Kalman filter-based platform vibration compensation calculation, control method and system

Abstract

The application provides a platform vibration compensation calculation, control method and system based on Kalman filtering, comprising: according to the motion state of a motion platform, proposing a dynamics model under the vibration of the motion platform, and discretizing the dynamics model to obtain a state space equation under discretization; measuring the vibration signal of the motion platform by using a laser sensor, considering the measurement noise, and obtaining a measurement equation; through an extended Kalman filter, fusing the measurement data obtained from the measurement equation and the prior state estimation which is discrete and iterated, and obtaining a state estimation value close to the real state; and subtracting the displacement expected value from the state estimation value to determine a compensation control signal for platform vibration compensation. The application realizes the fusion of the prior state estimation and the measurement value through the Kalman filter, thereby improving the signal-to-noise ratio of the system measurement data.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of control method design, in particular, to a platform vibration compensation calculation and control method and system based on Kalman filtering BACKGROUND

[0002] In recent years, high-precision motion platforms are increasingly widely used in modern industries, and the progress of science and technology has increasingly strict requirements for the precision of the platform, especially in the field of high-speed machining and semiconductor industry. In the process of motion, the platform inevitably produces micro-vibration, which has a significant impact on positioning accuracy, so it is crucial to monitor and compensate for vibration.

[0003] In order to reduce the impact of vibration on the motion accuracy of the platform, appropriate control strategies must be taken for compensation, including feedforward control, PID control, robust control, adaptive control, and composite control methods. Among these control methods, feedforward control requires the establishment of an accurate vibration mathematical model, which is difficult; while robust control, adaptive control and composite control can effectively eliminate vibration errors and improve positioning accuracy, but they are more expensive and difficult to implement. In contrast, PID control technology is mature, simple in algorithm, and does not depend on the accurate model of the controlled object, so it is more widely used.

[0004] The characteristics of the vibration model are difficult to accurately describe, which leads to the possibility of calculation errors caused by model errors in the calculation process of the vibration model. In addition, due to the high-frequency characteristics of vibration, it is difficult for the observer to accurately capture these high-frequency dynamics in real time, and the noise of the observer itself makes it difficult to accurately observe the vibration state. SUMMARY

[0005] In view of the defects in the prior art, the purpose of the present application is to provide a platform vibration compensation calculation and control method and system based on Kalman filtering.

[0006] According to one aspect of the present application, a platform vibration compensation calculation method based on Kalman filtering is provided, comprising:

[0007] According to the motion state of the motion platform, a dynamic model of the motion platform under vibration is determined and discretized to obtain a state space equation under discretization;

[0008] The vibration signal of the motion platform is measured by a laser sensor, and a measurement equation is obtained by considering the measurement noise;

[0009] The measurement data obtained by the measurement equation and the prior state estimation which is discretized and iterated are fused by an extended Kalman filter to obtain a state estimation value close to the true state;

[0010] The displacement expectation value and the state estimation value are subtracted to determine a compensation control signal for platform vibration compensation.

[0011] Preferably, the determination of the dynamic model of the motion platform under vibration according to the motion state of the motion platform comprises:

[0012] Based on the assumed mode method, high-order modes are ignored, only the first-order mode is retained, and the coupling relationship between degrees of freedom is not considered. The single degree of freedom deformation w(x, t) of the motion platform is specifically represented as:

[0013] w(x, t) = Φ(x)q(t)

[0014] Wherein x represents the displacement of a single degree of freedom, t represents time, Φ(x) is the first-order modal function of the motion platform, and q(t) is the generalized coordinate;

[0015] The displacement P of any point on the motion platform is represented as:

[0016] P = w(x, t) + s(t)

[0017] Wherein s(t) is the macroscopic motion displacement of the motion platform;

[0018] The square of the velocity of the P point is represented as:

[0019]

[0020] The total kinetic energy of the motion platform includes the kinetic energy generated by the total displacement caused by the macroscopic displacement and the microscopic displacement of the motion platform, and is specifically:

[0021]

[0022] Wherein m is the total mass of the motion platform;

[0023] The motion platform moves on a plane, and only the elastic potential energy generated by the microscopic vibration is considered, and the specific is:

[0024]

[0025] Wherein E is the elastic modulus of the motion platform, and A is the cross-sectional area of the motion platform;

[0026] The Lagrangian function L is represented as: L = T - V

[0027] The macro-micro dynamic model of the motion platform is obtained by using the Lagrange equation:

[0028]

[0029] Wherein F(t) is the driving force received by the motion platform.

[0030] Preferably, the dynamic model of the motion platform under vibration is discretized to obtain a state space equation in the discrete form, comprising:

[0031] The system state variable and the system input control variable are defined as:

[0032]

[0033] The macro-micro dynamic model is discretized, and process noise w is added [k] ~ N(0, Q c ) to establish a state space equation of the discrete system:

[0034]

[0035] k and k-1 represent the kth value and the (k-1)th value in the discrete state;

[0036] For the nonlinear equation x [k] The Taylor series expansion is used to obtain a Jacobian matrix:

[0037]

[0038] where A [k] and W [k] are the Jacobian matrices of the partial derivatives of f with respect to x and w, respectively.

[0039] Preferably, the vibration signal of the motion platform is measured by using a laser sensor, and a measurement equation is obtained by considering the measurement noise, comprising:

[0040] The vibration signal of the platform is measured by using a laser sensor, and the measurement noise v [k] ~ N(0, R c ) is considered at the same time to obtain a measurement equation:

[0041]

[0042] z [k] represents the displacement signal with measurement noise, x 1[k] represents the displacement of the motion platform, v 1[k] represents the measurement noise of the laser sensor for measuring the displacement of the motion platform, x 2[k] represents the velocity of the motion platform, v 2[k] represents the measurement noise of the laser sensor for measuring the velocity of the motion platform, x 3[k] represents a constant value;

[0043] For the nonlinear measurement equation z [k] The Taylor series expansion is used to obtain a Jacobian matrix:

[0044]

[0045] where H m[k] and V [k] are Jacobians of h with respect to x and v, respectively.

[0046] Preferably, the data fusion of the measurement data obtained from the measurement equation and the discrete and constantly iterated prior state estimation is performed by an extended Kalman filter to obtain a state estimation value close to the real state, comprising:

[0047] According to the initial conditions of the motion platform, appropriate noise covariance matrices Q c and R c are selected, and time update and measurement update formulas of the Kalman filter are used;

[0048] The optimal vibration state estimation x (t) is obtained by constantly iterating the time update and measurement update formulas.

[0049] Preferably, the time update formula is:

[0050]

[0051] The measurement update formula is:

[0052]

[0053] where x is the prior state estimation; is the prior state estimation error covariance matrix; K [k] is the Kalman gain; is the posterior state estimation; P [k] is the posterior state estimation error covariance matrix.

[0054] According to a second aspect of the present application, a platform vibration compensation calculation system based on Kalman filtering is provided, comprising:

[0055] A dynamics model establishment module: according to the motion state of the motion platform, a dynamics model under vibration of the motion platform is determined, and is discretized to obtain a state space equation under discretization;

[0056] A measurement equation establishment module: a vibration signal of the motion platform is measured by using a laser sensor, and a measurement equation is obtained by considering the measurement noise;

[0057] A Kalman filtering module: data fusion of measurement data obtained from the measurement equation and discrete and constantly iterated prior state estimation is performed by an extended Kalman filter to obtain a state estimation value close to the real state;

[0058] The feedback compensation module determines a compensation control signal by subtracting the displacement expectation value from the state estimation value for platform vibration compensation.

[0059] According to a third aspect of the present application, a Kalman filter-based platform vibration compensation control method is provided, in which a voltage value is input into a linear motor, and an acting force obtained by motor operation is output;

[0060] The acting force is applied to a motion platform, and the motion platform is displaced;

[0061] For the displacement process of the motion platform, the Kalman filter-based platform vibration compensation calculation method or the Kalman filter-based platform vibration compensation calculation system according to any one of the aspects is used to obtain a compensation control signal;

[0062] The compensation control signal is taken as an input of PID control to obtain a voltage value for controlling the linear motor, which is cyclically input into the linear motor to realize platform vibration compensation control.

[0063] According to a fourth aspect of the present application, a terminal is provided, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor can be used to execute the method according to any one of the aspects or run the system.

[0064] According to a fifth aspect of the present application, a computer readable storage medium is provided, which stores a computer program executable by a processor to execute the method according to any one of the aspects or run the system.

[0065] Compared with the prior art, the embodiments of the present application have at least one of the following beneficial effects:

[0066] In the embodiments of the present application, the Kalman filter-based platform vibration compensation calculation method and system are used, the fusion of prior state estimation and measurement values is realized through a Kalman filter, and thus the signal-to-noise ratio of system measurement data is improved. The method aims to solve the problems in the prior art, i.e., the influence of vibration on a motion platform at a microscopic level and the difficulty in constructing an accurate model due to the high-frequency characteristics of vibration. These problems will cause large errors in the calculation and measurement processes, and thus the accuracy of obtained data is reduced and the signal-to-noise ratio is decreased.

[0067] In the embodiments of the present application, the Kalman filter-based platform vibration compensation calculation method and system are used, a macroscopic and microscopic dynamics model of a motion platform is constructed, and the model is discretized, so as to derive a state space equation of a discrete system. Meanwhile, the influence of process noise is considered in the modeling process. The vibration signal of the motion platform is measured by a laser sensor, and measurement noise is taken into account, so as to obtain data closer to the actual situation.

[0068] In the embodiment of the present application, a Kalman filter-based platform vibration compensation calculation method, system, and control method are adopted, and the vibration dynamics model of the motion platform belongs to a nonlinear system. By using an extended Kalman filter to fuse the prior state estimation and measurement values, the accuracy of the estimated values is improved. In addition, by applying a PID control algorithm to control the motion platform, compared with directly using a laser sensor for feedback compensation, the present application significantly improves the positioning accuracy of the motion platform in a vibration state by applying Kalman filter technology. BRIEF DESCRIPTION OF DRAWINGS

[0069] Other features, objects, and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments with reference to the attached drawings:

[0070] Figure 1 A flowchart of a Kalman filter-based platform vibration compensation calculation method in an embodiment of the present application. DETAILED DESCRIPTION

[0071] The present application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made. These all belong to the protection scope of the present application.

[0072] As shown in Figure 1 An embodiment of the present application provides a Kalman filter-based platform vibration compensation calculation method, which comprises:

[0073] Step 1: According to the motion state of the motion platform, a dynamics model under vibration of the motion platform is proposed, and is discretized to obtain a state space equation under discretization;

[0074] Step 2: The vibration signal of the motion platform is measured by using a laser sensor, and a measurement equation is obtained by considering the measurement noise;

[0075] Step 3: The measurement data obtained from the measurement equation in step 2 and the discretized and iterated prior state estimation obtained in step 1 are fused by using an extended Kalman filter to obtain a state estimation value close to the true state;

[0076] Step 4: The displacement expectation value and the state estimation value obtained in step 3 are subtracted to determine a compensation control signal for platform vibration compensation.

[0077] The Kalman filter improves the signal-to-noise ratio of the measurement data of the system by fusing the prior state estimation and the measurement value. It should be noted that the execution order of steps 1 and 2 is not limited, and in other embodiments, the order of steps 1 and 2 can be interchanged or performed simultaneously.

[0078] In a preferred embodiment of the present application, step 1 is implemented. Specifically as follows:

[0079] Since the high-order vibration mode has little effect on the motion platform, the dynamic characteristics mainly depend on the first-order deformation mode. Based on the assumed mode method, the high-order mode is ignored, and only the first-order mode is retained. Since the actual working processes of each degree of freedom are the same, the coupling relationship between each degree of freedom is not considered, and the single-degree-of-freedom deformation e(x, t) of the motion platform can be written as follows:

[0080] w(x, t) = Φ(x)q(t)

[0081] where x represents the displacement of a single degree of freedom, t represents time, φ(x) is the first-order modal function of the motion platform, and q(t) is the generalized coordinate;

[0082] The displacement P of any point on the motion platform is represented as:

[0083] P = w(x, t) + s(t)

[0084] where s(t) is the macroscopic motion displacement of the motion platform.

[0085] Therefore, the velocity square of the P point is:

[0086]

[0087] The total kinetic energy of the motion platform includes the kinetic energy generated by the total displacement of the macroscopic displacement and the microscopic displacement of the motion platform:

[0088]

[0089] where m is the total mass of the motion platform.

[0090] The motion platform moves on a plane, and the gravitational potential energy is ignored, and only the elastic potential energy generated by the microscopic vibration is considered:

[0091]

[0092] where E is the elastic modulus of the motion platform, and A is the cross-sectional area of the motion platform.

[0093] The Lagrangian function L can be represented as:

[0094] L = T - V

[0095] From the above formula, the macro-micro dynamics model of the motion platform can be derived by using Lagrange equation:

[0096]

[0097] where F(t) is the driving force received by the motion platform.

[0098] The aforementioned macro-micro dynamics model considers the influence of micro-vibration on the macro-motion equation and sets the vibration state by a proper first-order modal assumption method. The model is based on Lagrange equation and constructs the mathematical model of the motion platform from the energy angle. Compared with the prior art, the model is more accurate in describing the dynamics equation considering the vibration state, and therefore, the reliability of the obtained model is higher and the model is more suitable for the actual motion state of the motion platform.

[0099] In order to facilitate subsequent application in the Kalman filtering process, the macro-micro dynamics model in the foregoing example needs to be further discretized. In another embodiment of the present application, the discretization process is as follows:

[0100] The system state variable and the system input control variable are defined as:

[0101]

[0102] The system is discretized, and process noise w is added to the system [k] ~ N(0, Q c ) to establish the state space equation of the discrete system:

[0103]

[0104] where k and k-1 represent the kth value and the (k-1)th value in the discrete state, and the discretization of the continuous space state equation is equivalent to taking a point of the original continuous function to represent the first value, taking a second value, and so on until the Nth value. The number of times depends on the value of the interval time. The longer the interval time, the fewer the number of times in the discretization.

[0105] Since x [k] is a nonlinear equation, the nonlinear equation is linearized by using Taylor series expansion to obtain the Jacobian matrix, which can well describe the value near the original equation.

[0106]

[0107] where A [k] and W [k] are the Jacobian matrices of the partial derivatives of f with respect to x and w, respectively.

[0108] In the measurement process, the measurement noise is mainly determined by the characteristics of the sensor. Since any sensor cannot achieve absolute accuracy, a certain measurement error will inevitably occur, which is the measurement noise. In order to reduce such error as much as possible, in a preferred embodiment of the present application, step 2 is performed. The detailed steps are as follows: the laser sensor is used to detect the platform vibration signal, and the measurement noise is considered at the same time, so as to obtain the corresponding measurement equation.

[0109]

[0110] z [k] represents the displacement signal with measurement noise, x 1[k] represents the displacement of the motion platform, v 1[k] represents the measurement noise of the laser sensor for measuring the displacement of the motion platform, x 2[k] represents the velocity of the motion platform, v 2[k] the measurement noise of the laser sensor for measuring the velocity of the motion platform, x 3[k] represents a constant value;

[0111] The measurement equation z [k] is expanded by Taylor series to obtain the Jacobian matrix:

[0112]

[0113] where H m[k] and V [k] are the Jacobian matrices of h with respect to x and v, respectively.

[0114] In the prior art, model errors often lead to calculation errors due to the difficulty in constructing an accurate mathematical model. In addition, due to the high vibration frequency, the data changes rapidly during the collection of vibration data, which not only occupies a large amount of memory resources, but also the accuracy of the collected data is not ideal. Therefore, in a preferred embodiment of the present application, an improved scheme of step 3 is proposed, that is, by applying Kalman filtering technology, even if the accuracy of the mathematical model and the measurement data is not high, the relatively accurate target value can be obtained through data fusion processing. The specific process is as follows:

[0115] According to the initial conditions of the motion platform, select appropriate noise covariance matrices Q c and R c , and according to the time update and measurement update formulas of Kalman filtering.

[0116] Specifically, the time update formula is:

[0117] The time update formula is:

[0118]

[0119] The measurement update formula is:

[0120]

[0121] wherein is the prior state estimation; is the prior state estimation error covariance matrix; K [k] is the Kalman gain; is the posterior state estimation; P [k] is the posterior state estimation error covariance matrix.

[0122] The posterior state estimation obtained through the above time update formula and measurement update formula in the last iteration is the optimal vibration state estimation x (t) . The optimal vibration state estimation x (t) is fed back to compensate the controlled object through PID control to reduce the control precision error.

[0123] In the above embodiment, the Kalman filtering technology is realized through the iterative fusion process of the time update equation and the measurement update equation. First, the technology combines a macro-micro dynamic model with high accuracy, which has taken the process noise into account; second, it integrates the measurement data, which also takes the influence of measurement noise into account. Based on the continuous iteration of the Kalman filtering technology, accurate feedback compensation can be obtained.

[0124] It should be pointed out that in some specific embodiments, the selection of the noise covariance matrix should be based on the physical model of the system and the sensor characteristics. First, Qc and Rc are preliminarily estimated. The value of Rc can be obtained by observing or querying the sensor parameters. Then, through experimental testing, the experimental data are used to adjust Qc and Rc accordingly. In addition, a unit matrix can also be used as a starting point in the initial stage.

[0125] Based on the same inventive concept, in other embodiments of the present application, a platform vibration compensation system based on Kalman filtering is provided, comprising:

[0126] A dynamic model establishment module: according to the motion state of the motion platform, a dynamic model of the motion platform under vibration is proposed; a discretization module: the dynamic model is discretized to obtain the state space equation under discretization;

[0127] A measurement equation establishment module: the vibration signal of the motion platform is measured by using a laser sensor, and the measurement noise is considered to obtain a measurement equation;

[0128] A Kalman filtering module: through an extended Kalman filter, the measurement data and the prior state estimation are fused to obtain a state estimation value close to the true state.

[0129] Feedback compensation control module: feedback the state estimation value to the system for PID control to generate corresponding control signal.

[0130] The modules / units in the above examples of the present application can specifically refer to the implementation techniques of the corresponding steps of the platform vibration compensation calculation method based on Kalman filtering in the above embodiments, which will not be repeated here.

[0131] Based on the same inventive concept, in other embodiments of the present application, a platform vibration compensation control method based on Kalman filtering is provided, as shown in Figure 1 The specific steps are as follows:

[0132] S100, voltage value U m Input into the linear motor, output the force obtained by the motor running;

[0133] S200, the force is applied to the motion platform, and the motion platform is displaced;

[0134] S300, for the motion platform displacement process, the platform vibration compensation calculation method or system based on Kalman filtering in any of the above embodiments is used to obtain a compensation control signal;

[0135] S400, the compensation control signal is used as the input of PID control to obtain the voltage value of the linear motor, which is input into the linear motor in a loop to realize platform vibration compensation control.

[0136] Further, in a preferred embodiment, a preferred process of S300 is provided, specifically:

[0137] S301, the vibration signal of the motion platform is measured by using a laser sensor to obtain X t , considering its measurement noise V n , obtaining the measurement equation, so as to obtain the measurement data Z considering the noise interference;

[0138] S302, according to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined and discretized, and the process noise W n is added to obtain the state space equation under discretization considering noise interference, and the output prior state estimation is obtained;

[0139] S303, by expanding the Kalman filter, the measurement data obtained by the measurement equation and the prior state estimation which is discrete and iterated are fused to obtain the state estimation value close to the real state;

[0140] S304, the state estimation value and the expected displacement value X r are subtracted to obtain the compensation control signal.

[0141] The above embodiment controls the motion platform by applying a PID control algorithm, compared with directly using a laser sensor for feedback compensation, and the application significantly improves the positioning accuracy of the motion platform in a vibration state by applying Kalman filtering technology.

[0142] Based on the same inventive concept, in other embodiments of the application, a terminal is provided, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, can be used to execute the above method, or run the above system.

[0143] Optionally, the memory is used to store programs; the memory can include volatile memory (English: volatile memory), such as random access memory (English: random-access memory, abbreviated: RAM), such as static random access memory (English: static random-access memory, abbreviated: SRAM), double data rate synchronous dynamic random access memory (English: Double Data Rate Synchronous Dynamic Random Access Memory, abbreviated: DDR SDRAM) and the like; the memory can also include non-volatile memory (English: non-volatile memory), such as flash memory (English: flash memory). The memory is used to store computer programs (such as application programs, functional modules and the like for implementing the above method), computer instructions and the like, and the above computer programs, computer instructions and the like can be stored in one or more memories.

[0144] The processor is used to execute the computer program stored in the memory to realize each step in the method related to the above embodiment. For details, please refer to the related description in the above method embodiment.

[0145] The processor and the memory can be an independent structure, or an integrated structure. When the processor and the memory are independent structures, the memory and the processor can be coupled and connected through a bus.

[0146] Based on the same inventive concept, in other embodiments of the application, a computer readable storage medium is provided, which stores a computer program, and the program is executed by a processor to execute the above method, or run the above system.

[0147] Computer readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media can be any available media that can be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired computer program code means in the form of computer readable instructions or data structures and that can be accessed by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Also, any connection is properly termed a computer readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, or twisted pair, then the coaxial cable, fiber optic cable, or twisted pair are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, Blu-ray® disc, etc. Therefore, a computer medium can also take the form of a propagated signal on a carrier wave or other transport mechanism.

[0148] Those skilled in the art will appreciate that embodiments of the present application can be readily used as software, hardware, or a combination of software and hardware. In one

[0149] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart Figure 1 one or more functions specified by one or more of the blocks. Figure 1 one or more functions specified by one or more of the blocks.

[0150] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the Figure 1 one or more functions specified by one or more of the blocks. Figure 1 one or more functions specified by one or more of the blocks.

[0151] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart Figure 1one or more processes and / or blocks Figure 1 the steps of a function specified in one or more blocks.

[0152] It will be apparent to those skilled in the art that various modifications and variations can be made to the present application without departing from the spirit or scope of the application. Thus, it is intended that the present application cover the modifications and variations of this application provided they come within the scope of the appended claims and their equivalents.

Claims

1. A Kalman filter based platform vibration compensation calculation method, characterized in that, The method comprises the following steps: According to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined, and the dynamic model is discretized to obtain a state space equation under discretization; The vibration signal of the motion platform is measured by using a laser sensor, and the measurement equation is obtained by considering the measurement noise; The measurement data obtained by the measurement equation and the prior state estimation which is discretized and iterated continuously are fused by using an extended Kalman filter to obtain a state estimation value close to the real state; The displacement expectation value and the state estimation value are subtracted to determine a compensation control signal for platform vibration compensation; The method comprises the following steps: Based on the assumed mode method, the high order modes are ignored, only the first order mode is reserved, and the coupling relationship between the degrees of freedom is not considered , which is specifically represented as: ； where x represents a single degree of freedom displacement and t represents time, is a first order modal function of the motion platform, is a generalized coordinate; Displacement of any point on the motion platform P is represented as: ； wherein is the macroscopic motion displacement of the motion platform; Will P The square of the velocity of a point is expressed as: ； The total kinetic energy of the motion platform includes the kinetic energy generated by the total displacement caused by the macroscopic displacement and the microscopic displacement of the motion platform, specifically: ； wherein m Mtot is the total mass of the motion platform; The motion platform moves on a plane, and the gravitational potential energy is ignored, only the elastic potential energy generated by the microscopic vibration is considered, specifically: ； wherein E is the modulus of elasticity of the motion platform, A is the cross-sectional area of the motion platform; The Lagrangian function L is expressed as: ; The macro-micro dynamic model of the motion platform is obtained by using Lagrange equation: ； wherein F(t) is the driving force experienced by the motion platform; The dynamic model of the motion platform under vibration is discretized to obtain a state space equation under discretization, which comprises the following steps: The system state variable and the system input control variable are defined as: ； ； Discretizing the macro-micro dynamics model while adding process noise Establish the state-space equation of the discrete system: ； k and k-1 represent the kth value and the k-1 value under discretization; Nonlinear equations Using Taylor series expansion, the Jacobian matrix is obtained: ； wherein and are respectively f to x and w the Jacobian matrix of the partial derivatives; The measurement equation is obtained by measuring the vibration signal of the motion platform by using a laser sensor and considering the measurement noise, which comprises the following steps: The vibration signal of the platform is measured by using a laser sensor, and the measurement noise is considered simultaneously , and a measurement equation is obtained ； a displacement signal with measurement noise, a displacement of a motion stage, a measurement noise of a laser sensor measuring a displacement of a motion stage, a velocity of a motion stage, a measurement noise of a laser sensor measuring a velocity of a motion stage, a constant value; The measurement equation is nonlinear Using a Taylor series expansion, the Jacobian matrix is obtained: ； ； wherein and are respectively h to x and v the Jacobian matrix of the partial derivatives.

2. The platform vibration compensation calculation method based on Kalman filtering according to claim 1, wherein The measurement data obtained by the measurement equation and the prior state estimation which is discretized and iterated continuously are fused by using an extended Kalman filter to obtain a state estimation value close to the real state, which comprises the following steps: According to the initial condition of the motion platform, a suitable noise covariance matrix is selected Q c and R c According to the time update and measurement update formulas of the Kalman filter; By continuously iterating the time update and measurement update equations, the best vibration state estimate is obtained .

3. The platform vibration compensation calculation method based on Kalman filtering according to claim 2, wherein The time update formula is: ； The measurement update formula is: ； ； ； wherein is the prior state estimate; is the prior state estimate error covariance matrix; is the Kalman gain; is the posterior state estimate; is the posterior state estimate error covariance matrix.

4. A Kalman filter based platform vibration compensation computing system for implementing the Kalman filter based platform vibration compensation computing method of any one of claims 1-3, characterized in that, The method comprises the following steps: The dynamic model establishment module: according to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined, and the dynamic model is discretized to obtain a state space equation under discretization; The measurement equation establishment module: the vibration signal of the motion platform is measured by using a laser sensor, and the measurement equation is obtained by considering the measurement noise; The Kalman filtering module: the measurement data obtained by the measurement equation and the prior state estimation which is discretized and iterated continuously are fused by using an extended Kalman filter to obtain a state estimation value close to the real state; The feedback compensation module: the displacement expectation value and the state estimation value are subtracted to determine a compensation control signal for platform vibration compensation.

5. A Kalman filter based platform vibration compensation control method, characterized in that, The method comprises the following steps: The voltage value is input into the linear motor, and the acting force obtained by the motor operation is output; The acting force is applied to the motion platform, and the motion platform is displaced; The compensation control signal is obtained by using the platform vibration compensation calculation method based on Kalman filtering according to any one of claims 1-3 or the platform vibration compensation calculation system based on Kalman filtering according to claim 4 during the displacement process of the motion platform. The compensation control signal is taken as the input of PID control to obtain the voltage value of the linear motor, which is input into the linear motor in a loop to realize the vibration compensation control of the platform.

6. A terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor, when executing the program, can be configured to execute the method in any one of claims 1-3, 5, or run the system in claim 4.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, can be configured to execute the method in any one of claims 1-3, 5, or run the system in claim 4.

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