[0019] As an embodiment, the above-mentioned dynamic model building module is specifically configured as follows: according to the piezoelectric drive system to be controlled, a dynamic model is established, such as the formula: , in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value.

[0020] As an embodiment, the controller construction module is specifically configured to construct a proportional differential sliding surface, such as the formula: , , , , , , , , , in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as the formula: , , , , , , , in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter.

[0021] It should be noted that in order to prove the stability of the control strategy of this embodiment, the stability proof process is given here: definition The Lyapunov equation can be constructed as:

[0022] Differentiation with respect to time:

[0023] in,

[0024]

[0025] Substituting in:

[0026]

[0027]

[0028]

[0029] s because ,so

[0030]

[0031] Then according to the formula:

[0032] get: ,definition ,so It can be expressed as:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Then choose the appropriate positive parameter in the experiment , so that: and , because is bounded, so choose satisfy ,so:

[0041]

[0042]

[0043] and:

[0044]

[0045]

[0046] Then select , so we can get and ; so we can get According to Lyapunov's second method, we can get that under the condition of positive definiteness, the derivative of the Lyapunov equation with respect to time is always negative definite, so the system is stable.

[0047] In an exemplary embodiment, the above-mentioned single-degree-of-freedom compliant precision positioning platform control method verifies the feasibility of the algorithm through experiments, and the specific situation is as follows: In this embodiment, the experiment involves hardware such as a piezoelectric drive system, a dSPACE control board, a piezoelectric controller, a pressure sensor, and software such as Controldesk, MATLAB, digital-to-analog conversion, and analog-to-digital conversion; and the piezoelectric drive system also requires a preload system to preload it; Experimental pictures Figure 2 As shown, firstly, the experimental model is designed and built in the computer, and the experimental program is written; the digital-to-analog conversion is realized through the dSPACE control board, and the signal is transmitted to the piezoelectric controller for signal integration, and finally the piezoelectric drive system is excited; the output signal of the piezoelectric drive system is collected by the piezoelectric controller and converted into a digital signal through the dSPACE control board, output to the computer, and downloaded for display; The experimental results are as follows Figure 3-8 As shown, the experimental input signal is a fixed frequency signal and composite frequency signal , where f=1Hz, 20Hz, 50Hz, 80Hz, 100Hz; Figure 3 The input signal is 1Hz. Figure 4 is 20Hz, Figure 5 is 50Hz, Figure 6 is 80Hz, Figure 7 is 100Hz, Figure 8 is the composite frequency; At the same time, the adaptive algorithm is compared with the traditional sliding mode algorithm and PID algorithm, and its mean absolute error e a As shown in Table 1; Table 1: Mean absolute error (μm)

[0048] Root mean square error e r As shown in Table 2.

[0049] Table 2: Root mean square error (μm)

[0050] In this embodiment, an adaptive control algorithm based on a smoothing function for a compliant precision positioning platform based on piezoelectric drive is innovatively designed in structure. Not only are the adaptive parameters of the sliding surface designed, but also a set of adaptive convergence laws combined with the smoothing function are proposed. The stability of the system is proved by the second Lyapunov method, and the effectiveness of the algorithm is also verified by experiments. The experimental results show that the root mean square error of each group of experiments is around 0.5%. This embodiment provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method are implemented. Among them, the storage medium can be a disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory (Flash Memory), a hard disk (HDD) or a solid-state drive (SSD), etc.; the storage medium can also include a combination of the above-mentioned types of memory.

[0051] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method are implemented.

[0052] like Fig. 9 As shown, the computer device may include: at least one processor 121, such as a central processing unit (CPU), at least one communication interface 123, a memory 124, and at least one communication bus 122. Among them, the communication bus 122 is used to realize the connection and communication between these components. Among them, the communication interface 123 may include a display screen (Display), a keyboard (Keyboard), and the optional communication interface 123 may also include a standard wired interface and a wireless interface. The memory 124 may be a high-speed random access memory (Random Access Memory, RAM), or a non-volatile memory (non-volatile memory), such as at least one disk storage. The memory 124 may also be at least one storage device located away from the aforementioned processor 121. Among them, the memory 124 stores an application program, and the processor 121 calls the program code stored in the memory 124 to perform any of the above method steps. Among them, the communication bus 122 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus 122 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig. 9Only one line is used to represent it, but it does not mean that there is only one bus or one type of bus. Among them, the memory 124 may include a volatile memory (volatile memory), such as a random-access memory (random-access memory, RAM); the memory may also include a non-volatile memory (non-volatile memory), such as a flash memory (flash memory), a hard disk drive (hard disk drive, HDD) or a solid-state drive (solid-state drive, SSD); the memory 124 may also include a combination of the above-mentioned types of memory. Among them, the processor 121 may be a central processing unit (central processing unit, CPU), a network processor (network processor, NP) or a combination of CPU and NP. Among them, the processor 121 may further include a hardware chip. The above-mentioned hardware chip may be an application-specific integrated circuit (application-specific integrated circuit, ASIC), a programmable logic device (programmable logic device, PLD) or a combination thereof. The above-mentioned PLD may be a complex programmable logic device (complex programmable logic device, CPLD), a field-programmable gate array (field-programmable gate array, FPGA), a generic array logic (generic array logic, GAL) or any combination thereof. Optionally, the memory 124 is also used to store program instructions. The processor 121 can call the program instructions to implement the single-degree-of-freedom compliant precision positioning platform control method of this embodiment.

[0053] This embodiment provides a computer program product, including a computer program, which implements the steps of the above-mentioned single-degree-of-freedom compliant precision positioning platform control method when executed by a processor.

[0054] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A single-degree-of-freedom compliant precision positioning platform control method, characterized in that: The following steps are involved: S1: Establish a dynamic model according to the piezoelectric drive system to be controlled; S2: constructing a proportional differential sliding surface, and obtaining a controller according to the dynamic model and the proportional differential sliding surface; S3: Using the controller to control the piezoelectric drive system to be controlled.

2. The single-degree-of-freedom compliant precision positioning platform control method according to claim 1, characterized in that: Step S1 specifically includes: establishing a dynamic model according to the piezoelectric drive system to be controlled, such as the formula: ， in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value.

3. The single-degree-of-freedom compliant precision positioning platform control method according to claim 1, characterized in that: Step S2 specifically includes: S21: Construct proportional differential sliding surface, such as formula: ， ， ， ， ， ， ， ， ， in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; S22: According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as formula: ， ， ， ， ， ， ， in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter.

4. A single-degree-of-freedom compliant precision positioning platform control system, characterized in that: Includes the following modules: The dynamic model building module is configured to: establish a dynamic model according to the piezoelectric drive system to be controlled; A controller construction module is configured to: construct a proportional differential sliding surface, and obtain a controller according to the dynamic model and the proportional differential sliding surface; The control module is configured to: use the controller to control the piezoelectric drive system to be controlled.

5. The single-degree-of-freedom compliant precision positioning platform control system according to claim 4, characterized in that: The dynamic model building module is specifically configured as follows: according to the piezoelectric drive system to be controlled, a dynamic model is established, such as the formula: ， in, represents the output displacement acceleration of the piezoelectric drive system to be controlled, represents the damping coefficient of the system, represents the natural frequency of the piezoelectric drive system to be controlled, represents the output displacement velocity of the piezoelectric drive system to be controlled, represents the output displacement of the piezoelectric drive system to be controlled, represents the steady-state gain of the system, represents a fixed parameter, Represents the input voltage signal, To estimate the hysteresis term, To estimate the error between the hysteresis term and the actual hysteresis of the system, represents the system bias, represents the disturbance estimate, Represents the error between the actual disturbance value and its estimated value.

6. The single-degree-of-freedom compliant precision positioning platform control system according to claim 4, characterized in that: The controller building module is specifically configured to build a proportional differential sliding surface, such as the formula: ， ， ， ， ， ， ， ， ， in, is the proportional differential sliding surface, and are the system displacement tracking error, is the actual output displacement of the system, is the system output speed, is the expected displacement of the system, is the expected speed of the system, is the adaptive gain, is the derivative of the adaptive gain, is a constant parameter, represents the first-order derivative of the error, represents the second derivative of the error; According to the dynamic model and the proportional differential sliding surface, a controller is obtained, such as the formula: ， ， ， ， ， ， ， in, For the controller, is an equivalent control term, is the switching rate control term, represents the hysteresis term, is a variable parameter, is a smooth function, is the adaptive gain, is the auxiliary function of the adaptive gain, is a fixed parameter of the adaptive gain, represents a fixed parameter, represents the first-order derivative of the auxiliary function, represents a fixed parameter, About The smooth function of represents a fixed parameter, represents a fixed parameter, is a positive parameter, is a positive parameter.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the single-degree-of-freedom compliant precision positioning platform control method as described in any one of claims 1-6 are implemented.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the single-degree-of-freedom compliant precision positioning platform control method as described in any one of claims 1-6 are implemented.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the single-degree-of-freedom compliant precision positioning platform control method described in any one of claims 1-6 are implemented.

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