Predetermined performance control method and device for precision motion platform

Abstract

The invention belongs to the related technical field of precision motion platform control, and discloses a preset performance control method and equipment for a precision motion platform, and the method comprises the steps: (1) obtaining the dynamic response of the precision motion platform under external disturbance; (2) setting a predetermined performance function of the precision motion platform based on the obtained dynamic response; (3) setting a coordinate transformation mechanism based on the predetermined performance function; (4) sequentially setting a non-singular fast terminal continuous layering sliding mode surface and a superhelix reaching law based on the coordinate transformation mechanism; and (5) designing a predetermined performance controller based on the dynamic response, the predetermined performance function, the coordinate transformation mechanism, the non-singular fast terminal continuous layered sliding mode surface and the superhelix reaching law, and further performing predetermined performance control on the precision motion platform by adopting the predetermined performance controller. According to the method, the precise motion platform can effectively cope with complex disturbance, and convergence speed and positioning precision are improved while it is guaranteed that expected output of the system meets preset performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of precise motion platform control, and more particularly, to a predetermined performance control method and device for a precise motion platform. BACKGROUND

[0002] In recent years, with the increasing demand for precise motion control in the fields of space exploration, microelectronic manufacturing, optical detection, biomedical micro-operation, etc., precise motion platforms have gradually become the core components of high-precision industrial equipment, and their application scenarios have covered nanoscale positioning, sub-micron trajectory tracking, multi-degree-of-freedom cooperative motion, and other high-difficulty tasks. To meet the stringent requirements of precise operation at the microscale, the motion platform not only needs to overcome multiple disturbances caused by the external environment and its own structure, but also must achieve millisecond-level dynamic response and micro-radian-level attitude adjustment, while maintaining sub-micron-level positioning accuracy in long-term operation. These factors may cause trajectory tracking errors, positioning overshoots, and even system instability under high-frequency response, directly restricting the application efficiency of the platform in the fields of space exploration, micro-nano manufacturing, quantum device manipulation, etc.

[0003] In the field of precise motion platform control, traditional control methods often have difficulty in simultaneously considering transient response quality and steady-state control accuracy, especially under the influence of multiple source disturbances and system uncertainties, which may easily cause problems such as excessive overshoot, slow convergence, or steady-state error fluctuations. Predetermined performance control transforms complex control objectives into explicit constraints on error evolution trajectories by predefining performance boundaries (such as convergence speed, maximum overshoot, and steady-state error range) during the design phase, providing a theoretical and quantifiable design framework for system performance. For precise motion platforms, predetermined performance control not only strictly limits the convergence process of trajectory tracking errors in micro-nano positioning, but also actively compensates for external disturbances and model uncertainties by adjusting control gains online, ensuring that the preset transient and steady-state performance is maintained under complex working conditions such as multi-axis coupled motion and high-speed start-stop.

[0004] However, the predetermined performance control still faces multiple challenges in practical applications: on the one hand, the continuous effect of complex disturbances may cause the system state to repeatedly oscillate near the predetermined performance boundary, resulting in frequent switching of the control input between the saturation region and the non-saturation region, which not only destroys the stability of the equilibrium state, but also exacerbates the mechanical wear of the actuator. On the other hand, the strict constraints of the predetermined performance control on the error convergence path may limit the system response speed: when pursuing fast convergence, aggressive adjustment of the control gain is easy to trigger the overshoot constraint, resulting in an overly conservative response process; while relaxing the constraint can improve the response speed, it may sacrifice the steady-state accuracy, forming an inherent contradiction between convergence and response speed. In addition, under the influence of model uncertainty or unmodeled dynamics, the predetermined performance boundary may not accurately match the actual system characteristics, causing deviations between the theoretically designed convergence trajectory and the actual response, further affecting the control effectiveness. Precise motion platforms not only expect the system output to meet the predetermined performance, but also hope to improve the convergence speed and positioning accuracy as much as possible. However, the above problems still lack effective solutions. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a predetermined performance control method and device for a precise motion platform, which aims to solve the problem that existing control methods are difficult to handle the desired system output of the precise motion platform while meeting the predetermined performance, improving the convergence speed and positioning accuracy.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present application, a predetermined performance control method for a precise motion platform is provided, comprising the following steps: (1) obtaining the dynamic response of the precise motion platform under external disturbance; (2) setting a predetermined performance function of the precise motion platform based on the obtained dynamic response; (3) setting a coordinate transformation mechanism based on the predetermined performance function; (4) sequentially setting a non-singular fast terminal continuous layered sliding mode surface and a super-helical approaching law based on the coordinate transformation mechanism; (5) designing a predetermined performance controller based on the dynamic response, the predetermined performance function, the coordinate transformation mechanism, the non-singular fast terminal continuous layered sliding mode surface and the super-helical approaching law, and then using the predetermined performance controller to perform predetermined performance control on the precise motion platform.

[0007] Further, the nonlinear dynamic response of the precise motion platform under external disturbance is:

[0008] wherein, is the coefficient of the control input, is the control input, This is the actual speed of the motor. For the motor rotation angle, The frictional resistance torque of the system, Let be the moment of inertia of the motor. It is the damping coefficient of the motor subjected to damping force during rotation.

[0009] Furthermore, the predetermined performance function is:

[0010] In the formula, and It is a decision The constant weighting factors of the upper and lower bounds, Let represent a bounded performance function, where yes The speed of convergence, It is a predefined positive value related to stable tracking accuracy. Is the recipient and The initial value of the constraint, where t is time.

[0011] Furthermore, the coordinate transformation mechanism is as follows:

[0012] In the formula, This refers to the position tracking error; It is a bounded performance function.

[0013] Furthermore, The derivative is:

[0014] in, ; and The second derivative is:

[0015] For the position tracking error, we have:

[0016] In the formula, For the desired turning angle.

[0017] Furthermore, define the following auxiliary variables. , Then the control system with predetermined performance constraints is transformed into:

[0018] in , ; The nonsingular fast terminal continuous layered sliding mode surface is:

[0019] wherein, and are the coordinate-transformed , ; is a normal number, is designed as:

[0020] in the formula, , and are positive odd integer numbers, , , and are constants to be designed.

[0021] Further, the super-spiral control approaching law is:

[0022] wherein:

[0023] in the formula, , are control gains; , are nonlinear construction items of the super-spiral control approaching law; , , , , are control gains; is a designed sliding mode surface function.

[0024] Further, the predetermined performance controller is: .

[0025] The application further provides a predetermined performance control system of a precision motion platform, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program to execute the predetermined performance control method of the precision motion platform as described above.

[0026] The application further provides a computer readable storage medium, the computer readable storage medium storing machine executable instructions, the machine executable instructions, when called and executed by a processor, causing the processor to implement the predetermined performance control method of the precision motion platform as described above.

[0027] Compared with the prior art, the predetermined performance control method and device of the precision motion platform provided by the present application mainly has the following beneficial effects: 1. The present application sets the super-helical approach law and applies it to the predetermined performance controller, effectively suppresses the chattering of the system by using the high-order sliding mode control characteristics, improves the stability and ultra-high positioning accuracy of the precision motion platform control process, and enables the precision motion platform to effectively cope with complex disturbances, while ensuring that the expected output of the system meets the predetermined performance, the convergence speed and positioning accuracy are improved.

[0028] 2. The predetermined performance controller based on the super-helical non-singular fast terminal sliding mode is designed. Compared with the existing method, the predetermined performance controller can not only ensure that the expected system output of the precision motion platform can still maintain the predetermined performance under disturbance, but also improve the convergence speed of the error and the positioning accuracy of the platform.

[0029] 3. The non-singular fast terminal continuous layered sliding surface is designed and used, which effectively avoids the singularity problem, speeds up the convergence speed of the system, and ensures convergence within a limited time. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a motion process schematic diagram of an embodiment of the present application; Figure 2 is a flow schematic diagram of a motion control method of an embodiment of the present application; Figure 3 is a schematic diagram of a motion control structure of an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0032] The present application provides a predetermined performance control method for a precision motion platform, which sets a predetermined performance function for the precision motion platform, then designs a coordinate transformation mechanism according to the predetermined performance function, designs a non-singular fast terminal continuous layered sliding surface and a super-helical control law, and then designs a predetermined performance controller, and performs predetermined performance control on the precision motion platform based on the predetermined performance controller.

[0033] The predetermined performance control method mainly includes the following steps: Step one, obtain the dynamic response of the precision motion platform under external disturbance.

[0034] The nonlinear dynamic response of the precision motion platform under external disturbance is:

[0035] wherein, is a coefficient of control input, is a control input, is an actual rotating speed of the motor, is a rotating angle of the motor, is a friction resistance torque of the system, is a rotating inertia of the motor, is a damping coefficient of the damping force in the rotating process of the motor.

[0036] Step two, setting a predetermined performance function of the precision motion platform based on the obtained dynamic response.

[0037] Output tracking error which needs to be always kept within a predefined attenuation boundary, and the corresponding predetermined performance function is:

[0038] wherein, and are constant weight factors determining the upper and lower boundaries of , and represents a bounded performance function, wherein is a convergence speed of , and is a predefined positive value about stable tracking accuracy, is an initial value constrained by and , and t is time.

[0039] Step three, setting a coordinate transformation mechanism based on the predetermined performance function.

[0040] In order to achieve the predetermined performance, the set coordinate transformation mechanism is:

[0041] wherein, is a position tracking error; is a bounded performance function.

[0042] The derivative thereof is:

[0043] wherein, ; and the second derivative thereof is:

[0044] For position tracking error, we have:

[0045] where, is the desired rotation angle.

[0046] Based on the obtained nonlinear dynamic response of the precision motion platform, we have:

[0047] where, is the measured value of motor speed, is the measurement error of motor speed, is the measured value of system friction torque, is the measurement error of system friction torque.

[0048] According to and definitions, the second derivative of

[0049] where: .

[0050] Step four, based on the coordinate transformation mechanism, set the nonsingular fast terminal continuous layered sliding mode surface and super-spiral approach law in turn.

[0051] Define the following auxiliary variables , , then the control system with predetermined performance constraints is converted to:

[0052] where , .

[0053] For the above system, the known disturbance is , the unknown disturbance is , which can be weakened by compensation for subsequent design.

[0054] The designed nonsingular fast terminal continuous layered sliding mode surface is:

[0055] where, and are the transformed , respectively; is a normal number, is designed as:

[0056] wherein, , and is a positive odd integer, , , and are constants to be designed.

[0057] The super-spiral control approaching law is:

[0058] wherein:

[0059] wherein, , is a control gain; , is a nonlinear construction term of the super-spiral control approaching law; , , , , is a control gain; is a designed sliding mode surface function.

[0060] Step five, a predetermined performance controller is designed based on the dynamic response, the predetermined performance function, the coordinate transformation mechanism, the non-singular fast terminal continuous layered sliding mode surface and the super-spiral approaching law, and the predetermined performance controller is used to perform predetermined performance control on the precision motion platform.

[0061] The predetermined performance controller is: .

[0062] The present application is further described in detail below with specific embodiments.

[0063] The precision motion platform of the embodiment is a locking and releasing mechanism in a space gravitational wave detection task. In the space gravitational wave detection task, in order to ensure that the space inertial sensor can be safely and reliably transferred to the scientific operation stage, a special locking and releasing mechanism must be designed to realize the locking of the test mass in the launching process and the accurate positioning and releasing in the space. The movement process of the locking and releasing mechanism in the task space mainly includes three stages: the locking stage, the capturing and positioning stage and the releasing stage, as shown in Figure 1The locking top rod of the locking unit fixes the test mass with a locking force of about 1500N during the rocket launching process. Then, the locking top rod is retracted after the satellite is put into orbit, the test mass is transferred to the plunger of the capture positioning unit for constraint, and is positioned to the center position of the electrode frame with high precision. Finally, the release pin advances, the plunger retreats, and the test mass is completely handed over to the release pin for constraint. The test mass is released by the release pin in a symmetrical manner, and the test mass is released at an extremely low residual speed, and then is captured and controlled by the electrostatic control system. However, in actual application, the locking release mechanism is faced with multiple source disturbances, for example, adhesion effect generated by contact between the test mass and the locking release mechanism, external contact force impact, end load change, friction between the moving parts and the fixed parts, etc. These disturbance factors not only affect the release precision of the locking release mechanism, but also can even cause system vibration. In order to ensure smooth and high-precision release of the test mass, the locking release mechanism urgently needs an effective disturbance suppression method and control method.

[0064] To achieve the above object, the embodiment of the present application provides a pre-determined performance control method of a precision motion platform, and the motion control method flow is shown, and the specific implementation is as follows: Please refer to Figure 2 and Figure 3 In the present example, the locking unit and the capture unit of the locking release mechanism adopt a hollow non-magnetic single-output shaft ultrasonic motor as a bottom excitation source. The motion of the capture unit is the rotation motion of the split nut driven by the ultrasonic motor, and the split nut drives the linear motion of the lead screw. In the embodiment, the nonlinear dynamics of the capture unit of the locking release mechanism driven by the ultrasonic motor can be expressed as:

[0065] In the formula, is the driving torque of the motor, is the system identification parameter, is the ideal rotating speed of the motor, is the actual rotating speed of the motor, is the rotating angle of the motor, is the friction resistance torque of the system, is the moment of inertia of the motor, is the damping coefficient of the damping force in the rotating process of the motor, is the frequency of the driving voltage, is the phase difference of the two driving voltages, and is generally , is the wavelength number in one cycle of the stator, is the diameter of the stator, is the thickness of the stator. It can be seen that the control of the rotating speed can be realized by changing the frequency of the driving voltage.

[0066] According to the dynamic response characteristics of the capture unit of the locking release mechanism under external disturbance, the one-time measurement errors of position and velocity are and respectively, and the identification error of the friction resistance moment of the system is .

[0067] The output tracking error needs to be always kept within a predefined attenuation boundary. In this example, the predetermined performance function is designed as:

[0068] wherein and are constant weight factors determining the upper and lower bounds of , represents a bounded performance function, wherein is the convergence speed of , is a predefined positive value related to the stable tracking accuracy, is the initial value constrained by and .

[0069] In this embodiment, in order to achieve the predetermined performance, the designed coordinate transformation mechanism is specifically expressed as follows:

[0070] The derivative thereof is:

[0071] wherein, according to the definitions of , and , it can be inferred that:

[0072] and the second derivative of is:

[0073] For the position tracking error, there is:

[0074] Therefore, it can be known that:

[0075] Then, it can be obtained that:

[0076] According to Definition, The second derivative is rewritten as:

[0077] In this embodiment:

[0078] In this embodiment, the designed non-singular fast terminal (FNTSC) continuously layered sliding surface and the improved superspiral control law are as follows: Define the following auxiliary variables , and Then, the precision motion table trajectory tracking control system with predetermined performance constraints is transformed into:

[0079] in ,

[0080] For the above system, the known disturbance is... Unknown disturbance is This can be mitigated through compensation and used in subsequent design. The design of this control method is crucial for... It is robust.

[0081] In this embodiment, the designed non-singular fast terminal continuous layered sliding surface is as follows:

[0082] in For positive integers, Designed as follows:

[0083] Its derivative is:

[0084] In the formula, , and is a positive odd integer, , , and It is a constant to be designed.

[0085] The derivative of the designed sliding surface is as follows:

[0086] In this embodiment, the improved superhelical reaching law is designed as follows:

[0087] wherein and is a control gain.

[0088] On this basis, according to the definitions of and , the controller designed in this example is:

[0089] Through the above steps, the predetermined performance control method for realizing the precision motion platform is finally obtained, which can not only effectively avoid or suppress system chattering, ensure motion stability, but also accelerate system convergence speed and ensure convergence within a limited time, on the basis of ensuring that the expected system output of the precision motion platform meets the predetermined performance.

[0090] The application further provides a predetermined performance control system for a precision motion platform, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the predetermined performance control method for the precision motion platform as described above.

[0091] The application further provides a computer readable storage medium, which stores machine executable instructions, the machine executable instructions, when called and executed by a processor, cause the processor to realize the predetermined performance control method for the precision motion platform as described above.

[0092] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the application, and is not used to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for controlling the predetermined performance of a precision motion platform, characterized in that, The steps are as follows: (1) Obtain the dynamic response of the precision motion platform under external disturbances; (2) Based on the obtained dynamic response, set the predetermined performance function of the precision motion platform; (3) Set the coordinate transformation mechanism based on the predetermined performance function; (4) Based on the coordinate transformation mechanism, the non-singular fast terminal continuous layered sliding surface and the superspiral reaching law are set sequentially; (5) Based on the dynamic response, the predetermined performance function, the coordinate transformation mechanism, the non-singular fast terminal continuous layered sliding surface and the super-spiral approach law, a predetermined performance controller is designed, and then the predetermined performance controller is used to perform predetermined performance control on the precision motion platform.

2. The method for controlling the predetermined performance of a precision motion platform as described in claim 1, characterized in that: The nonlinear dynamic response of the precision motion platform under external disturbance is as follows: In the formula, To control the input coefficients, To control the input, This is the actual speed of the motor. For the motor rotation angle, The frictional resistance torque of the system, Let be the moment of inertia of the motor. It is the damping coefficient of the motor subjected to damping force during rotation.

3. The method for controlling the predetermined performance of a precision motion platform as described in claim 2, characterized in that: The predetermined performance function is: In the formula, and It is a decision The constant weighting factors of the upper and lower bounds, Let represent a bounded performance function, where yes The speed of convergence, It is a predefined positive value related to stable tracking accuracy. Is the recipient and The initial value of the constraint, where t is time.

4. The method for controlling the predetermined performance of a precision motion platform as described in claim 3, characterized in that: The coordinate transformation mechanism is as follows: In the formula, This refers to the position tracking error; It is a bounded performance function.

5. The method for controlling the predetermined performance of a precision motion platform as described in claim 4, characterized in that: The derivative is: in, ; and The second derivative is: For the position tracking error, we have: In the formula, For the desired turning angle.

6. The method for controlling the predetermined performance of a precision motion platform as described in claim 5, characterized in that: Define the following auxiliary variables , Then the control system with predetermined performance constraints is transformed into: in , ; The non-singular fast terminal continuous layered sliding surface is: in, and These are the coordinate transformations. , ; For positive integers, Designed as follows: In the formula, , and is a positive odd integer, , , and It is a constant to be designed.

7. The method for controlling the predetermined performance of a precision motion platform as described in claim 6, characterized in that: The superhelical control reaching law is: in: In the formula, , To control the gain; , For the nonlinear construct of the superspiral control reaching law; , , , , To control the gain; The function for the designed sliding surface.

8. The method for controlling the predetermined performance of a precision motion platform as described in claim 7, characterized in that: The predetermined performance controller is: 。 9. A predetermined performance control system for a precision motion platform, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the predetermined performance control method of the precision motion platform according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement a predetermined performance control method for the precision motion platform according to any one of claims 1-8.

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