A galvanometer motor control method based on resonant filter and luenberger observer

By using a three-closed-loop control method with resonant filtering and a Luneburg observer, the problems of delay and dynamic performance limitations in galvanometer motor control were solved, achieving higher control accuracy and dynamic response speed, and adapting to wideband scanning requirements.

CN121150540BActive Publication Date: 2026-04-21FUJIAN AGRI & FORESTRY UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
FUJIAN AGRI & FORESTRY UNIV
Filing Date
2025-11-18
Publication Date
2026-04-21

AI Technical Summary

Technical Problem

Existing galvanometer motor control methods suffer from hardware dependence and dynamic performance limitations, resulting in a trade-off between delay, phase margin decay, and dynamic response speed and tracking accuracy, making them unsuitable for wideband scanning requirements.

Method used

A three-loop control method based on resonant filtering and Luneburg observer is adopted, including position loop, velocity loop and current loop. The periodic disturbance of position loop is eliminated by resonant filter, and velocity is estimated by Luneburg observer. The stability of observer is judged by Lyapunov exponent, and the observation gain matrix is ​​adjusted to ensure system stability.

Benefits of technology

It enhances the dynamic performance of the galvanometer motor, reduces the influence of inter-loop coupling, improves control accuracy and response speed, reduces delay and noise interference, and adapts to wideband scanning requirements.

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Abstract

A galvanometer motor control method based on resonant filtering and a Luneburg observer, relating to the field of motor control, is disclosed. The drive control system of the galvanometer motor includes a position PI controller, a resonant filter, a speed PI controller, a current PI controller, and a DA conversion drive circuit connected in sequence, and a Luneburg observer positioned between the resonant filter and the speed PI controller. The method includes the following steps: the position PI controller processes position-related information; the resonant filter performs resonant filtering on the parameters output by the position PI controller; the Luneburg observer introduces an observation gain matrix to stabilize itself and estimates the speed; and the speed PI controller processes the speed estimate to generate the voltage controlling the galvanometer motor. This invention employs coordinated control of position, speed, resonant filter, Luneburg observer, and current, enhancing the system's dynamic performance, reducing inter-loop coupling effects, and improving control accuracy.
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Description

Technical Field

[0001] This invention relates to the field of motor control, and more specifically to a galvanometer motor control method based on resonant filtering and a Luneburg observer. Background Technology

[0002] As the core actuator of a laser scanning system, the control precision and dynamic performance of the galvanometer motor directly determine the overall performance of laser processing or laser inspection equipment.

[0003] Existing control methods for galvanometer motors generally employ a three-closed-loop architecture consisting of a position loop, a speed loop, and a current loop connected in series. This type of control method suffers from hardware dependence and dynamic performance limitations. At the hardware level, the structural limitations of galvanometer motors prevent the installation of speed measuring devices. Traditional methods typically calculate speed using position differentiation, requiring differential calculations of encoder pulses. This introduces a delay of at least one control cycle, leading to phase margin decay during high-frequency scanning and increasing the risk of oscillation. At the dynamic performance level, the differentiation of the position signal from a high-resolution encoder amplifies high-frequency noise, forcing a limitation on the bandwidth of the speed loop controller, resulting in a trade-off between dynamic response speed and tracking accuracy. To suppress speed observation noise, some designs incorporate a low-pass filter before the speed loop. However, this low-pass filtering introduces additional phase lag, and the fixed cutoff frequency cannot meet the requirements of wideband scanning. Furthermore, when the scanning frequency approaches the mechanical resonance point, the cutoff frequency needs to be manually adjusted to avoid excitation, further degrading dynamic performance.

[0004] In view of this, this application has conducted in-depth research on this basis, resulting in this case. Summary of the Invention

[0005] The purpose of this invention is to provide a galvanometer motor control method based on resonant filtering and Luneburg observer, which can enhance dynamic performance, reduce the coupling effect between loops, reduce delay, and improve control accuracy.

[0006] To achieve the above objectives, the solution of the present invention is:

[0007] A galvanometer motor control method based on resonant filtering and a Luneburg observer is disclosed. The drive control system of the galvanometer motor includes a position loop, a resonant filter, a speed loop, a current loop, and a DA conversion drive circuit connected in sequence, as well as a Luneburg observer disposed between the resonant filter and the speed loop. The position loop includes a position PI controller, the speed loop includes a speed PI controller, and the current loop includes a current PI controller. The galvanometer motor resonant filtering control method includes the following steps:

[0008] S1. The position PI controller is used to compare the transmitted target position signal with the actual position signal transmitted by the galvanometer motor, and a speed command is output. This speed command is... ;

[0009] S2. The resonant filter provides attenuation at the resonant point, suppressing the ripple amplitude to a set range to eliminate the periodic disturbances output by the position PI controller.

[0010] S3. The Luneburger observer is based on the state-space equation of the galvanometer motor and estimates the velocity by introducing an observation gain matrix.

[0011] S4. Establish the Lyapunov index and use it to determine the stability of the Luneburger observer. After the Luneburger observer is in a stable state, the velocity estimate output by the Luneburger observer is input into the velocity PI controller. When the Luneburger observer is determined to be in an unstable state, the observation gain matrix is ​​adjusted using a mapping function to restore the stability of the Luneburger observer.

[0012] S5. After the speed PI controller obtains the speed estimate output by the Luneburger observer, the speed PI controller processes it and compares the speed signal output by the Luneburger observer with the speed signal output by the resonant filter to output a reference current signal. Then, the current PI controller processes the real-time current signal acquired in real time with the reference current signal to generate a voltage for controlling the galvanometer motor. This voltage is output to the galvanometer motor through the DA conversion drive circuit.

[0013] In step S2, the resonant filter employs a quasi-resonant controller, whose transfer function is: In the formula, This represents the mechanical resonant frequency of the drive control system. Indicates the gain coefficient. This represents the frequency parameters related to the damping coefficient. This represents the complex frequency variable in the Laplace transform.

[0014] The transfer function is sequentially discretized and digitally filtered to generate a reference signal for the velocity loop after removing the resonant ripple. The data is then input into the speed PI controller.

[0015] In step S3, the state equation of the Luneburg observer is as follows: (1), where, , and All are system matrices. The observation gain matrix; It is the derivative of the state estimate, representing the prediction of the Luneburg observer of the system state over time; This indicates a state estimate, representing the Romberg observer's prediction of how the system state changes over time. This represents the voltage signal that serves as the control input to the drive control system. This represents the actual output measured position signal of the drive control system;

[0016] In formula (1) ,

[0017] Therefore, the further state equations for the Romberg observer are as follows:

[0018] ,

[0019] In the formula, This represents the torque coefficient of the galvanometer motor. Indicates the viscous damping coefficient. Represents the back electromotive force coefficient. This indicates the resistance of the galvanometer motor. Indicates the motor inductance. This represents the moment of inertia of the galvanometer motor; This represents the estimated angular position of the rotor of the galvanometer motor. For the estimated angular velocity of the rotor of the galvanometer motor, Estimate the current for the galvanometer motor, where, , and These are all estimates from the Lundberg observer; This represents the process quantity of the Romberg observer in the computation process, which is... The derivative, To estimate the derivative of the angular position, To estimate the derivative of the angular velocity, To estimate the derivative of the current;

[0020] Then select an appropriate observation gain matrix. To obtain a speed estimate, the speed estimate is .

[0021] In step S4, the stability of the Luneburg observer is determined using the Lyapunov exponent. The determination method is as follows: A1. Define the observation error as... Then the error dynamics are In the formula, Indicates observation error. The derivative representing the error;

[0022] A2. Using Lyapunov solution First, the dynamic equation for the observer error is established as follows: ;

[0023] Then, the Jacobian matrix of the error dynamic equation is calculated, and the expression of the Jacobian matrix is ​​as follows: In the formula, Indicates time, Represents the row index of the matrix. Represents the matrix column index. Represents the Jacobian matrix. This represents the dynamic equation function in the matrix row index. This represents the error component of the matrix column index. express Error at any given time;

[0024] Then, solve for the Jacobian matrix. The largest eigenvalue in And calculate the Lyapunov index. The calculation formula is: ,in, This indicates that the Luneburg observer is stable. This indicates that the Luneburg observer has lost stability. Represented as The real part;

[0025] A3. When the Luneburger observer is in a stable state, the observation gain matrix in step S3 is... The output is sent to the Luneburg observer;

[0026] When the Romberg observer is in an unstable state, the mapping function is used to adjust the undetermined observation gain matrix. The expression for this mapping function is: = In the formula, Represents the observation gain matrix. This represents the constraint relationship obtained through NURBS surface fitting. The Lyapunov index represents the Lyapunov index. This indicates the operating frequency of the galvanometer motor. This represents the parameter eigenvectors of the galvanometer motor; then the acquired observation gain matrix is... Substitute this into step A1 and re-evaluate.

[0027] In the formula, It is the basic observation gain matrix (the initial gain in the steady state). It is an adaptive adjustment coefficient; It is a normalized reference value. This is the critical stability threshold; This is the maximum operating frequency allowed by the system. It is a weight matrix, which is used for adjustment. The contribution ratio of each parameter.

[0028] The drive control system also includes a host computer. In step S1, the position PI controller receives the target position signal transmitted by the host computer.

[0029] A position sensor is installed on the galvanometer motor. In step S1, the position sensor is used to obtain the actual position signal of the galvanometer motor.

[0030] A current sensor is installed on the galvanometer motor, and the real-time current signal of the galvanometer motor is obtained using the current sensor.

[0031] After adopting the above method, the present invention has the following beneficial effects: The drive control system of the present invention adopts a three-closed-loop structure of speed loop, position loop and current loop. The input of the speed loop is provided through a Luneburger observer to suppress speed estimation noise and provide a speed estimation without delay. At the same time, a resonant filter is connected in series at the output of the position PI (position loop) controller to eliminate the periodic disturbance of the position loop output. The two form an anti-interference chain of suppression and cancellation. The present invention adopts the coordinated control of position-speed-resonant filter-Luneburger observer-current, which enhances the dynamic performance of the drive control system in the present invention, reduces the coupling effect between loops and improves the control accuracy. Furthermore, in the present invention, the Lyapunov exponent is used to judge the stability of the Luneburger observer, and the bandwidth of the Luneburger observer can be automatically matched and adjusted with the operating frequency of the galvanometer motor through the mapping function, thereby ensuring the stability of the Luneburger observer and further reducing the speed estimation delay of the Luneburger observer. Attached Figure Description

[0032] Figure 1 This is a circuit topology diagram of the drive control system in this invention.

[0033] Figure 2 This is a position comparison diagram using the galvanometer motor control method of the present invention.

[0034] Figure 3 This is a speed estimation comparison diagram using the galvanometer motor control method of the present invention.

[0035] Figure 4 This is a comparison diagram of the velocity loop reference signals before and after filtering in this invention. Detailed Implementation

[0036] To further explain the technical solution of the present invention, the present invention will be described in detail below through specific embodiments.

[0037] A galvanometer motor control method based on resonant filtering and a Luneburg observer is proposed. This method is based on common drive control systems for galvanometer motors, such as... Figure 1 As shown, the drive control system includes a host computer, a three-loop control system, and a DA conversion drive circuit connected in sequence. The three-loop control system includes a position loop, a speed loop, and a current loop. The position loop includes a position PI controller, the speed loop includes a speed PI controller, and the current loop includes a current PI controller. The drive control system also includes a resonant filter and a Luenberger observer. The resonant filter is connected in series between the position PI controller and the speed PI controller, and the Luenberger observer is connected in series between the resonant filter and the speed PI controller.

[0038] Furthermore, the drive control system also includes a position sensor, which can be a conventional encoder. The position sensor is mounted on the galvanometer motor to collect the real-time position signal of the galvanometer motor. In this embodiment, the real-time position signal collected by the position sensor is output to the position PI controller through AD sampling.

[0039] Furthermore, the drive control system also includes a current sensor, which is a commercially available current sensor. The current sensor is fixedly mounted on the galvanometer motor to collect the current signal of the galvanometer motor. In this embodiment, the real-time current signal collected by the current sensor is output to the current PI controller through AD sampling.

[0040] Furthermore, in this embodiment, the host computer is a commonly used host computer in existing conventional drive control systems, and the three-closed-loop control system is a commonly used control system in existing drive control systems. Its input, output, and control methods are all conventional operations. The DA conversion drive circuit is a conventional DA conversion drive circuit. The current sensor and position sensor are installed in the galvanometer motor in a conventional manner.

[0041] In this embodiment, the resonant filtering control method for the galvanometer motor includes the following steps.

[0042] Step S1: The position PI controller compares the target position signal output by the host computer with the actual position signal obtained by the position sensor. That is, the target position signal and the actual position signal are subtracted to obtain the position error between the two, so as to eliminate the static position error and ensure positioning accuracy.

[0043] To elaborate, the position loop uses existing conventional operations to output speed commands. In other words, the position PI controller achieves high-precision positioning through the coordinated action of proportional (P) and integral (I) components. Its basic principle is: to measure the deviation between the target position and the actual feedback position. As input, where For positional error, For the target location, For actual feedback location, proportional link The current position error is linearly amplified to quickly generate a control action proportional to the deviation, thereby reducing dynamic error. The proportional circuit outputs the control quantity. The proportionality coefficient; the integral element The historical error is accumulated, and even a small static error will force the system to adjust due to the continuous increase of the integral term until the error returns to zero, thereby eliminating the steady-state deviation. The integral element outputs a control quantity. The integral coefficient; The variable is the integral variable, used to represent the time accumulation process; then in the position loop, the output of the PI controller is the speed command. This command serves as a reference input for the speed loop, driving the motor to move towards the target position at the desired speed.

[0044] Step S2: The resonant filter is located at the output of the position PI controller and acts directly on the front feedback of the speed PI controller. The resonant filter provides attenuation at the resonant point, suppressing the ripple amplitude to the set range, thereby eliminating the periodic disturbance of the position PI controller output and ensuring the laser scanning accuracy.

[0045] In detail, in the three-closed-loop control system of this embodiment, the output parameter of the resonant filter is the speed loop reference signal after filtering. This signal originates from the output of the position PI controller and is used to filter out the speed setpoint after periodic disturbances. It directly acts on the input of the speed loop PI controller to suppress fluctuations.

[0046] The ripple amplitude mentioned above refers to the periodic fluctuation amplitude in the output signal of the position PI controller caused by factors such as mechanical resonance and control algorithm jitter. If this type of ripple is directly input into the speed loop, it will cause the motor speed to fluctuate, thus affecting the laser scanning position accuracy. Therefore, a resonant filter is used to provide targeted attenuation of this type of ripple at the resonant frequency, control its fluctuation amplitude within the range allowed by the system, and thus eliminate the periodic disturbance to the speed loop reference value.

[0047] It should be noted that the set range to which the ripple amplitude is suppressed is determined by the parameter configuration of the resonant filter, which is a standard operation of the resonant filter, and therefore will not be described in detail.

[0048] Furthermore, the aforementioned resonant filter employs a quasi-resonant controller, whose transfer function is: In the formula, This represents the mechanical resonant frequency of the drive control system; This represents the gain coefficient, which is determined through experimental debugging. This represents the frequency parameters related to the damping coefficient. This represents the complex frequency variable in the Laplace transform.

[0049] The transfer function of the quasi-resonant controller is used at the mechanical resonant frequency (i.e., the frequency at which the mechanical resonant frequency is located in the drive control system) in this context. (At the location), the periodic ripple output of the targeted attenuation position loop is addressed, and subsequent operations follow existing standard procedures, generally as follows:

[0050] 1. Discretization: Converting the transfer function in the continuous domain to the digital domain, suitable for real-time computation on FPGAs; 2. Digital Filtering: Implementing the discretization algorithm in the FPGA to filter the output signal of the position PI controller; 3. Output Result: Generating a velocity loop reference signal after filtering out resonance ripple. The speed PI controller is directly input to suppress periodic disturbances in the speed loop.

[0051] Step S3: The Luneburger observer estimates the velocity based on the state-space equation of the galvanometer motor by introducing the observation gain matrix.

[0052] To elaborate, the state equations for the Romberg observer are as follows:

[0053] (1), where, , and All are system matrices. is the observation gain matrix; is the derivative of the state estimate, representing the Romberg observer's prediction of the system state over time. It is the state estimate, representing the Lundberg observer's prediction of how the system state changes over time; This represents the voltage signal that is the control input of the drive control system, that is, the voltage signal output to the DA conversion drive circuit (i.e., the driver). In other words, the voltage signal generated during the start-up of the galvanometer motor will be fed back to the Luneburg observer in real time.

[0054] This represents the actual output measurement value of the drive control system, i.e., the actual position signal in step S1.

[0055] Furthermore, in equation (1), ,

[0056] ,

[0057] Therefore, the state equations for the more specific Luneburg observer are as follows:

[0058] ,

[0059] In the formula, This represents the torque coefficient of the galvanometer motor. Indicates the viscous damping coefficient. Represents the back electromotive force coefficient. This indicates the resistance of the galvanometer motor. Indicates the motor inductance. This represents the moment of inertia of the galvanometer motor; This represents the estimated angular position of the rotor of the galvanometer motor. For the estimated angular velocity of the rotor of the galvanometer motor, Estimate the current for the galvanometer motor, where, , and These are all estimates from the Lundberg observer; This represents the process quantity of the Romberg observer in the computation process, which is... The derivative, To estimate the derivative of the angular position (i.e., to estimate the angular velocity). To estimate the derivative of the angular velocity, To estimate the derivative of the current.

[0060] It should be noted that by appropriately selecting the observation gain matrix... To ensure the asymptotic convergence of the error output in step S1; in this embodiment, a suitable observation gain matrix is ​​selected. In order to obtain a speed estimate (i.e. ).

[0061] Step S4: Establish the Lyapunov index and use it to determine the stability of the Luneburg observer. When the Luneburg observer is determined to be in a stable state, the Luneburg observer outputs a velocity estimate ( The speed PI controller is given; when the Luneburg observer is determined to be in an unstable state, the observation gain matrix is ​​adjusted using a mapping function to restore the stability of the Luneburg observer.

[0062] To elaborate, the judgment method is as follows:

[0063] A1. Define the observation error as... Then the error dynamics are In the formula, Indicates observation error. The derivative represents the error.

[0064] A2. Using Lyapunov solution value.

[0065] To elaborate, in A2-1, the dynamic equation for the observer error is first established as follows: In this process, the observation error is incorporated into the dynamic equation of the observer error.

[0066] A2-2, Calculate the Jacobian matrix of the error dynamic equation. The expression for the Jacobian matrix is: In the formula, Indicates time, Represents the row index of the matrix. Represents the matrix column index. Represents the Jacobian matrix. This represents the dynamic equation function in the matrix row index. This represents the error component of the matrix column index. express Error at time t; Solving the Jacobian matrix The largest eigenvalue in The largest eigenvalue of the Jacobian matrix refers to the largest eigenvalue after eigenvalue decomposition of the matrix, and is not reflected in the matrix itself. In the definition formula.

[0067] Then, the Lyapunov exponent is calculated. The calculation formula is: ,in, This indicates that the Luneburg observer has lost stability. Represented as The real part.

[0068] A3. When it is determined that the Romberg observer is in a stable state, the observation gain matrix in step S3 is... The output is sent to the Luneburger observer.

[0069] When the Romberg observer is determined to be in an unstable state, the following mapping function is used to adjust the observation gain matrix. The expression for this mapping function is: = In the formula, Represents the observation gain matrix. This represents the constraint relationship obtained through NURBS surface fitting. The Lyapunov index represents the Lyapunov index. This indicates the operating frequency of the galvanometer motor. This represents the parameter eigenvectors of the galvanometer motor; then the acquired observation gain matrix is... Substitute this into step A1 and re-evaluate.

[0070] To elaborate further, In the formula, It is the basic observation gain matrix (the initial gain in the steady state). It is an adaptive adjustment coefficient; It is a normalized reference value. This is the critical stability threshold; This is the maximum operating frequency allowed by the system. It is a weight matrix, which is used for adjustment. The contribution ratio of each parameter.

[0071] Step S5: After the speed PI controller acquires the speed estimate output by the Lumberjack observer, the speed PI controller processes the speed signal output by the Lumberjack observer. Speed ​​signal output from resonant filter A comparison is performed to output a reference current signal. Then the current PI controller will collect the real-time current signal. With reference current signal The process generates a voltage that controls the galvanometer motor, which is then output to the galvanometer motor via a DA converter drive circuit (i.e., a driver).

[0072] Furthermore, the galvanometer motor control method is employed; see [link / reference]. Figures 2-3 As can be seen from the simulation results, under the condition of periodic velocity changes, the Luneburger observer can perfectly match the actual velocity change trend without significant phase lag; and the Luneburger observer is significantly better than the position differential method in terms of velocity estimation accuracy, dynamic tracking performance and anti-interference ability, and has reliable substitution advantages.

[0073] To elaborate further, see Figure 4 As can be seen from the simulation results, the fluctuation amplitude of the velocity loop reference signal before and after the position loop output ripple of the resonant controller is significantly reduced, effectively eliminating the ability of periodic disturbances.

[0074] This invention discloses a mirror motor control method based on resonant filtering and a Luneburger observer. The method utilizes speed estimation based on a Luneburger observer, combined with a post-resonant filter in the position loop, to form a three-loop composite control architecture. This three-loop structure consists of a position loop, a speed loop, and a current loop. The resonant filter is designed for the resonant frequency, filtering out resonant components in the position loop output, thus preventing this disturbance from entering the speed loop and breaking the coupling chain of "resonance → position fluctuation → speed loop oscillation → current loop distortion." This suppresses periodic resonant disturbances in the system and reduces the coupling effect between loops. Furthermore, the Luneburger observer accurately estimates the speed, reducing noise and error in the speed loop feedback value, resulting in a more stable speed loop output and preventing the transmission of inter-loop fluctuations caused by speed feedback distortion. The coordinated action of the three-loop structure, the resonant filter, and the Luneburger observer enhances the dynamic performance of the system (reflected in response speed, disturbance rejection capability, and tracking accuracy) and improves control precision.

[0075] Furthermore, the aforementioned dynamic performance is reflected in response speed, disturbance rejection capability, and tracking accuracy:

[0076] Three-loop hierarchical control: current loop (high frequency, quickly suppresses current disturbances), speed loop (medium frequency, tracks speed), and position loop (low frequency, ensures position accuracy), working together to improve dynamic bandwidth.

[0077] The Luneburger observer enables real-time, accurate velocity estimation, allowing for more timely feedback compensation in the velocity loop and enhancing disturbance rejection.

[0078] The resonant filter can directly suppress resonance, reduce the tracking error and overshoot of the position loop, and, together with the precise feedback of the velocity loop, make the dynamic response of the entire system "smoother and faster".

[0079] The above description is only a preferred embodiment of this invention. Any equivalent changes and modifications made within the scope of the claims of this invention shall fall within the scope of the claims of this invention.

Claims

1. A galvanometer motor control method based on resonant filtering and a Luneburg observer, characterized in that, The drive control system of the galvanometer motor includes a position loop, a resonant filter, a speed loop, a current loop, and a DA conversion drive circuit connected in sequence, as well as a Luneburg observer located between the resonant filter and the speed loop; the position loop includes a position PI controller, the speed loop includes a speed PI controller, and the current loop includes a current PI controller; the resonant filtering control method of the galvanometer motor includes the following steps: S1. The position PI controller is used to compare the transmitted target position signal with the actual position signal transmitted by the galvanometer motor, and a speed command is output. This speed command is... ; S2. The resonant filter provides attenuation at the resonant point, suppressing the ripple amplitude to a set range to eliminate the periodic disturbances output by the position PI controller. The resonant filter employs a quasi-resonant controller, whose transfer function is: In the formula, This represents the mechanical resonant frequency of the drive control system. Indicates the gain coefficient. This represents the frequency parameters related to the damping coefficient. The complex frequency variable in the Laplace transform is represented; the transfer function is sequentially discretized and digitally filtered to generate a reference signal for the velocity loop after filtering out resonance ripple. And input it into the speed PI controller; S3. The Luneburger observer is based on the state-space equation of the galvanometer motor and estimates the velocity by introducing an observation gain matrix. S4. Establish the Lyapunov index and use it to determine the stability of the Luneburger observer. After the Luneburger observer is in a stable state, the velocity estimate output by the Luneburger observer is input into the velocity PI controller. When the Luneburger observer is determined to be in an unstable state, the observation gain matrix is ​​adjusted using a mapping function to restore the stability of the Luneburger observer. The stability of the Luneburg observer is determined using the Lyapunov exponent, and the determination method is as follows: A1. Define the observation error as... Then the error dynamics are In the formula, Indicates observation error. The derivative representing the error, Indicates the actual value of the state. This represents the state estimate. and Both represent system matrices. Represents the observation gain matrix; A2. Using Lyapunov solution First, the dynamic equation for the observer error is established as follows: ; Then, the Jacobian matrix of the error dynamic equation is calculated, and the expression of the Jacobian matrix is ​​as follows: In the formula, Indicates time, Represents the row index of the matrix. Represents the matrix column index. Represents the Jacobian matrix. This represents the dynamic equation function in the matrix row index. This represents the error component of the matrix column index. express Error at any given time; Then, solve for the Jacobian matrix. The largest eigenvalue in And calculate the Lyapunov index. The calculation formula is: ,in, This indicates that the Luneburg observer is stable. This indicates that the Luneburg observer has lost stability. Represented as The real part; A3. When the Luneburger observer is in a stable state, the observation gain matrix in step S3 is... The output is sent to the Luneburg observer; When the Romberg observer is in an unstable state, the mapping function is used to adjust the undetermined observation gain matrix. The expression for the mapping function is: = In the formula, This represents the constraint relationship obtained through NURBS surface fitting. The Lyapunov index represents the Lyapunov index. This indicates the operating frequency of the galvanometer motor. This represents the parameter eigenvectors of the galvanometer motor; then the acquired observation gain matrix is... Substitute the results into step A1 and re-evaluate; in, In the formula, It is the basic observation gain matrix. It is an adaptive adjustment coefficient; It is a normalized reference value. This is the critical stability threshold; This is the maximum operating frequency allowed by the system. It is a weight matrix, which is used for adjustment. The contribution ratio of each parameter; S5. After the speed PI controller obtains the speed estimate output by the Luneburger observer, the speed PI controller processes it and compares the speed signal output by the Luneburger observer with the speed signal output by the resonant filter to output a reference current signal. Then, the current PI controller processes the real-time current signal acquired in real time with the reference current signal to generate a voltage for controlling the galvanometer motor. This voltage is output to the galvanometer motor through the DA conversion drive circuit.

2. The galvanometer motor control method based on resonant filtering and a Luneburg observer according to claim 1, characterized in that: In step S3, the state equation of the Luneburg observer is as follows: (1), where, For the system matrix, It is the derivative of the state estimate, representing the derivative of the Romberg observer's prediction of the system state changing over time; This also indicates that the Lundberg observer can predict how the system state changes over time; This represents the voltage signal that serves as the control input to the drive control system. This represents the actual output measured position signal of the drive control system; In formula (1) , Therefore, the further state equations for the Romberg observer are as follows: , In the formula, This represents the torque coefficient of the galvanometer motor. Indicates the viscous damping coefficient. Represents the back electromotive force coefficient. This indicates the resistance of the galvanometer motor. Indicates the motor inductance. This represents the moment of inertia of the galvanometer motor; This represents the estimated angular position of the rotor of the galvanometer motor. For the estimated angular velocity of the rotor of the galvanometer motor, Estimate the current for the galvanometer motor, where, , and These are all estimates from the Lundberg observer; This represents the process quantity of the Romberg observer in the computation process, which is... The derivative of To estimate the derivative of the angular position, To estimate the derivative of the angular velocity, To estimate the derivative of the current; Then select an appropriate observation gain matrix. To obtain a speed estimate, the speed estimate is .

3. A galvanometer motor control method based on resonant filtering and a Luneburg observer according to claim 1 or 2, characterized in that: The drive control system also includes a host computer. In step S1, the position PI controller receives the target position signal transmitted by the host computer.

4. The galvanometer motor control method based on resonant filtering and a Luneburg observer according to claim 3, characterized in that: A position sensor is installed on the galvanometer motor. In step S1, the position sensor is used to obtain the actual position signal of the galvanometer motor.

5. The galvanometer motor control method based on resonant filtering and a Luneburg observer according to claim 3, characterized in that: A current sensor is installed on the galvanometer motor, and the real-time current signal of the galvanometer motor is obtained using the current sensor.

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