Control method of permanent magnet linear motor based on extended kalman observation super-helix terminal sliding mode

Abstract

This invention discloses a permanent magnet linear motor control method based on extended Kalman observation of a superspiral terminal sliding mode, relating to the fields of permanent magnet linear motor control and precision positioning technology. First, a discrete extended state model of the linear motor is established, and the speed and total disturbance information of the motor are estimated using an extended Kalman filter algorithm combined with real-time position data. Second, terminal superspiral sliding mode control is executed, generating continuous control signals by using the terminal sliding surface and the superspiral approach rate to avoid the chattering problem of traditional sliding mode. Third, the observed total disturbance information is compensated for in the control output, and the final motor control command is generated by combining it with the path planning objective. This invention can improve the response speed and positioning accuracy of linear motor systems in precision positioning scenarios while ensuring control stability and robustness.

Description

Technical Field

[0001] This invention relates to the fields of permanent magnet linear motor control technology and precision positioning technology, specifically to a permanent magnet linear motor control method for extended Kalman observation superspiral terminal sliding mode. Background Technology

[0002] With the advancement of precision manufacturing technology, the scale of precision machinery and optical components continues to trend towards miniaturization. Driven by the demands of high-end equipment manufacturing industries such as medical devices, precision optics, and micro-robotics, the manufacturing and testing of micro- and nano-components has become a crucial cutting-edge technology. Positioning platforms, as the load-bearing and motion-actuating components of micro- and nano-component processing and testing equipment, are essential for ensuring processing and measurement accuracy. There are various options for the motion actuators of positioning platforms. Among them, permanent magnet linear motor servo systems, directly connected to the load, offer advantages such as a wide stroke range, ample power, and fast response speed, and have been widely researched and applied in the field of micro- and nano-processing. However, as a complex electromechanical system, linear motors have significant coupling between their electrical and mechanical systems, and their parameters are time-varying with changing operating conditions. While direct load connection reduces most transmission losses, disturbances on the load directly affect the motor's actuator, further increasing the control complexity.

[0003] Currently, linear motor control mostly employs the traditional PID control method (CN120601782 A). PID control cannot simultaneously achieve both high control accuracy and fast operating speed, and is constrained by various disturbances inherent in the motor itself, exhibiting significant delay and overshoot. This fails to meet the dual requirements of positioning accuracy and response speed in high-precision positioning applications, limiting the further application of linear motors in precision machining. Alternatively, it lacks statistically optimal estimation processing for measurement noise and system random noise (such as Kalman filtering), limiting its performance in the extremely low-noise environments required for high-precision positioning. Compared to nonlinear variable structure control (such as sliding mode control), the PID architecture suffers from a waterbed effect when handling strong nonlinear coupling and rapid transient responses, making it difficult to completely resolve the contradiction between positioning accuracy and settling time (CN113472253 A).

[0004] Sliding mode control, as a nonlinear, variable-structure control method, is characterized by strong robustness and good dynamic performance, and has attracted much attention from scholars in various research fields in recent years. Sliding mode control uses a nonlinear method to maintain the system state on a sliding surface, therefore its biggest problem is chattering caused by discontinuous control signals; the linear sliding surface of classical sliding mode control also suffers from poor dynamic performance and slow convergence speed.

[0005] Therefore, how to suppress the mechanical and electrical interference of linear motors through active and passive methods, avoid the waterbed effect, improve the control accuracy of the system while ensuring the rapid response of the linear motor actuator, and ensure the robustness and stability of the algorithm are problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0006] To address the issues of parameter perturbation interference and insufficient PID accuracy and response speed in linear motors, this invention proposes a permanent magnet linear motor control method based on extended Kalman observation superspiral terminal sliding mode. This method ensures that the system converges quickly to the tracking target while reducing the demand on system gain through observation and estimation of disturbances, keeping overshoot and chattering within a low range, thereby improving the system's positioning accuracy and response speed.

[0007] The present invention is achieved by at least one of the following technical solutions.

[0008] A permanent magnet linear motor control method for extended Kalman observation of the terminal sliding mode of a superspiral device includes the following steps:

[0009] Step 1: Set the operating point, speed, and acceleration of the linear motor, and perform static path planning; Step 2: Collect the position information of the linear motor in real time using a grating ruler; Step 3: Establish a dynamic model of the linear motor system, combine it with disturbance information, construct an extended state model of the linear motor, and discretize it to obtain the extended state model of the linear motor in discrete state. Step 4: Input the position information of the linear motor and the prior state vector obtained in the previous control cycle into the extended Kalman filter algorithm to estimate the motor speed and total disturbance information in real time. Step 5: Input the motor position and speed information into the terminal super-helical sliding mode control algorithm, combine it with the target position determined by the path planning at the current time point, calculate the current command item given by the sliding mode controller, combine the total disturbance item of the extended Kalman filter with the sliding mode controller command item, and generate the final motor control command. Step 6: Based on the motor control command and the discretized linear motor extended state model, predict the system's position, velocity and total disturbance information in the next control cycle, that is, predict the system's prior state vector.

[0010] Furthermore, the specific process of step 3 is as follows: Step 31: Establish a dynamic model of the linear motor system based on the physical mechanism, use a high-order polynomial to represent the total disturbance of the linear motor electromechanical system, and regard it as the extended state of the linear motor dynamic model to obtain the extended state model of the linear motor. Step 32: Combine the control frequency discretization to obtain the discrete extended state model of the linear motor.

[0011] Furthermore, in step 32, the discretization is performed using the bilinear transform method.

[0012] Furthermore, the specific process of step 4 is as follows: Step 41: Calculate the Kalman filter coefficients for the current control cycle based on the prior error covariance matrix predicted in the previous control cycle. Step 42: Calculate the velocity and total disturbance information for the current control cycle using the Kalman filter coefficients of the current control cycle and the grating ruler count value of the current cycle. Step 43: Calculate the posterior error covariance matrix for this period using the Kalman filter coefficients for this period.

[0013] Furthermore, the specific process of step 5 is as follows: Step 51: Calculate the position error and velocity error at the start of the current control cycle; Step 52: Derive the first sliding mode control term based on the dynamic model of the terminal sliding surface and the current system; Step 53: Obtain the second sliding mode control term by integrating the terminal sliding surface with the superspiral approach algorithm; Step 54: Generate the control quantity for the current control cycle based on the total motor disturbance.

[0014] Furthermore, the terminal sliding surface for: ; in, , This indicates the position error and velocity error of the current control cycle. , , , All are constants.

[0015] Furthermore, the expression for the superspiral approach algorithm is: ; ; in This represents the output of the superspiral approximation algorithm. This represents the higher-order sliding mode term of the superhelical algorithm. For the derivative of the higher-order sliding mode term, 、 All are constants. Indicates the terminal sliding surface. Represents a symbolic function.

[0016] Furthermore, the specific process of step 6 is as follows: Step 61: Based on the extended state model of the linear motor under discrete state, and combining the control quantity of the current control cycle with the estimated position, velocity and disturbance state quantities, predict the position, velocity and disturbance state information of the linear motor at the beginning of the next control cycle. Step 62: Based on the linear motor extended state model and posterior error covariance matrix under discrete state, predict the prior error covariance matrix for the next cycle and save it for use in the next control cycle.

[0017] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0018] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0019] Compared with existing technologies, the beneficial effects of the present invention are as follows: This invention discloses a permanent magnet linear motor control method based on extended Kalman observation superspiral terminal sliding mode. First, a discrete extended state model of the linear motor is established, and the motor's speed and total disturbance information are calculated using Kalman observer and grating ruler position data. Second, a terminal superspiral sliding mode control method is executed. This method improves control dynamic performance through the terminal sliding surface and limits sliding mode chattering to the integral through the superspiral approach rate, generating a continuous control signal to avoid the chattering problem of traditional sliding mode control, thus improving control accuracy and dynamic performance compared to traditional methods. Third, the total disturbance information is compensated for on the control output, further reducing the system's dependence on sliding mode gain and improving system accuracy. Finally, the position and velocity disturbance information for the next cycle is predicted based on the model, enabling continuous algorithm operation. This invention is applicable to linear motors on macro-motion platforms using a macro-micro coordinate measuring machine. Compared to traditional control methods, it inherits the high robustness of sliding mode control while further improving the linear motor's response speed and control accuracy, solving the problem of traditional control methods struggling to balance response speed and control accuracy. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1This is a schematic diagram of the permanent magnet linear motor control method for the extended Kalman observation superspiral terminal sliding mode provided in this embodiment; Figure 2 The following is a flowchart of the extended Kalman observation superspiral terminal sliding mode algorithm execution in an embodiment; Figure 3 The block diagram of the extended Kalman observation superspiral terminal sliding mode controller is shown in the embodiment. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figure 1 As shown, in the permanent magnet linear motor control method for the extended Kalman observation superspiral terminal sliding mode in this embodiment, the electromechanical parameters of the permanent magnet linear motor are as follows: back electromotive force constant. Rotor flux viscous friction coefficient ,resistance ,inductance polar distance Motor mass The thrust constant is derived from the formula. The thrust constant can be determined. The control method specifically includes the following steps: S1. Set the running points, speed, and acceleration, and perform static path planning. k The expected displacement given by the time-matter path planning is The expected speed is The path planning method is a one-dimensional trapezoidal path planning, which ensures stable operation of the positioning process and improves positioning accuracy.

[0024] S2. The position information of the linear motor is acquired in real time using a grating ruler. k Location information at any time .

[0025] S3. Establish a dynamic model of the linear motor system, and combine it with disturbance information to construct an extended state model of the linear motor, and write it in matrix form (state matrix). Control matrix Observation matrix Discretize it to obtain the system extended state model under discrete states ( , , ); S4. Transfer the linear motor position information Compared with the system state vector predicted in the previous period The input is fed into the extended Kalman filter algorithm to estimate the motor speed in real time. Total disturbance information ; S5, Position the motor Speed ​​information output by Kalman filter The target position is input into the terminal's super-helical sliding mode control algorithm and determined by the path planning at the current time point. With speed Calculate the current command term given by the sliding mode controller. The total perturbation term of the extended Kalman filter will be... With sliding mode controller instruction items Combined, the final motor control commands are generated. .

[0026] S6. According to the motor control command Using a discretized linear motor extended state model, the system's position, velocity, and total disturbance information are predicted for the next control cycle, i.e., the system's prior state vector is predicted. .

[0027] In one specific embodiment, such as Figure 2 As shown, a dynamic model of the linear motor system is established, and an expansion state model of the linear motor is constructed by combining disturbance information. , , And discretize it to obtain the system extended state model under discrete states ( , , Its detailed execution process includes the following steps: S31. Based on the physical mechanism, establish the dynamic model of the linear motor system, and its formula is:

[0028] In the formula, Represents the viscous friction coefficient of the system. Represents the system thrust constant. This represents the mass of the motor's rotor and load. Represents the displacement of the linear motor system. Represents the speed of the linear motor system. This represents the electromagnetic thrust provided by the motor electrical system. Represents thrust fluctuation, This represents the vector control current command.

[0029] Utilize time changing The total disturbance of a linear motor electromechanical system can be represented in the form of a polynomial. The total disturbance takes the form of: ; In the formula, Let be the order of the polynomial. For polynomial coefficients, Represents perturbation modeling First-order components, The remainder term represents the unmodeled high-frequency time-varying components. Treating the total disturbance as an expanded state of the linear motor dynamics model, the expanded state equation of the linear motor is synthesized as follows:

[0030] In the formula, The derivative representing the displacement of the linear motor system. The derivative representing the speed of the linear motor system. Represents the viscous friction coefficient of the system. Represents the system thrust constant. This represents the mass of the motor's rotor and load. This represents the disturbance experienced by the linear motor system. The derivative representing the total disturbance of the linear motor system. Represents disturbance of The first derivative. The extended state equations of the linear motor are expressed in state-space matrix form, and the formula can be written as: ; In the formula, The system state vector represents the extended state model. The derivative of the system state vector in the extended state model. This is the system output vector of the extended state model. For the state matrix, For control matrix, For the output matrix, Indicates the system's control input, This represents unmodeled process state noise. This represents the system measurement noise. In this embodiment, the expansion order is... ,matrix , , The specific expression is: ; S32. The discretized linear motor extended state equations are obtained by discretizing using the bilinear transform method. , , The control frequency in this embodiment is Control cycle The expression for discretization using the bilinear transform method is: ; In the formula, For the Laplace operator in the continuous field, For discrete-domain Z-transform operators, For the system control cycle, this transformation establishes a mapping relationship between the continuous domain controlled motor system and the discrete domain control algorithm, resulting in the discretized extended state equation of the linear motor. , , ).

[0031] In one specific embodiment, such as Figure 2 As shown, the linear motor position information Compared with the system state vector predicted in the previous period The input is fed into the extended Kalman filter algorithm to estimate the motor speed in real time. Total disturbance information Its detailed execution process includes the following steps: S41. Based on the prior error covariance matrix predicted in the previous control cycle. Calculate the Kalman filter coefficients for the current control cycle. The expression is:

[0032] in, It is the output matrix of the motor model, which is calculated in step S32; It is the covariance matrix of the measured noise, and it is the set parameter; It is predicted from step S5 of the previous cycle.

[0033] In this embodiment, the matrix R takes the following values: ; S42. Based on the Kalman filter coefficients of the current period Compared with the grating ruler count value in this period Calculate the speed of this control cycle Total disturbance information The expression is: ; In the formula, It is the prior state vector of the current cycle, which is predicted by step S5 of the previous cycle; It is the state vector calculated using Kalman filtering, which includes the position of the current period. ,speed Total disturbance information ; S43. Calculate the posterior error covariance matrix for the current period using the Kalman filter coefficients of the current period. The expression is: ; In the formula, It is the identity matrix. It is the posterior error covariance matrix for this period.

[0034] In one specific embodiment, such as Figure 2 As shown, the motor position Speed ​​information output by Kalman filter The target position is input into the terminal's super-helical sliding mode control algorithm and determined by the path planning at the current time point. With speed Calculate the current command term given by the sliding mode controller. The total perturbation term of the extended Kalman filter will be... With sliding mode controller instruction items Combined, the final motor control commands are generated. The specific process is as follows: S51. Calculate the position error of the current control cycle. With speed error The expression is: , ; S52, Based on the set terminal sliding surface The first sliding mode control term is derived from the current system's dynamic model. The terminal sliding surface designed in this invention The expression is: The first sliding mode control term can be obtained by combining the motor dynamics model. The expression is: , In this embodiment, , , , ; , These are the system's viscous friction coefficient and the ratio of the motor's thrust coefficient to its mass, respectively. S53, via the terminal sliding surface Using the superspiral approach algorithm, the second sliding mode control term is obtained by integration. The expression for the superspiral approach algorithm is: ; in This represents the output of the superspiral approximation algorithm. This represents the higher-order sliding mode term of the superhelical algorithm. For the derivative of the higher-order sliding mode term, and All parameters are pre-set. This represents the terminal sliding surface; in this embodiment, , , The function expression is: ; S54. Combining the sliding mode control term and the total disturbance information given by the Kalman observer, calculate the motor control quantity, the expression of which is: ; in This is a motor control variable.

[0035] In one specific embodiment, such as Figure 2 As shown, according to the motor control command The linear motor expansion state model under discrete conditions ( , , This predicts the system's position, velocity, and total disturbance information for the next control cycle, i.e., the state vector. Its detailed execution process includes the following steps: S61, Extended state model based on discrete state of linear motor ( , , ), combined with the control quantity of this cycle and the current period state information calculated by the Kalman observer Prior estimate of the linear motor's state information for the next control cycle The expression is: ; S62, State Matrix Based on Discrete Extended State Model and posterior error covariance matrix Predicting the prior error covariance matrix for the next period The expression is: ; In the formula, The process noise covariance matrix is, in this embodiment, as follows: .

[0036] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0037] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A control method of permanent magnet linear motor based on extended Kalman observation super-hyperbolic terminal sliding mode, characterized in that, Includes the following steps: Step 1: Set the operating point, speed, and acceleration of the linear motor, and perform static path planning; Step 2: Collect the position information of the linear motor in real time using a grating ruler; Step 3: Establish a dynamic model of the linear motor system, combine it with disturbance information, construct an extended state model of the linear motor, and discretize it to obtain the extended state model of the linear motor in discrete state. Step 4: Input the position information of the linear motor and the prior state vector obtained in the previous control cycle into the extended Kalman filter algorithm to estimate the motor speed and total disturbance information in real time. Step 5: Input the motor position and speed information into the terminal super-helical sliding mode control algorithm, combine it with the target position determined by the path planning at the current time point, calculate the current command item given by the sliding mode controller, combine the total disturbance item of the extended Kalman filter with the sliding mode controller command item, and generate the final motor control command. Step 6: Based on the motor control command and the discretized linear motor extended state model, predict the system's position, velocity and total disturbance information in the next control cycle, that is, predict the system's prior state vector.

2. The control method of permanent magnet linear motor based on extended Kalman observer hyper-overshooting terminal sliding mode according to claim 1, characterized in that, The specific process of step 3 is as follows: Step 31: Establish a dynamic model of the linear motor system based on the physical mechanism, use a high-order polynomial to represent the total disturbance of the linear motor electromechanical system, and regard it as the extended state of the linear motor dynamic model to obtain the extended state model of the linear motor. Step 32: Combine the control frequency discretization to obtain the discrete extended state model of the linear motor.

3. The control method of permanent magnet linear motor based on extended Kalman observer hyper-overshooting terminal sliding mode according to claim 2, characterized in that, In step 32, the discretization is performed using the bilinear transform method.

4. The control method of permanent magnet linear motor based on extended Kalman observer hyper-overshooting terminal sliding mode according to claim 1, characterized in that, The specific process of step 4 is as follows: Step 41: Calculate the Kalman filter coefficients for the current control cycle based on the prior error covariance matrix predicted in the previous control cycle. Step 42: Calculate the velocity and total disturbance information for the current control cycle using the Kalman filter coefficients of the current control cycle and the grating ruler count value of the current cycle. Step 43: Calculate the posterior error covariance matrix for this period using the Kalman filter coefficients for this period.

5. The control method of permanent magnet linear motor based on extended Kalman observer hyper-overshooting terminal sliding mode according to claim 1, characterized in that, The specific process of step 5 is as follows: Step 51: Calculate the position error and velocity error at the start of the current control cycle; Step 52: Derive the first sliding mode control term based on the dynamic model of the terminal sliding surface and the current system; Step 53: Obtain the second sliding mode control term by integrating the terminal sliding surface with the superspiral approach algorithm; Step 54: Generate the control quantity for the current control cycle based on the total motor disturbance.

6. The permanent magnet linear motor control method for extended Kalman observation superspiral terminal sliding mode according to claim 5, characterized in that, The terminal sliding surface Is: ； wherein, , represents the position error and the velocity error of the current control period, , , , are constants.

7. The permanent magnet linear motor control method for extended Kalman observation superspiral terminal sliding mode according to claim 5, characterized in that, The expression for the superspiral approach algorithm is: ； ； in This represents the output of the superspiral approximation algorithm. This represents the higher-order sliding mode term of the superspiral algorithm. For the derivative of the higher-order sliding mode term, 、 All are constants. Indicates the terminal sliding surface. Represents a symbolic function.

8. The permanent magnet linear motor control method for extended Kalman observation superspiral terminal sliding mode according to claim 1, characterized in that, The specific process of step 6 is as follows: Step 61: Based on the extended state model of the linear motor under discrete state, and combining the control quantity of the current control cycle with the estimated position, velocity and disturbance state quantities, predict the position, velocity and disturbance state information of the linear motor at the beginning of the next control cycle. Step 62: Based on the linear motor extended state model and posterior error covariance matrix under discrete state, predict the prior error covariance matrix for the next cycle and save it for use in the next control cycle.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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