Platform vibration compensation calculation and control method and system based on Kalman filtering

Abstract

The invention provides a platform vibration compensation calculation and control method and system based on Kalman filtering, and the method comprises the steps: proposing a kinetic model under the vibration of a motion platform according to the motion state of the motion platform, and carrying out the discretization of the kinetic model, and obtaining a discrete state-space equation; a laser sensor is used for measuring a vibration signal of the motion platform, measurement noise is considered, and a measurement equation is obtained; carrying out data fusion on measurement data obtained by the measurement equation and discrete and continuously iterative prior state estimation by expanding a Kalman filter to obtain a state estimation value close to a real state; and the displacement expected value and the state estimation value are subtracted, and a compensation control signal is determined to be used for platform vibration compensation. According to the method, the fusion of the prior state estimation and the measured value is realized through the Kalman filter, so that the signal-to-noise ratio of the measured data of the system is improved.

Description

Technical Field

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

[0002] In recent years, high-precision motion platforms have been increasingly used in modern industries, and technological advances have placed increasingly stringent requirements on the accuracy of platforms, especially in the fields of high-speed processing and the semiconductor industry. During the motion process, the platform will inevitably produce microscopic vibrations, which have a significant impact on positioning accuracy. Therefore, it is very important to monitor and compensate for the vibrations.

[0003] In order to reduce the impact of vibration on the motion accuracy of the platform, corresponding control strategies must be adopted for compensation, including feedforward control, PID control, robust control, adaptive control and compound control. Among these control methods, feedforward control requires the establishment of an accurate vibration mathematical model, which is more difficult; while robust control, adaptive control and compound control can effectively eliminate vibration errors and improve positioning accuracy, but their cost is high and implementation is difficult. In contrast, PID control technology is mature, the algorithm is simple, and it does not rely on the accurate model of the controlled object, so it is more widely used.

[0004] The characteristics of the vibration model are difficult to describe accurately, which leads to the possibility that the model error will cause the calculation error during the calculation 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. In addition, the noise influence of the observer itself makes it difficult to accurately observe the vibration state. Summary of the invention

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

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

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

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

[0009] By extending the Kalman filter, data fusion is performed on the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation to obtain a state estimation value close to the actual state;

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

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

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

[0013] w(x,t)=Φ(x)q(t)

[0014] 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;

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

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

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

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

[0019]

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

[0021]

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

[0023] The motion platform moves on a plane, ignoring its gravitational potential energy, and only considering its elastic potential energy generated by microscopic vibration, specifically:

[0024]

[0025] Where 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 expressed as: L = TV

[0027] Using the Lagrange equation, the macro-micro dynamics model of the motion platform is obtained:

[0028]

[0029] Where F(t) is the driving force on the motion platform.

[0030] Preferably, the dynamic model of the motion platform under vibration is discretized to obtain a state space equation under discretization, including:

[0031] The system state variables and system input control quantities are defined as:

[0032]

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

[0034]

[0035] k and k-1 represent the kth and k-1th values ​​in the discrete state;

[0036] For the nonlinear equation x [k] Using Taylor series expansion, we get the Jacobian matrix:

[0037]

[0038] Among them 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 its measurement noise is taken into account to obtain a measurement equation, including:

[0040] The laser sensor is used to measure the vibration signal of the platform, and its measurement noise v is also considered. [k] ~N(0,R c ), and obtain the 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 that measures the displacement of the motion platform, x 2[k] represents the velocity of the moving platform, v 2[k] The measurement noise of the laser sensor measuring the velocity of the moving platform, x 3[k] Represents a fixed value;

[0043] The nonlinear measurement equation z [k] Using Taylor series expansion, we get the Jacobian matrix:

[0044]

[0045] Among them, H m[k] and V [k] are the Jacobian matrices of the partial derivatives of h with respect to x and v, respectively.

[0046] Preferably, the method of performing data fusion on the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation by extending the Kalman filter to obtain a state estimation value close to the actual state includes:

[0047] According to the initial conditions of the motion platform, select the appropriate noise covariance matrix Q c and R c , according to the time update and measurement update formula of Kalman filter;

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

[0049] Preferably, the time update formula is:

[0050]

[0051] The measurement update formula is:

[0052]

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

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

[0055] Dynamic model building module: According to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined and discretized to obtain the state space equation under discretization;

[0056] Measurement equation building module: Use the laser sensor to measure the vibration signal of the motion platform, consider its measurement noise, and obtain the measurement equation;

[0057] Kalman filter module: by expanding the Kalman filter, the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation are fused to obtain a state estimation value close to the actual state;

[0058] Feedback compensation module: subtract the expected displacement value from the state estimation value to determine a compensation control signal for platform vibration compensation.

[0059] According to a third aspect of the present invention, there is provided a platform vibration compensation control method based on Kalman filtering, wherein a voltage value is input into a linear motor, and a force obtained by the operation of the motor is output;

[0060] Applying the force to the motion platform, so that the motion platform moves;

[0061] For the displacement process of the motion platform, adopt any one of the platform vibration compensation calculation methods based on Kalman filtering or platform vibration compensation calculation systems based on Kalman filtering to obtain a compensation control signal;

[0062] The compensation control signal is used as the input of PID control to obtain the 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 invention, there is provided a terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor can be used to execute any one of the methods described, or to run the system described, when executing the program.

[0064] According to a fifth aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can be used to execute any of the methods described above, or to run the system described above.

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

[0066] In an embodiment of the present invention, a platform vibration compensation calculation method and system based on Kalman filtering is adopted, and the fusion of a priori state estimation and measurement value is realized through Kalman filtering, thereby improving the signal-to-noise ratio of the system measurement data. This method aims to solve the problems existing in the prior art, namely, the impact of vibration on the motion platform at the microscopic level, and the problem that it is difficult to build an accurate model due to the high-frequency characteristics of vibration. These problems will lead to large errors in the calculation and measurement process, thereby reducing the accuracy of the acquired data and the signal-to-noise ratio.

[0067] In the embodiment of the present invention, a platform vibration compensation calculation method and system based on Kalman filtering are used to construct a macroscopic and microscopic dynamic model of the motion platform, and discretize it, thereby deriving the state space equation of the discrete system. At the same time, 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 the measurement noise is taken into consideration, in order to obtain data that is closer to the actual situation.

[0068] In an embodiment of the present invention, a platform vibration compensation calculation method, system, and control method based on Kalman filtering are used, and the vibration dynamics model of the motion platform belongs to a nonlinear system. By using an extended Kalman filter to perform data fusion on a priori state estimation and measurement values, the method improves the accuracy of the estimated value. 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 invention significantly improves the positioning accuracy of the motion platform under vibration by applying Kalman filtering technology. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0070] Figure 1 The figure is a flow chart of a platform vibration compensation calculation method based on Kalman filtering in one embodiment of the present invention. DETAILED DESCRIPTION

[0071] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0072] like Figure 1 As shown, in one embodiment of the present invention, a platform vibration compensation calculation method based on Kalman filtering is provided, comprising:

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

[0074] Step 2: Use the laser sensor to measure the vibration signal of the motion platform, consider its measurement noise, and obtain the measurement equation;

[0075] Step 3: By extending the Kalman filter, the measurement data obtained by the measurement equation in step 2 and the discrete and continuously iterative prior state estimate obtained in step 1 are fused to obtain a state estimate close to the actual state;

[0076] Step 4: Subtract the expected displacement value from the state estimation value obtained in step 3 to determine the compensation control signal for platform vibration compensation.

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

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

[0079] Since the high-order vibration modes have little effect on the motion platform, its dynamic characteristics mainly depend on the first-order deformation mode. Based on the assumed modal method, the high-order modes are ignored and only the first-order modes are retained. Since the actual working process of each degree of freedom is the same, the coupling relationship between the degrees of freedom is not considered. 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 expressed as:

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

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

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

[0086]

[0087] The overall kinetic energy of the motion platform includes the kinetic energy generated by the total displacement caused by the macroscopic displacement and 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, ignoring its gravitational potential energy and only considering its elastic potential energy generated by microscopic vibration:

[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 expressed as:

[0094] L=TV

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

[0096]

[0097] Where F(t) is the driving force on the motion platform.

[0098] The aforementioned macro-micro dynamics model takes into account the influence of microscopic vibration on the macroscopic motion equation, and sets the vibration state through the appropriate first-order modal assumption method. Based on the Lagrange equation, the model constructs a mathematical model of the motion platform from the energy perspective. Compared with the prior art, the model is more accurate in describing the dynamic equation considering the vibration state. Therefore, the obtained model is more reliable and more in line with the actual motion condition of the motion platform.

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

[0100] The system state variables and system input control quantities are defined as:

[0101]

[0102] Discretize the system and add process noise w to the system [k] ~N(0,Q c ) Establish the state space equation of the discrete system:

[0103]

[0104] Among them, k and k-1 represent the kth value and k-1th value in the discrete state. Discretizing the continuous space state equation is equivalent to taking a point of the original continuous function to represent the first value, then the second value, and so on until the Nth time. 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 discrete state.

[0105] Due to x [k] It is a nonlinear equation. The nonlinear equation is linearized and expanded using Taylor series to obtain the Jacobian matrix, which can well describe the values ​​near the original equation.

[0106]

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

[0108] During the measurement process, the measurement noise is mainly determined by the characteristics of the sensor. Since no sensor can achieve absolute accuracy, it is inevitable to produce a certain measurement error, which is the measurement noise. In order to reduce such errors as much as possible, in a preferred embodiment of the present invention, step 2 is performed. The detailed steps are as follows: a 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 that measures the displacement of the motion platform, x 2[k] represents the velocity of the moving platform, v 2[k] The measurement noise of the laser sensor measuring the velocity of the moving platform, x 3[k] Represents a fixed value;

[0111] The nonlinear measurement equation z [k] Using Taylor series expansion, we get the Jacobian matrix:

[0112]

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

[0114] In the prior art, it is difficult to construct an accurate mathematical model, and model errors often lead to calculation errors. In addition, due to the high vibration frequency, the data changes rapidly during the collection of vibration data, which not only takes up a large amount of memory resources, but also the accuracy of the collected data may not be ideal. Therefore, in a preferred embodiment of the present invention, an improved solution for 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, a 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 the appropriate noise covariance matrix Q c and R c , according to the time update and measurement update formula of Kalman filter.

[0116] Specifically, the time update formula is:

[0117] The time update formula is:

[0118]

[0119] The measurement update formula is:

[0120]

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

[0122] The posterior state estimate obtained by the last iteration is the optimal vibration state estimate x (t) The best vibration state estimate x (t) Do feedback compensation and control the controlled object through PID to reduce its control accuracy error.

[0123] In the above embodiment, the Kalman filter technology is implemented through an iterative fusion process of the time update equation and the measurement update equation. First, the technology combines a high-precision macro-micro dynamic model that has taken process noise into consideration; second, it integrates measurement data that also takes into account the impact of measurement noise. Based on the continuous iteration of the Kalman filter technology, high-precision feedback compensation can be obtained.

[0124] It should be clearly 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, and Qc and Rc should be preliminarily estimated first. Among them, the value of Rc can be obtained by observing or querying the sensor parameters. Subsequently, through experimental testing, Qc and Rc are adjusted accordingly using experimental data. In addition, the unit matrix can also be used as a starting point in the initial stage.

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

[0126] Dynamic model building module: According to the motion state of the motion platform, a dynamic model of the motion platform under vibration is proposed; Discrete module: Discrete its dynamic model to obtain the state space equation under discretization;

[0127] Measurement equation building module: Use the laser sensor to measure the vibration signal of the motion platform, consider its measurement noise, and obtain the measurement equation;

[0128] Kalman filter module: By expanding the Kalman filter, the measurement data and the prior state estimation are fused to obtain a state estimation value close to the actual state;

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

[0130] The various modules / units in the above examples of the present invention may specifically refer to the implementation techniques of the corresponding steps of the platform vibration compensation calculation method based on Kalman filtering in the above embodiment, which will not be described in detail here.

[0131] Based on the same inventive concept, in another embodiment of the present invention, a platform vibration compensation control method based on Kalman filtering is provided, such as Figure 1 As shown, the specific steps are as follows:

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

[0133] S200, applying a force to the motion platform, causing the motion platform to move;

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

[0135] S400, using the compensation control signal as the input of PID control, obtaining the voltage value for controlling the linear motor, and cyclically inputting it into the linear motor to realize platform vibration compensation control.

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

[0137] S301, using a laser sensor to measure the vibration signal of the motion platform to obtain X t , considering its measurement noise V n , get the measurement equation, and thus get the measurement data Z taking into account the noise interference;

[0138] S302, according to the motion state of the motion platform, determine the dynamic model of the motion platform under vibration, discretize it, and add process noise W n , we get the discrete state space equation considering noise interference, and get the prior state estimate of the output;

[0139] S303, by extending the Kalman filter, data fusion is performed on the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation to obtain a state estimation value close to the actual state;

[0140] S304: The state estimation value and the expected displacement value X r The compensation control signal is obtained by making the difference.

[0141] The above-mentioned embodiment controls the motion platform by applying the PID control algorithm. Compared with directly using the laser sensor for feedback compensation, the present invention significantly improves the positioning accuracy of the motion platform under vibration by applying the Kalman filtering technology.

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

[0143] Optionally, the memory is used to store programs; the memory may 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), etc.; the memory may 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 applications, functional modules, etc. that implement the above method), computer instructions, etc., and the above-mentioned computer programs, computer instructions, etc. can be partitioned and stored in one or more memories.

[0144] The processor is used to execute the computer program stored in the memory to implement the various steps in the method involved in the above embodiment. For details, please refer to the relevant description in the above method embodiment.

[0145] The processor and the memory may be independent structures or integrated structures. When the processor and the memory are independent structures, the memory and the processor may be coupled and connected via a bus.

[0146] Based on the same inventive concept, in other embodiments of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, it can be used to execute the above method, or run the above system.

[0147] Among them, computer-readable media include computer storage media and communication media, wherein the communication media include any media that facilitates the transmission of computer programs from one place to another. The storage medium can be any available medium that can be accessed by a general or special-purpose computer. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and the storage medium can be located in an ASIC. In addition, the ASIC can be located in a user device. Of course, the processor and the storage medium can also be present in a communication device as discrete components.

[0148] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0149] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0150] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0151] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0152] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A platform vibration compensation calculation method based on Kalman filtering, characterized in that: include: According to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined and discretized to obtain the 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 its measurement noise. By extending the Kalman filter, data fusion is performed on the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation to obtain a state estimation value close to the actual state; The expected displacement value and the state estimation value are subtracted to determine a compensation control signal for platform vibration compensation.

2. A platform vibration compensation calculation method based on Kalman filtering according to claim 1, characterized in that: Determining the dynamic model of the motion platform under vibration according to the motion state of the motion platform includes: Based on the assumed modal method, the higher-order modes are ignored, only the first-order mode is retained, and the coupling relationship between the degrees of freedom is not considered. The single-degree-of-freedom deformation w(x, t) of the motion platform is specifically expressed as: w(x, t) = Φ(x)q(t) 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; The displacement P of any point on the motion platform is expressed as: P = w(x, t) + s(t) Where s(t) is the macroscopic motion displacement of the motion platform; The square of the velocity at point P is expressed as: The overall kinetic energy of the motion platform includes the kinetic energy generated by the total displacement caused by the macroscopic displacement and microscopic displacement of the motion platform, specifically: Where m is the total mass of the motion platform; The motion platform moves on a plane, ignoring its gravitational potential energy, and only considering its elastic potential energy generated by microscopic vibration, specifically: Where E is the elastic modulus of the motion platform, and A is the cross-sectional area of ​​the motion platform; The Lagrangian function L is expressed as: L = TV Using the Lagrange equation, the macro-micro dynamics model of the motion platform is obtained: Where F(t) is the driving force on the motion platform.

3. A platform vibration compensation calculation method based on Kalman filtering according to claim 2, characterized in that: Discretize the dynamic model of the motion platform under vibration and obtain the state space equation under discretization, including: The system state variables and system input control quantities are defined as: The macro-micro dynamics model is discretized and the process noise w is added [k] ~N(0,Q c ) Establish the state space equation of the discrete system: k and k-1 represent the kth value and k-1th value in the discrete state; For the nonlinear equation x [k] Using Taylor series expansion, we get the Jacobian matrix: where A[k] and W[k] are the Jacobian matrices of the partial derivatives of f with respect to x and w, respectively.

4. The platform vibration compensation calculation method based on Kalman filtering according to claim 1 is characterized in that: The vibration signal of the motion platform is measured by using a laser sensor, and its measurement noise is taken into account to obtain a measurement equation, including: The laser sensor is used to measure the vibration signal of the platform, and its measurement noise v is also considered. [k] ~N(0,R c ), and obtain the measurement equation: 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 that measures the displacement of the motion platform, x 2[k] represents the velocity of the moving platform, v 2[k] The measurement noise of the laser sensor measuring the velocity of the moving platform, x 3[k] Represents a fixed value; The nonlinear measurement equation z [k] Using Taylor series expansion, we get the Jacobian matrix: Among them, H m[k] and V [k] are the Jacobian matrices of the partial derivatives of h with respect to x and V, respectively.

5. The platform vibration compensation calculation method based on Kalman filtering according to claim 1 is characterized in that: The method of performing data fusion on the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation by extending the Kalman filter to obtain a state estimation value close to the actual state includes: According to the initial conditions of the motion platform, select the appropriate noise covariance matrix Q c and R c , according to the time update and measurement update formula of Kalman filter; The optimal vibration state estimation x is obtained by iterating the time update and measurement update formulas. (t) .

6. A platform vibration compensation calculation method based on Kalman filtering according to claim 5, characterized in that: The time update formula is: The measurement update formula is: in is the prior state estimate; is the prior state estimation error covariance matrix; K [k] is the Kalman gain; is the posterior state estimate; P [k] is the posterior state estimation error covariance matrix.

7. A platform vibration compensation calculation system based on Kalman filtering, characterized in that: include: Dynamic model building module: According to the motion state of the motion platform, the dynamic model of the motion platform under vibration is determined and discretized to obtain the state space equation under discretization; Measurement equation building module: Use the laser sensor to measure the vibration signal of the motion platform, consider its measurement noise, and obtain the measurement equation; Kalman filter module: by expanding the Kalman filter, the measurement data obtained by the measurement equation and the discrete and continuously iterative prior state estimation are fused to obtain a state estimation value close to the actual state; Feedback compensation module: subtract the expected displacement value from the state estimation value to determine the compensation control signal for platform vibration compensation.

8. A platform vibration compensation control method based on Kalman filtering, characterized in that: include: The voltage value is input into the linear motor, and the force obtained by the operation of the motor is output; Applying the force to the motion platform, so that the motion platform moves; For the displacement process of the motion platform, the platform vibration compensation calculation method based on Kalman filtering described in any one of claims 1 to 6 or the platform vibration compensation calculation system based on Kalman filtering described in claim 7 is adopted to obtain a compensation control signal; The compensation control signal is used as the input of PID control to obtain the voltage value for controlling the linear motor, which is cyclically input into the linear motor to realize platform vibration compensation control.

9. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it can be used to execute the method described in any one of claims 1 to 6 and 8, or to run the system described in claim 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, it can be used to execute the method described in any one of claims 1 to 6 and 8, or to run the system described in claim 7.

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