Fixed-time preset performance control method and device for macro-micro composite motion platform

Abstract

This invention belongs to the field of measurement and control, and relates to a fixed-time preset performance control method, device, computer equipment, and storage medium for a macro-micro composite motion platform. The method includes: constructing a dynamic system model of the macro-micro composite motion platform; transforming the dynamic system model into a state-space equation suitable for a backstepping recursive control framework; designing a fixed-time preset performance function to constrain the tracking error signal within a preset range within a fixed time; constructing a nonlinear filter to simplify the control design process and establishing a switching function to resolve coupling terms in the system; designing an adaptive fixed-time preset performance tracking control algorithm and proving the stability of the closed-loop system based on Lyapunov stability theory. By designing the controller using an adaptive backstepping recursive control framework, the control design process is simplified, and the computational load is reduced; the tracking error signal of the closed-loop system converges to the preset range within a fixed time, improving the transient performance and control accuracy of the system.

Description

Technical Field

[0001] This invention relates to the field of measurement and control technology, and in particular to a fixed-time preset performance control method, device, computer equipment, and storage medium for a macro-micro composite motion platform. Background Technology

[0002] Macro-micro hybrid motion platforms, as the core carriers of modern ultra-precision manufacturing and measurement, possess a core value that lies in the deep integration of macro-motion systems providing a wide range of motion capabilities with micro-motion systems achieving nanometer-level precision positioning. These platforms play an irreplaceable role in cutting-edge fields such as semiconductor lithography, micro-nano manipulation, and optical precision alignment. However, their control technology consistently faces severe challenges from multi-source complexity: the inherent mechanical inertia, nonlinear friction, and external disturbances of the macro-motion system transfer energy to the micro-motion subsystem through mechanical coupling structures, forming time-varying disturbances that are difficult to model; micro-motion actuators (such as piezoelectric ceramic devices) exhibit strong nonlinear dynamic characteristics such as hysteresis and creep, and their response characteristics are easily affected by temperature and load changes. More importantly, the overall performance of the platform is constrained by two contradictory physical requirements—the need for millisecond-level rapid response during large-stroke motion and the maintenance of sub-micron or even nanometer-level positioning accuracy in the steady-state phase, a contradiction that traditional control architectures often struggle to reconcile.

[0003] Existing solutions suffer from several drawbacks: while PID and its improved algorithms are simple in structure, they struggle to balance dynamic and steady-state performance and lack robustness to time-varying disturbances; sliding mode control, despite its strong disturbance rejection capabilities, excites unmodeled dynamics due to high-frequency chattering, thus degrading micro-motion accuracy; adaptive control, while allowing online parameter adjustment, suffers from convergence speed heavily dependent on initial errors and lacks stringent transient performance guarantees; and preset performance control constrains error boundaries through nonlinear mapping, but its convergence process is still limited by the conservative design of the preset decay function. These methods all exhibit bottlenecks in theoretical framework or engineering implementation when addressing fundamental issues such as cross-scale disturbance coupling, nonlinear superposition, and rapid-precision tradeoffs on macro-micro platforms. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a fixed-time preset performance control method for a macro-micro composite motion platform, employing the following technical solution, including:

[0005] S1, Construct the dynamic system model of the macro-micro composite motion platform;

[0006] S2, transform the dynamic system model into a state-space equation suitable for a backstepping recursive control framework;

[0007] S3, design a fixed-time preset performance function to constrain the tracking error signal within a preset range within a fixed time;

[0008] S4. Construct a nonlinear filter to simplify the control design process and establish a switching function to resolve coupling terms in the system;

[0009] S5. Design an adaptive fixed-time preset performance tracking control algorithm and prove the stability of the closed-loop system based on Lyapunov stability theory.

[0010] Preferably, step S1, constructing the dynamic system model of the macro-micro composite motion platform, specifically includes:

[0011] The formula for the dynamic system model is:

[0012] Where H1 represents the mass of the voice coil motor shaft, H1 represents the acceleration of the voice coil motor shaft during movement, and H2 represents the overall mass of the macro-micro composite motion platform and the piezoelectric actuator. The acceleration of the platform during motion is represented by B1 and B2, respectively, and the stiffness coefficients of the voice coil motor shaft and the spring element are represented by x1 and x2, respectively, and the displacements of the voice coil motor shaft and the macro-micro composite motion platform are represented by ω1 and ω2, respectively, and the damping coefficients of the voice coil motor shaft and the spring element are represented by u1, u2, and ε. The driving force for macro-motion in the voice coil motor is represented by u1, u2 by u2, and the damping force applied by the piezoelectric actuator to the macro-micro composite motion platform is represented by ε. This indicates the speed of the voice coil motor shaft during movement. This indicates the speed at which the platform moves.

[0013] Preferably, step S2, which transforms the dynamic system model into a state-space equation suitable for a backstepping recursive control framework, specifically includes:

[0014] S21, let x 1,1 =x1, x 2,1 =x2, The dynamic system model is then transformed into a state-space equation suitable for a backstep recursive control framework:

[0015]

[0016] Where, x 1,1 x represents the displacement of the voice coil motor shaft. 1,2 x represents the speed of the voice coil motor shaft. 2,1 x represents the displacement of the platform. 2,2 Indicates the platform's movement speed. Represents the system state vector. x represents 1,1 The derivative of x represents1,2 The derivative of x represents 2,1 The derivative of x represents 2,2 The derivative of u i Indicates the system input signal. This represents the disturbance signal caused by unknown external interference, modeling error and instrument aging, where i = 1 and 2 represent the macro-motion system and micro-motion system respectively, and g = 1 and 2 represent the system order respectively;

[0017] S22, Based on the state-space equation, define a nonlinear function. and And interconnected terms η1 and η2,

[0018]

[0019]

[0020] The dynamic system model is simplified to:

[0021] Among them, y i Indicates system output, and For control parameters, i = 1 and 2 represent the macro-motion system and the micro-motion system, respectively.

[0022] Preferably, step S3, designing a fixed-time preset performance function to constrain the tracking error signal within a preset range over a fixed time period, specifically includes:

[0023] S31, Tracking error ρ i,1 and virtual error ρ i,2 Satisfying the inequality -φ i,g (t)<ρ i,g <φ i,g (t), g=1,2, where, φ i,g (t) represents a fixed-time preset performance function. in, Indicates the steady-state error bound. Indicates the set time, φ i,g,0 Represents the initial design parameters, β i,g Represents a constant greater than zero. Indicates the initial error bound. Represents the design parameters, θ i,g and o i,g Let O and E represent odd and even integers respectively, and satisfy O(n). i,g ≥θ i,g ;

[0024] S32, Fixed-time preset performance function φi,g (t) satisfies: φ i,g (t)>0 and and and

[0025] S33, the design error transformation function is: in, Indicates the transformation error. Describes a smooth, strictly increasing function that satisfies and

[0026] S34, obtain the inequality That is, ρ i,g and The one-to-one mapping relationship between them can be represented as:

[0027] Preferably, step S4, which involves constructing a nonlinear filter, simplifying the control design process, and establishing a switching function to resolve coupling terms in the system, specifically includes:

[0028] S41, Construct a nonlinear filter in, This indicates the filtering error signal. σ i,1 and γ i All are design parameters that are greater than zero, χ i,1 express The upper realm, Represents χ i,1 The estimated value, By adaptive law Updated and obtained, and and All are design parameters that are greater than zero.

[0029] Preferably, step S5, designing an adaptive fixed-time preset performance tracking control algorithm and proving the stability of the closed-loop system based on Lyapunov stability theory, specifically includes:

[0030] S51, Define the tracking error signal ρ i,1 and virtual error signal ρ i,2 for Among them, y i,r Indicates the reference signal. Indicates the filtered output signal;

[0031] S52, for ρ i,1 and ρ i,2 After differentiation and integration, we get:

[0032]

[0033] S53 Define function Γ i,g and Ξ i,g ,

[0034] S54, yielding the state equation and

[0035] In the backstep recursive control design process, the state equation for S55 is rewritten as follows:

[0036] in, Indicates the filtering error;

[0037] S56, Approximating an unknown nonlinear function using a radial basis function neural network. and

[0038] in, and This represents the weight vector, and h represents the number of nodes in the neural network. and Represents the Gaussian function. and This represents the bounded approximation error. and All are constants that are greater than zero and arbitrarily small;

[0039] S57, according to the state equation and The neural network approximation error and filtering error are used to construct the barrier Lyapunov functions for steps 1 and 2, respectively:

[0040] Among them, c i,1 and c i,2 All are constants greater than zero. and Both are neural network approximation errors, and and They represent and The estimated value, It is the filtering estimation error.

[0041] Preferably, in the first step of the backstep recursive control design process, a virtual control signal α is designed. i,1 for:

[0042] in,

[0043] ζi,1 Indicates a design parameter that is greater than zero;

[0044] In step 2 of the backstepping recursive control design process, the actual controller u... i Designed as follows:

[0045] in, and Design and switching functions The relevant structure is as follows:

[0046]

[0047] in, ζ i,2 For design parameters that are greater than zero, d i,g Represents a constant greater than zero. Represents a known continuous nonlinear function;

[0048] The adaptive laws for steps 1 and 2 of the backstep recursive control design process are shown below:

[0049] in, and All are design parameters that are greater than zero.

[0050] To address the aforementioned technical problems, this invention also provides a fixed-time preset performance control device for a macro-micro composite motion platform, employing the following technical solution, including:

[0051] A construction module is used to construct the dynamic system model of the macro-micro composite motion platform;

[0052] The transformation module is used to transform the dynamic system model into a state-space equation suitable for a backstepping recursive control framework;

[0053] The first design module is used to design a fixed-time preset performance function to constrain the tracking error signal within a preset range within a fixed time.

[0054] The construction module is used to construct nonlinear filters, simplify the control design process, and establish switching functions to resolve coupling terms in the system;

[0055] The second design module is used to design an adaptive fixed-time preset performance tracking control algorithm, and to prove the stability of the closed-loop system based on Lyapunov stability theory.

[0056] To address the aforementioned technical problems, the present invention also provides a computer device that employs the technical solution described below, comprising a memory and a processor. The memory stores computer-readable instructions, and the processor, when executing the computer-readable instructions, implements the steps of the aforementioned fixed-time preset performance control method for a macro-micro composite motion platform.

[0057] To address the aforementioned technical problems, the present invention also provides a computer-readable storage medium, which employs the technical solution described below. The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, implement the steps of the aforementioned fixed-time preset performance control method for a macro-micro composite motion platform.

[0058] Compared with existing technologies, the present invention has the following advantages: by constructing a time-varying performance boundary function to dynamically constrain the transient and steady-state envelopes of the tracking error, the predictability of core indicators such as overshoot and convergence speed is guaranteed from the source; a fixed-time convergence control law is designed based on Lyapunov stability theory, so that the system state converges to the equilibrium point within a preset maximum time, completely eliminating the dependence on initial conditions; and a parameter adaptive law is introduced to realize real-time estimation and active compensation for unmodeled dynamics and time-varying disturbances. This control strategy theoretically overcomes the inherent contradiction between convergence speed and disturbance rejection robustness in traditional methods, providing a technical path for macro-micro composite platforms that balances theoretical rigor and engineering applicability, marking a significant paradigm breakthrough in the field of ultra-precision motion control. Compared with traditional PID control strategies applicable to macro-micro composite motion platforms, the dynamic system model of this platform is transformed into a non-strict feedback interconnected nonlinear system. The controller is then designed using an adaptive backstepping recursive control framework, simplifying the control design process and reducing the computational load. Applying an adaptive fixed-time preset performance control method to this system platform ensures that the tracking error signal of the closed-loop system converges to a preset range within a fixed time, effectively improving the system's transient performance and control accuracy. Furthermore, the convergence time is independent of the system's initial state. Attached Figure Description

[0059] To more clearly illustrate the solutions in this invention, the accompanying drawings used in the description of the embodiments of this invention will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0060] Figure 1 This is a schematic diagram of the macro-micro composite motion platform used in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention.

[0061] Figure 2This is a flowchart of an embodiment of the fixed-time preset performance control method for the macro-micro composite motion platform of the present invention;

[0062] Figure 3 This is a principle block diagram of the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention;

[0063] Figure 4 This is a schematic diagram of the tracking error signal and fixed-time preset performance function of the macro-micro composite motion platform used in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention.

[0064] Figure 5 This is a schematic diagram showing the change of adaptive parameters over time in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention.

[0065] Figure 6 This is a schematic diagram illustrating the change of control input signal over time in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention.

[0066] Figure 7 This is a schematic diagram of the filter error changing over time in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention.

[0067] Figure 8 This is a schematic diagram of a structure of an embodiment of the fixed-time preset performance control device for the macro-micro composite motion platform of the present invention;

[0068] Figure 9 This is a schematic diagram of the structure of an embodiment of the computer device of the present invention.

[0069] In the diagram, 1-vibration-resistant base, 2-guide rail, 3-platform, 4-piezoelectric ceramic as actuator, 5-spring, 6-voice coil motor bearing, 7-voice coil motor. Detailed Implementation

[0070] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein in the specification is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings are used to distinguish different objects and not to describe a particular order.

[0071] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0072] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0073] It should be noted that the fixed-time preset performance control method of the macro-micro composite motion platform provided in the embodiments of the present invention is generally executed by the macro-micro composite motion platform, and correspondingly, the fixed-time preset performance control device of the macro-micro composite motion platform is generally set in the macro-micro composite motion platform.

[0074] It should be understood that the number of macro-micro composite motion platforms is merely illustrative. Depending on the implementation requirements, any number of macro-micro composite motion platforms can be used.

[0075] Example 1

[0076] Please refer to Figure 1 The diagram illustrates the architecture of the macro-micro composite motion platform, which is the execution platform for the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention. The macro-micro composite motion platform includes a shock-resistant base 1, a guide rail 2 mounted on the shock-resistant base, a platform 3, a piezoelectric ceramic 4 serving as an actuator, a spring 5, a voice coil motor bearing 6, and a voice coil motor 7, etc.

[0077] The anti-vibration base 1 serves as the supporting structure for the entire platform 3, ensuring its stability and anti-vibration performance. Guide rails 2, installed on the anti-vibration base 1, guide the macro and micro movements of the platform 3. The platform 3, mounted on the guide rails 2, can move linearly or planarly along them.

[0078] The piezoelectric ceramic 4 and voice coil motor 7, acting as actuators, are the key driving forces for the platform's movement. The piezoelectric ceramic 4 generates minute deformations by applying voltage, thereby achieving micro-motion control. The voice coil motor 7 drives the platform 3 to perform rapid macro-motion adjustments via electromagnetic force. The spring 5 and the voice coil motor bearing 6 serve to buffer, support, and guide, ensuring the smoothness and precision of the movement.

[0079] The guide rail 2 is fixed on the anti-vibration base 1 to ensure the straightness and parallelism of the guide rail 2.

[0080] Platform 3 is connected to guide rail 2 via a sliding joint or rolling joint, allowing it to move linearly or planarly on guide rail 2. This connection method ensures the stability and accuracy of platform 3's movement.

[0081] The piezoelectric ceramic 4 is connected to the micro-motion part of the platform 3 via a preload spring or directly. When a voltage is applied, the piezoelectric ceramic 4 produces a small deformation, which is transmitted to the platform 3 via the spring 5 or directly, thus achieving micro-motion control.

[0082] Piezoelectric ceramics 4 have the characteristics of fast response speed and high positioning accuracy, making them very suitable for micro-motion control.

[0083] Spring 5 plays a role in buffering and pre-tensioning in the macro-micro composite motion platform. It can absorb the impact and vibration during the motion process, improving the stability and accuracy of platform 3.

[0084] Meanwhile, the preload of spring 5 ensures that piezoelectric ceramic 4 maintains a certain deformation during operation, thereby improving the accuracy and stability of micro-motion control.

[0085] The voice coil motor 7 drives the platform for macroscopic adjustments via electromagnetic force. The voice coil motor bearing 6 ensures the stability and precision of the connection between the motor and the platform.

[0086] When current passes through the coil of the voice coil motor 7, it generates an electromagnetic force in the magnetic field, thereby driving the platform 3 to perform rapid and smooth macro motion.

[0087] The macro-motion is mainly driven by the voice coil motor 7. The voice coil motor 7 has the characteristics of fast response speed and large driving force, which can quickly adjust the position of the platform.

[0088] The micro-motion is achieved by driving the piezoelectric ceramic 4. The minute deformation of the piezoelectric ceramic 4 is transmitted to the platform 3 through the spring 5 or directly, achieving high-precision positioning and adjustment.

[0089] Macro and micro motions are coordinated and controlled by the control system to ensure that platform 3 can move precisely according to the preset trajectory and speed.

[0090] Please refer to Figure 2 The flowchart illustrates an embodiment of the fixed-time preset performance control method for the macro-micro composite motion platform of the present invention. The fixed-time preset performance control method for the macro-micro composite motion platform includes the following steps:

[0091] Step S1: Construct the dynamic system model of the macro-micro composite motion platform.

[0092] In this embodiment, step S1, constructing the dynamic system model of the macro-micro composite motion platform, may specifically include the following steps:

[0093] S11, the dynamic system model formula is:

[0094] Where H1 represents the mass of the voice coil motor shaft, H1 represents the acceleration of the voice coil motor shaft during movement, and H2 represents the overall mass of the macro-micro composite motion platform and the piezoelectric actuator. The acceleration of the platform during motion is represented by B1 and B2, respectively, and the stiffness coefficients of the voice coil motor shaft and the spring element are represented by x1 and x2, respectively, and the displacements of the voice coil motor shaft and the macro-micro composite motion platform are represented by ω1 and ω2, respectively, and the damping coefficients of the voice coil motor shaft and the spring element are represented by u1, u2, and ε. The driving force for macro-motion in the voice coil motor is represented by u1, u2 by u2, and the damping force applied by the piezoelectric actuator to the macro-micro composite motion platform is represented by ε. This indicates the speed of the voice coil motor shaft during movement. This indicates the speed at which the platform moves.

[0095] A dynamic system model is a mathematical model that describes how the various parts of a system interact with each other over time or other variables. In the context of a macro-micro composite motion platform, this model is used to reveal the laws governing the evolution of the platform's motion state (such as position, velocity, and acceleration) over time.

[0096] The benefits of constructing a dynamic system model include: providing a solid theoretical foundation for the design of platform control strategies; analyzing the parameters in the model allows for the design of more precise and efficient controllers to achieve stable, fast, and high-precision platform motion; the dynamic model helps predict the platform's behavior under different operating conditions, which is of great significance in motion planning, avoiding motion saturation, and optimizing point motion time; and the model is a key tool for simulation analysis. Before implementing control strategies in a real system, computer simulation can verify the effectiveness of the control algorithm and reduce risks in practical applications.

[0097] Step S2: Transform the dynamic system model into a state-space equation suitable for a backstepping recursive control framework.

[0098] In this embodiment, step S2, transforming the dynamic system model into a state-space equation suitable for a backstepping recursive control framework, may specifically include the following steps:

[0099] S21, let x 1,1 =x1, x 2,1 =x2, The dynamic system model is then transformed into a state-space equation suitable for a backstep recursive control framework:

[0100]

[0101] Where, x 1,1 x represents the displacement of the voice coil motor shaft.1,2 x represents the speed of the voice coil motor shaft. 2,1 x represents the displacement of the platform. 2,2 Indicates the platform's movement speed. Represents the system state vector. x represents 1,1 The derivative of x represents 1,2 The derivative of x represents 2,1 The derivative of x represents 2,2 The derivative of u i Indicates the system input signal. This represents the disturbance signal caused by unknown external interference, modeling errors, and instrument aging. i = 1 and 2 represent the macro-motion system and the micro-motion system, respectively, and g = 1 and 2 represent the system order, respectively.

[0102] State-space equations are used to accurately describe the behavior of dynamic systems.

[0103] The purpose of transforming a dynamic system model into state-space equations is to simplify complex dynamic system models into a form that is easier to handle and analyze. Through state-space equations, we can see the patterns of change in the system's internal states and how these states are affected by external inputs.

[0104] S22, Based on the state-space equation, define a nonlinear function. and And interconnected terms η1 and η2,

[0105]

[0106]

[0107] The dynamic system model is simplified to:

[0108] Among them, y i Indicates system output, and For control parameters, i = 1 and 2 represent the macro-motion system and the micro-motion system, respectively.

[0109] In the backstep recursive control framework, nonlinear functions and interconnection terms are key elements describing the dynamic characteristics of the system. Nonlinear functions describe nonlinear effects in the system, such as friction, dead zone, and saturation. Interconnection terms describe the interactions between system states. By defining these functions and terms, the dynamic behavior of the system can be described more accurately, leading to the design of more precise control strategies. This step improves the adaptability and robustness of the control strategy, enabling it to better cope with uncertainties and nonlinear effects in the system.

[0110] Step S3: Design a fixed-time preset performance function to constrain the tracking error signal within a preset range within a fixed time.

[0111] Tracking error signal refers to the difference between the target position or trajectory and the actual position or trajectory; it is a key indicator for evaluating the tracking performance of a control system. In macro-micro composite motion platforms, due to the need for high-speed and high-precision positioning, the tracking error signal is used to reflect the deviation between the platform's actual motion state and the target state in real time. By accurately measuring and calculating the tracking error signal, the control system can adjust its control strategy in a timely manner to reduce deviation and improve positioning accuracy.

[0112] Virtual error signals, obtained through mathematical transformations or filtering, provide additional degrees of freedom in controller design to better achieve preset performance targets. In the fixed-time preset performance control of macro-micro composite motion platforms, virtual error signals are used to design preset performance functions that limit the range of variation in the tracking error signal, thereby ensuring the boundedness of the system state. Simultaneously, virtual error signals can also be used to design adaptive controllers or fixed-time convergent controllers to improve system robustness and convergence speed.

[0113] In this embodiment, step S3, designing a fixed-time preset performance function to constrain the tracking error signal within a preset range over a fixed time period, may specifically include the following steps:

[0114] S31, Tracking error ρ i,1 and virtual error ρ i,2 Satisfying the inequality -φ i,g (t)<ρ i,g <φ i,g (t), g=1,2, where, φ i,g (t) represents a fixed-time preset performance function. in, Indicates the steady-state error bound. Indicates the set time, φ i,g,0 Represents the initial design parameters, β i,g Represents a constant greater than zero. Indicates the initial error bound. Represents the design parameters, θ i,g and o i,g Let O and E represent odd and even integers respectively, and satisfy O(n). i,g ≥θ i,g .

[0115] Tracking error refers to the difference between the position value given in the control command and the actual position value reached by the platform during the positioning motion of a macro-micro composite motion platform. This error reflects the accuracy of the platform's response to control commands and is one of the important indicators for measuring the performance of the control system.

[0116] Virtual error is a hypothetical error introduced into a control strategy to assist in achieving fixed-time preset performance control. By pre-setting a virtual error trajectory, the control system can more precisely control the platform's motion while ensuring that the actual tracking error does not exceed a preset limit. The introduction of virtual error enables the control system to quickly converge to the desired performance index within a fixed time, improving the platform's motion accuracy and response speed.

[0117] S32, Fixed-time preset performance function φ i,g (t) satisfies: φ i,g (t)>0 and and and

[0118] Step S32 is used to further explain the preset performance function. These conditions need to be met in order to achieve the desired preset performance control effect.

[0119] S33, the design error transformation function is: in, Indicates the transformation error. Describes a smooth, strictly increasing function that satisfies and Obtaining inequalities That is, ρ i,g and The one-to-one mapping relationship between them can be represented as:

[0120] In the error transformation process of the backstepping recursive control framework, the error signal needs to be transformed into an error transformation function (one-to-one mapping transformation), and then a Lyapunov function about the error transformation function is constructed for control design and stability analysis.

[0121] Step S4: Construct a nonlinear filter to simplify the control design process and establish a switching function to resolve coupling terms in the system.

[0122] In this embodiment, step S4, constructing a nonlinear filter to simplify the control design process and establishing a switching function to resolve coupling terms in the system, may specifically include the following steps:

[0123] S41, Construct a nonlinear filter in, This indicates the filtering error signal. σ i,1 and γ i All are design parameters that are greater than zero, χ i,1 express The upper realm, Represents χ i,1 The estimated value, By adaptive law Updated and obtained, and and All are design parameters that are greater than zero.

[0124] By constructing a nonlinear filter to estimate the virtual control signal, and then using the filtered output signal to replace the virtual control signal, the partial derivative of the virtual control signal is eliminated, simplifying the control design process.

[0125] In practice, switching functions can also be established to resolve coupling terms in the system. The switching function and the nonlinear filter are independent modules. The switching function is established to handle the interconnect terms in the system and resolve system coupling problems.

[0126] Establish switching functions to resolve coupling terms in the system.

[0127] in, Ψ1 and Ψ2 are both constants greater than zero, and Ψ2 < Ψ1.

[0128] Step S5: Design an adaptive fixed-time preset performance tracking control algorithm and prove the stability of the closed-loop system based on Lyapunov stability theory.

[0129] In this embodiment, step S5, designing an adaptive fixed-time preset performance tracking control algorithm, and proving the stability of the closed-loop system based on Lyapunov stability theory, may specifically include the following steps:

[0130] S51, Define the tracking error signal ρ i,1 and virtual error signal ρ i,2 for Among them, y i,r Indicates the reference signal. This represents the filtered output signal.

[0131] In backstepping recursive control, coordinate transformation involves defining tracking error signals and virtual error signals. These two error signals are needed for subsequent coordinate transformation, control design, and stability analysis.

[0132] S52, for ρ i,1 and ρ i,2 After differentiation and integration, we get:

[0133]

[0134] We take derivatives and integrate them to prepare for subsequent transformations.

[0135] S53, Define function Γ i,g and Ξ i,g ,

[0136] Define the function, simplify the process, and obtain the following state equation.

[0137] S54, yielding the state equation and

[0138] Obtaining the derivative of the transformation error prepares us for the subsequent differentiation of the Lyapunov function, which is quite complex. It can be understood as providing the derivative of the transformation error in advance to facilitate the later differentiation of the Lyapunov function.

[0139] In the backstep recursive control design process, the state equation for S55 is rewritten as follows:

[0140] in, This indicates the filtering error.

[0141] Backstepping recursive control design, which involves substituting some state variables, can be understood as... and Write it completely.

[0142] S56, Approximating an unknown nonlinear function using a radial basis function neural network. and

[0143] in, and This represents the weight vector, and h represents the number of nodes in the neural network. and Represents the Gaussian function. and This represents the bounded approximation error. and All are constants that are greater than zero and arbitrarily small.

[0144] Unknown nonlinear functions cannot be directly used for controller design. Therefore, we use radial basis function neural networks to approximate the function and obtain the approximate expression, which is known and can be used for control design.

[0145] S57, according to the state equation and The neural network approximation error and filtering error are used to construct the barrier Lyapunov functions for steps 1 and 2, respectively:

[0146] Among them, c i,1 and c i,2 All are constants greater than zero. and Both are neural network approximation errors, and and They represent and The estimated value, It is the filtering estimation error.

[0147] The controlled system is a second-order system. In the backstepping recursive control framework, the control design can be carried out in two steps. In both the first and second steps, a barrier Lyapunov function needs to be constructed.

[0148] and This represents the approximation error of the neural network. This indicates the filtering error.

[0149] In the first step of the backstep recursive control design process (the first step involves constructing a virtual control signal, which can be understood as a conventional step in the backstep recursive control framework), the virtual control signal α is designed. i,1 for: in, ζ i,1 Indicates a design parameter that is greater than zero;

[0150] In the second and final step of the backstepping recursive control design process, the actual controller u is constructed. i Designed as follows:

[0151] in, and Design and switching functions The relevant structure is as follows:

[0152] in, ζ i,2 For design parameters that are greater than zero, d i,g Represents a constant greater than zero. Represents a known continuous nonlinear function;

[0153] The adaptive laws for steps 1 and 2 are as follows:

[0154] in, and All are design parameters that are greater than zero.

[0155] In some optional implementations of this embodiment, after step S5, the electronic device may further perform the following steps:

[0156] S6. Based on the Lyapunov function stability theory, the system stability is analyzed, and it is proved that the designed controller can make the system stable.

[0157] In the first step of the backstep recursive control design framework, by applying the barrier Lyapunov function V... i,1 Differentiation yields

[0158]

[0159] By using the mathematical lemma Young's inequality and radial basis function neural networks to approximate the unknown nonlinear function, we can obtain:

[0160]

[0161] in, and Represents a constant greater than zero.

[0162] Apply the above inequalities and the virtual control signal α i,1 And adaptive law Substitution After sorting, we can obtain:

[0163]

[0164] In the second step of the backstep recursive control design framework, V i,2 Differentiation yields

[0165]

[0166] By using the mathematical lemma Young's inequality and radial basis function neural networks to approximate the unknown nonlinear function, we can obtain:

[0167]

[0168] in, and d i,g Both represent constants greater than zero.

[0169] According to the switching function This can be explained in three cases:

[0170] (1) When make According to the relevant mathematical lemma, we can obtain... Where γ iThis represents a constant greater than zero. Then... It can be rewritten as:

[0171]

[0172] Using Young's inequality, we can obtain:

[0173]

[0174] Substituting the above inequality into We can obtain: in,

[0175]

[0176] (2) When but:

[0177] Similar to case (1), it can be Summarized as follows:

[0178]

[0179] (3) When make Can Summarized as follows:

[0180]

[0181] Combining the above three situations, we can Integrated into:

[0182] in, By integrating the constructed Lyapunov functions, we can obtain:

[0183] Differentiating with respect to V, we get: Finally, it can be integrated as follows: in:

[0184] Based on the switching function expression, the analysis is divided into three segments. Different derivatives of the Lyapunov function will be obtained when the function takes different values.

[0185] Integrating both sides of the above inequality simultaneously, we get:

[0186] Based on this inequality and ξ i,1 (0) The boundedness of is known ξi,1 and Both are bounded. Therefore, based on the definition of the fixed-time preset performance function and the error transformation mechanism, the tracking error ρ can be determined. i,1 It can converge to a preset range within a fixed time, and the virtual error ρ i,2 The Lyapunov function can be constrained within a specified constant bound by a barrier. (By Y) i,g and χ i,1 The boundedness of, and and From the definition, we can obtain and It is also bounded. Therefore, the stability of the system can be determined based on the stability analysis process described above.

[0187] Figure 3 This is a principle block diagram of the fixed-time preset performance control method for the macro-micro composite motion platform of the present invention. (See diagram for example.) Figure 3 As shown, the macro-motion system is driven by a macro-motion actuator to drive a macro-motion platform. A first sensor detects the actual position of the macro-motion platform in real time and compares it with a preset reference signal to generate a first calculation error. This error signal is input to an adaptive fixed-time preset performance controller u1 (macro-motion controller). The controller quickly adjusts the output of the macro-motion actuator according to preset performance indicators and algorithms to reduce the error and approach the desired trajectory.

[0188] The micro-motion system is used to further compensate for the residual error of the macro-motion system. A high-precision second sensor detects the actual position of the micro-motion platform and compares it with the expected position after macro-motion compensation, generating a second calculation error. This error signal is input to the adaptive fixed-time preset performance controller u2 (micro-motion controller). The controller uses a high-precision control algorithm to drive the micro-motion actuator to make minute adjustments, ensuring that the platform achieves nanometer-level positioning accuracy.

[0189] The collaborative operation between the two systems, through hierarchical control and adaptive algorithms, enables the preset performance control of the macro-micro composite motion platform within a fixed time period. This method not only improves the platform's positioning accuracy and motion stability but also optimizes control efficiency and response speed, providing strong technical support for fields such as semiconductor manufacturing and precision measurement.

[0190] To demonstrate the effectiveness of this embodiment, the following simulation verification was performed:

[0191] according to Figure 1The macro-micro composite motion platform shown has a corresponding dynamic system model as shown in step S1. In the simulation experiment, this dynamic system model is used as the controlled system. The system parameters are selected as follows: H1 = 1 kg, H2 = 0.8 kg, B1 = 60 N / mm, B2 = 160 N / mm, ω1 = 0.0001 Ns / mm, ω2 = 0.0001 Ns / mm, ε = 0.000055 Ns / mm; the initial system state value is selected as: x 1,1 (0) = 2, x 1,2 (0) = 1.5, x 1,2 (0) = -2, x 2,2 (0) = 1.5; The design parameters for the fixed-time preset performance function are as follows: φ i,1,0 =2.5, β i,1 =0.5, θ i,1 =5,o i,1 =10, τ i,1 =0.5, φ i,2,0 =2, β i,2 =0.5, θ i,2 =5,o i,2 =10, τ i,2 =0.5, The reference signal is selected as: y i,r =sin(t); Other control parameters are selected as follows: A i,1 =25, A i,2 =20, λ1=1, λ2=1.25, c i,1 =80,c i,2 =80, ζ i,1 =5, ζ i,2 =5, σ i,1 =0.5, γ1=γ2=1.5,

[0192] Based on the above system model, system parameters, and control parameters, the control method proposed in this embodiment was applied using Matlab simulation software to perform simulations, and the simulation results were obtained, such as... Figure 4-7 As shown.

[0193] Figure 4 This is a schematic diagram of the tracking error signal and fixed-time preset performance function of the macro-micro composite motion platform used in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention. Figure 4 As shown, the tracking error ρ i,1 and virtual error ρ i,2 All can be done at the preset time Converging to the steady-state error bound The error accuracy can be controlled within 0.003mm, so the system control accuracy can be effectively improved by using this control scheme according to its own control needs.

[0194] Figure 5 This is a schematic diagram illustrating the time-varying adaptive parameters used in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention. (See diagram for example.) Figure 5 As shown, the adaptive law of the design Update the obtained adaptive parameters

[0195] Figure 6 This is a schematic diagram illustrating the change of the control input signal over time in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention. Figure 6 As shown, the control input signal u i (i = 1, 2) remains bounded throughout the execution of the control task, indicating that the system remains stable.

[0196] Figure 7 This is a schematic diagram illustrating the time-varying filter error used in the fixed-time preset performance control method of the macro-micro composite motion platform of the present invention. (See diagram for example.) Figure 7 As shown, the filtering error signal ξ i,1 (i=1,2), thus demonstrating the stability of the nonlinear filter.

[0197] This embodiment addresses the high-precision control requirements of a macro-micro composite motion platform. Using a backstepping recursive method as the control design framework, it proposes an adaptive tracking control scheme based on a fixed-time preset performance function. To optimize the system's transient performance and control objectives, a fixed-time preset performance function and a barrier Lyapunov function are constructed to limit tracking and transformation errors within preset ranges, respectively. Simultaneously, a nonlinear filter is designed to estimate the virtual control signal, thus avoiding differentiation of the virtual control signal and simplifying the control design process. For the coupling interconnection term between the macro and micro motion platforms, a switching function is established to compensate for this interconnection term, effectively avoiding singular value problems. Furthermore, the stability of the closed-loop system under the described control scheme is verified using fixed-time and Lyapunov function stability theory. Finally, simulation experiments demonstrate the effectiveness of the control scheme described in this embodiment.

[0198] The beneficial effects of implementing this embodiment are as follows: by constructing a time-varying performance boundary function to dynamically constrain the transient and steady-state envelopes of the tracking error, the predictability of core indicators such as overshoot and convergence speed is guaranteed from the root; a fixed-time convergence control law is designed based on Lyapunov stability theory, so that the system state converges to the equilibrium point within a preset maximum time, completely eliminating the dependence on initial conditions; and a parameter adaptive law is introduced to realize real-time estimation and active compensation for unmodeled dynamics and time-varying disturbances. This control strategy theoretically overcomes the inherent contradiction between convergence speed and disturbance rejection robustness in traditional methods, providing a technical path for macro-micro composite platforms that balances theoretical rigor and engineering applicability, marking a significant paradigm breakthrough in the field of ultra-precision motion control. Compared with traditional PID control strategies applicable to macro-micro composite motion platforms, the dynamic system model of this platform is transformed into a non-strict feedback interconnected nonlinear system. The controller is then designed using an adaptive backstepping recursive control framework, simplifying the control design process and reducing the computational load. Applying an adaptive fixed-time preset performance control method to this system platform ensures that the tracking error signal of the closed-loop system converges to a preset range within a fixed time, effectively improving the system's transient performance and control accuracy. Furthermore, the convergence time is independent of the system's initial state.

[0199] This invention can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0200] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing related hardware with computer-readable instructions. These computer-readable instructions can be stored in a computer-readable storage medium. When executed, the program can include the processes of the embodiments of the above methods. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, optical disk, or read-only memory (ROM), or random access memory (RAM).

[0201] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0202] Example 2

[0203] Further reference Figure 8 As a response to the above Figure 2 The present invention provides an embodiment of a fixed-time preset performance control device for a macro-micro composite motion platform, which is implemented by the method shown. Figure 2 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0204] like Figure 8 As shown, the fixed-time preset performance control device 60 of the macro-micro composite motion platform described in this embodiment includes: a construction module 61, a conversion module 62, a first design module 63, a construction module 64, and a second design module 65. Wherein:

[0205] Module 61 is used to construct the dynamic system model of the macro-micro composite motion platform;

[0206] The transformation module 62 is used to transform the dynamic system model into a state-space equation suitable for a backstepping recursive control framework;

[0207] The first design module 63 is used to design a fixed-time preset performance function so that the tracking error signal is constrained to a preset range within a fixed time.

[0208] Module 64 is used to construct nonlinear filters, simplify the control design process, and establish switching functions to resolve coupling terms in the system.

[0209] The second design module 65 is used to design an adaptive fixed-time preset performance tracking control algorithm and prove the stability of the closed-loop system based on Lyapunov stability theory.

[0210] The beneficial effects of implementing this embodiment are as follows: Compared with the traditional PID control strategy applicable to macro-micro composite motion platforms, the dynamic system model of this platform is transformed into a non-strict feedback interconnected nonlinear system. Then, the controller is designed through an adaptive backstepping recursive control framework, which simplifies the control design process and reduces the amount of control calculation. Applying the adaptive fixed-time preset performance control method to this system platform ensures that the tracking error signal of the closed-loop system can converge to the preset range within a fixed time, which effectively improves the transient performance and control accuracy of the system. Moreover, the convergence time does not depend on the initial state of the system.

[0211] Example 3

[0212] To address the aforementioned technical problems, embodiments of the present invention also provide a computer device. Please refer to [link / reference needed]. Figure 9 , Figure 9 This is a basic structural block diagram of the computer device in this embodiment.

[0213] The aforementioned computer device 7 includes a memory 71, a processor 72, and a network interface 73 that are interconnected via a system bus. It should be noted that the figure only shows a computer device 7 with components 71, 72, and 73; however, it should be understood that it is not required to implement all the shown components, and more or fewer components may be implemented instead. Those skilled in the art will understand that the computer device described here is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0214] The aforementioned computer devices can be desktop computers, laptops, handheld computers, and cloud servers, among other computing devices. These devices can facilitate human-computer interaction with users through keyboards, mice, remote controls, touchpads, or voice-activated devices.

[0215] The aforementioned memory 71 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the aforementioned memory 71 may be an internal storage unit of the aforementioned computer device 7, such as the hard disk or memory of the computer device 7. In other embodiments, the aforementioned memory 71 may also be an external storage device of the aforementioned computer device 7, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the computer device 7. Of course, the aforementioned memory 71 may also include both the internal storage unit and its external storage device of the aforementioned computer device 7. In this embodiment, the aforementioned memory 71 is typically used to store the operating system and various application software installed on the aforementioned computer device 7, such as computer-readable instructions for a fixed-time preset performance control method of a macro-micro composite motion platform. In addition, the aforementioned memory 71 can also be used to temporarily store various types of data that have been output or will be output.

[0216] In some embodiments, the processor 72 may be a central processing unit (CPU), controller, microcontroller, microprocessor, or other data processing chip. The processor 72 is typically used to control the overall operation of the computer device 7. In this embodiment, the processor 72 is used to execute computer-readable instructions stored in the memory 71 or to process data, such as executing computer-readable instructions for the fixed-time preset performance control method of the macro-micro composite motion platform.

[0217] The network interface 73 may include a wireless network interface or a wired network interface, which is typically used to establish a communication connection between the computer device 7 and other electronic devices.

[0218] The beneficial effects of implementing this embodiment are as follows: Compared with the traditional PID control strategy applicable to macro-micro composite motion platforms, the dynamic system model of this platform is transformed into a non-strict feedback interconnected nonlinear system. Then, the controller is designed through an adaptive backstepping recursive control framework, which simplifies the control design process and reduces the amount of control calculation. Applying the adaptive fixed-time preset performance control method to this system platform ensures that the tracking error signal of the closed-loop system can converge to the preset range within a fixed time, which effectively improves the transient performance and control accuracy of the system. Moreover, the convergence time does not depend on the initial state of the system.

[0219] Example 4

[0220] The present invention also provides another embodiment, namely, providing a computer-readable storage medium storing computer-readable instructions that can be executed by at least one processor to cause the at least one processor to perform the steps of the fixed-time preset performance control method for the macro-micro composite motion platform as described above.

[0221] The beneficial effects of implementing this embodiment are as follows: Compared with the traditional PID control strategy applicable to macro-micro composite motion platforms, the dynamic system model of this platform is transformed into a non-strict feedback interconnected nonlinear system. Then, the controller is designed through an adaptive backstepping recursive control framework, which simplifies the control design process and reduces the amount of control calculation. Applying the adaptive fixed-time preset performance control method to this system platform ensures that the tracking error signal of the closed-loop system can converge to the preset range within a fixed time, which effectively improves the transient performance and control accuracy of the system. Moreover, the convergence time does not depend on the initial state of the system.

[0222] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0223] Obviously, the embodiments described above are merely some embodiments of the present invention, not all embodiments. The accompanying drawings show preferred embodiments of the present invention, but do not limit the patent scope of the present invention. The present invention can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the patent protection scope of this invention.

Claims

1. A fixed-time preset performance control method for a macro-micro compound motion platform, characterized in that, The method comprises the following steps: S1, constructing a dynamic system model of the macro-micro compound motion platform; S2, converting the dynamic system model into a state space equation suitable for a backstepping recursive control framework; S3, designing a fixed-time preset performance function to constrain a tracking error signal within a preset range in a fixed time; S4, constructing a nonlinear filter to simplify the control design process and establishing a switching function to solve the coupling terms in the system; S5, designing an adaptive fixed-time preset performance tracking control algorithm, and proving the stability of the closed-loop system based on Lyapunov stability theory; The step S1 of constructing the dynamic system model of the macro-micro compound motion platform specifically comprises: The kinetic system model formula is: (Formula 1); wherein, represents the mass of the voice coil motor shaft, represents the acceleration when the voice coil motor shaft moves, represents the overall mass of the macro-micro compound motion platform and the piezoelectric element actuator, represents the acceleration when the platform moves, and respectively represent the stiffness of the voice coil motor shaft and the stiffness coefficient of the spring element, and respectively represent the displacement of the voice coil motor shaft and the macro-micro compound motion platform, and respectively represent the damping coefficient of the voice coil motor shaft and the spring element, represents the driving force for macro motion in the voice coil motor, represents the damping force exerted by the piezoelectric element actuator on the macro-micro compound motion platform, represents the viscosity coefficient between the macro-micro compound motion platform and the guide rail, represents the speed when the voice coil motor shaft moves, represents the speed when the platform moves, The step S2 of converting the dynamic system model into a state space equation suitable for a backstepping recursive control framework specifically comprises: S21, let , , , transforming the kinetic system model into state space equations suitable for a backstepping recursive control framework: (Formula 2); wherein, denotes the voice coil motor shaft motion displacement, denotes the voice coil motor shaft motion velocity, denotes the platform motion displacement, denotes the platform motion velocity, denotes the system state vector, denotes the derivative of denotes the derivative of denotes the derivative of denotes the derivative of denotes the system input signal, denotes the disturbance signal caused by unknown external disturbances, modeling errors and instrument aging, denote the macro-motion system and micro-motion system, respectively, denote the system order, respectively; S22, defining a nonlinear function based on the state space equation , , and and interconnection terms and , ， ， ， ， ， ， Simplifying the kinetic system model to: (Equation 3), wherein, represents a system output, and is a control parameter, respectively represent a macro-motion system and a micro-motion system; The step S3 of designing a fixed-time preset performance function to constrain a tracking error signal within a preset range in a fixed time specifically comprises: S31, tracking error and virtual error satisfying inequality wherein, denotes a fixed-time pre-specified performance function, wherein, denotes a steady-state error bound, denotes a settling time, denotes an initial design parameter, denotes a constant greater than zero, denotes an initial error bound, denotes a design parameter, and denote odd and even integers, respectively, and satisfy ; S32, fixed time preset performance function satisfies: and and and , ; S33, the design error transformation function is: wherein, denotes the transformation error, denotes a smooth strictly increasing function satisfying and , the inequality is obtained, that is and between a pair of one-to-one mapping relationship can be expressed as: .

2. The fixed-time pre-specified performance control method of the macro-micro compound motion platform according to claim 1, wherein, The step S4 of constructing a nonlinear filter to simplify the control design process and establishing a switching function to solve the coupling terms in the system specifically comprises: S41, configuring a nonlinear filter : wherein, denotes a filtered error signal, , and are design parameters greater than zero, denotes an upper bound of , denotes an estimate of , is obtained by an adaptive law , and and are design parameters greater than zero.

3. The fixed-time pre-specified performance control method of the macro-micro compound motion platform according to claim 2, characterized in that, The step S5 of designing an adaptive fixed-time preset performance tracking control algorithm, and proving the stability of the closed-loop system based on Lyapunov stability theory specifically comprises: S51, defining a tracking error signal and a virtual error signal is wherein denotes a reference signal, denotes a filtered output signal; S52, to and After derivation, integration is obtained: ； S53, define function and , ; S54, obtaining the state equation and , ; In the backstepping recursive control design process, the state equation is rewritten as: wherein, denotes the filtered error; S56, approximating the unknown nonlinear function with a radial basis function neural network and : wherein, and denotes a weight vector, denotes the number of neural network nodes, and denotes a Gaussian function, and denotes a bounded approximation error, and are both positive constants and arbitrarily small. S57, according to the equation of state and , neural network approximation error and filtering error, the first step and the second step of the barrier Lyapunov function are constructed as follows: , where, and are constants greater than zero, and are neural network approximation errors, and and represent estimates of and respectively, is a filtering estimation error.

4. The fixed-time pre-specified performance control method of the macro-micro compound motion platform according to claim 3, wherein, In the first step of the backstepping control design procedure, a virtual control signal is designed as where , denotes a design parameter greater than zero; In the second step of the backstepping control design procedure, the actual controller is designed as: wherein, and the design and switching function are related, constructed as follows: , wherein, , is a design parameter greater than zero, denotes a constant greater than zero, denotes a known continuous non-linear function; The adaptive laws of the first and second steps of the backstepping recursive control design process are as follows: wherein, and are both design parameters greater than zero.

5. A fixed-time preset performance control device of a macro-micro hybrid motion platform, configured to perform the fixed-time preset performance control method of the macro-micro hybrid motion platform according to any one of claims 1 to 4, characterized in that, The fixed-time preset performance control device of the macro-micro compound motion platform comprises: A construction module for constructing a dynamic system model of the macro-micro compound motion platform; A conversion module for converting the dynamic system model into a state space equation suitable for a backstepping recursive control framework; A first design module for designing a fixed-time preset performance function to constrain a tracking error signal within a preset range in a fixed time; A construction module for constructing a nonlinear filter to simplify the control design process and establishing a switching function to solve the coupling terms in the system; A second design module for designing an adaptive fixed-time preset performance tracking control algorithm, and proving the stability of the closed-loop system based on Lyapunov stability theory.

6. A computer device, comprising: A computer readable storage medium having computer readable instructions stored thereon, wherein the computer readable instructions are executed by a processor to implement the steps of the fixed-time preset performance control method of the macro-micro compound motion platform according to any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, A computer readable storage medium having computer readable instructions stored thereon, wherein the computer readable instructions are executed by a processor to implement the steps of the fixed-time preset performance control method of the macro-micro compound motion platform according to any one of claims 1 to 4.

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