MEMS galvanometer scanning method and system based on integral terminal sliding mode control

Abstract

The invention belongs to the technical field of laser radar scanning control, and discloses an MEMS galvanometer scanning method and system based on integral terminal sliding mode control, and the method comprises the steps: constructing an integral terminal sliding mode surface, introducing a minimum operator reaching law, enabling a system state to be converged to the sliding mode surface in a finite step, and enabling the system state to be converged to the sliding mode surface; the tracking error reaches the preset bandwidth within the limited step, high-precision trajectory tracking can still be achieved even under the large-angle and high-speed scanning working condition, and the edge is not obviously distorted. Besides, according to the method, external disturbance is estimated and compensated in real time through the disturbance observer so as to reduce gain needed by switching items in sliding mode control, sudden disturbance and periodic disturbance are estimated and dynamically compensated on line through the disturbance observer, and therefore small steady-state errors and phase stability are maintained. In complex scenes such as composite disturbance, the control method can significantly improve the scanning precision and stability of the MEMS galvanometer.

Description

Technical Field

[0001] This invention belongs to the field of lidar scanning control technology, specifically relating to a MEMS galvanometer scanning method and system based on integral terminal sliding mode control. Background Technology

[0002] MEMS galvanometers, as the core scanning actuators in lidar systems, employ electrostatic drive to achieve high-speed single-axis or dual-axis scanning. These galvanometers are simple in structure, low in power consumption, and fast in response. However, a nonlinear relationship exists between their driving voltage and deflection angle. Furthermore, factors such as mechanical damping, uncertainties in torsional spring stiffness, and manufacturing errors can lead to deviations in the system model. Lidar systems place extremely high demands on the scanning performance of MEMS galvanometers, and existing control methods have several shortcomings.

[0003] Conventional open-loop control systems suffer from large overshoot and long settling times, making it difficult to achieve high-precision scanning. In open-loop control, electrostatically driven MEMS galvanometers exhibit a significant nonlinear relationship between their driving voltage and deflection angle, particularly pronounced at large deflections. This makes it difficult for the MEMS galvanometer to accurately track the desired trajectory required by the lidar system, leading to deviations in the reflected laser beam and affecting image quality. Furthermore, lidar systems are subject to sudden disturbances such as external impacts, spring stiffness changes due to temperature drift, and periodic disturbances such as structural resonance and drive power supply ripple during actual operation. Traditional open-loop driving strategies struggle to effectively compensate for these nonlinearities and disturbances.

[0004] While PID control, as a traditional closed-loop method, is easy to implement, the driving voltage and deflection angle of the MEMS mirror exhibit a significant nonlinear relationship. PID control suffers from poor robustness in nonlinear systems, and its dynamic response is lag-dependent and accuracy is limited during high-speed, large-range scanning. Furthermore, model parameter perturbations and external disturbances can easily induce significant trajectory tracking errors during high-frequency and large-range scanning, even jeopardizing system stability. Because PID control is prone to large overshoot and long settling times during large-amplitude, rapid scanning, and its robustness to external disturbances is poor, it is difficult to meet the performance requirements of lidar in high-frequency, large-range scanning applications.

[0005] Sliding mode control (SMC) exhibits strong robustness, but it suffers from chattering when discretized on digital platforms such as FPGAs and DSPs. Terminal sliding mode control (TSMC) can accelerate convergence, but it faces singularity issues and the risk of chatter amplification. In digital control platforms, both sliding mode control and terminal sliding mode control struggle to achieve accurate trajectory tracking over a large range of high-speed scans within a finite number of steps due to reduced convergence performance and severe chattering. Furthermore, both sliding mode control and terminal sliding mode control are particularly inadequate in suppressing sudden and periodic composite disturbances, leading to a significant decrease in scanning accuracy.

[0006] Therefore, there is an urgent need to design a MEMS galvanometer closed-loop scanning control method that is suitable for discrete digital control platforms and has limited-step convergence, chatter suppression, and disturbance rejection capabilities. Summary of the Invention

[0007] The purpose of this invention is to propose a MEMS galvanometer scanning method based on integral terminal sliding mode control. This method combines the integral terminal sliding mode surface, the minimum operator reaching law, and the dynamic compensation of the disturbance observer. It can effectively suppress chattering in the small error range while achieving finite-step convergence and high-speed scanning trajectory tracking, thereby significantly improving the robust performance of the lidar system under strong nonlinearity and complex disturbances.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A MEMS galvanometer scanning method based on integral terminal sliding mode control includes the following steps: Step 1. Construct a dynamic model of the MEMS galvanometer and discretize it to obtain a discretized model; Step 2. Based on the discretized model obtained in Step 1, design a disturbance observer to estimate unknown disturbances in the system in real time. Combine the disturbance estimates to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation. Step 3. Implement trajectory tracking control of the MEMS galvanometer using a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

[0009] Furthermore, based on the MEMS galvanometer scanning method based on integral terminal sliding mode control mentioned above, this invention also proposes a lidar system, which includes a laser, a MEMS galvanometer, a position sensor, an analog-to-digital converter, an FPGA-based controller, and a driving circuit. The laser, as a laser source, emits laser light that is incident on the mirror surface of the MEMS galvanometer. The position sensor is used to receive the laser light reflected from the mirror surface of the MEMS galvanometer and convert it into an electrical signal; An analog-to-digital converter is used to convert the electrical signals output by the position sensor into digital signals, which are then sent to an FPGA-based controller. The FPGA-based controller has a readable storage medium stored within it, and when the readable storage medium is executed, it is used to implement the steps of the MEMS galvanometer scanning method based on integral terminal sliding mode control mentioned above. The scanning method of MEMS galvanometer based on integral terminal sliding mode control is calculated and then the voltage control signal is output by the FPGA-based controller. The driving voltage is amplified by the voltage amplifier of the driving circuit and input to the bottom and side driving electrodes of the MEMS galvanometer to drive the MEMS galvanometer to track the desired trajectory for scanning.

[0010] Furthermore, based on the above-mentioned MEMS galvanometer scanning method based on integral terminal sliding mode control, this invention also proposes a computer-readable storage medium storing a program thereon; when the program is executed by a processor, it is used to implement the steps of the above-mentioned MEMS galvanometer scanning method based on integral terminal sliding mode control.

[0011] The present invention has the following advantages: As described above, this invention discloses a MEMS galvanometer scanning method based on integral terminal sliding mode control. This invention is the first to apply discrete minimum operator integral terminal sliding mode control to the control of a MEMS galvanometer. The control method of this invention achieves system state convergence to the sliding surface within a finite number of steps, effectively solving the problem of insufficient convergence in high-frequency, large-range scanning using traditional control methods. This invention also proposes a minimum operator reaching law, which automatically reduces the reaching speed in the small error region, thereby achieving an effective balance between chatter suppression and convergence speed. This avoids chattering caused by excessively high reaching speeds while ensuring rapid system convergence. Furthermore, this invention designs a disturbance observer that can estimate and compensate for external disturbances in real time, significantly enhancing the system's robustness in complex disturbance environments and maintaining high-precision trajectory tracking performance. In addition, the discrete control method proposed in this invention has a clear structure, high computational efficiency, and is easy to implement in embedded platforms such as FPGAs and DSPs, supporting large-scale deployment in industrial applications such as LiDAR. Attached Figure Description

[0012] Figure 1 This is a flowchart of a MEMS galvanometer scanning method based on integral terminal sliding mode control in an embodiment of the present invention.

[0013] Figure 2 This is a closed-loop control block diagram of the MEMS galvanometer scanning method based on integral terminal sliding mode control in an embodiment of the present invention.

[0014] Figure 3 This is a schematic diagram of a lidar system in an embodiment of the present invention.

[0015] Figure 4 The image shows the scanning tracking effect obtained using the traditional PID control method at f = 200 Hz and an amplitude of 1.5°.

[0016] Figure 5 The image shows the scanning tracking effect obtained by using the control method proposed in this invention at f = 200 Hz and an amplitude of 1.5°.

[0017] Figure 6 The image shows the scanning tracking effect obtained using the traditional PID control method at f = 400 Hz and an amplitude of 1.5°.

[0018] Figure 7 The image shows the scanning tracking effect obtained by using the control method proposed in this invention at f = 400 Hz and an amplitude of 1.5°.

[0019] Figure 8 The image shows the scanning tracking effect obtained using the traditional PID control method at f = 600 Hz and an amplitude of 1.5°.

[0020] Figure 9 The image shows the scanning tracking effect obtained by using the control method proposed in this invention at f = 600 Hz and an amplitude of 1.5°. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This invention is geared towards lidar applications. For high-precision closed-loop scanning control of electrostatically driven MEMS galvanometers, it proposes a MEMS galvanometer scanning method based on integral terminal sliding mode control. Specifically, this method is a discrete minimum operator integral terminal sliding mode control method based on disturbance observer compensation. By constructing a discrete integral terminal sliding mode surface, designing a minimum operator reaching law, and introducing a disturbance observer to estimate and compensate for system disturbances in real time, it improves the system's finite-step convergence, chattering suppression capability, and disturbance resistance performance. It can also significantly improve the system's robustness and finite-time convergence performance under complex conditions.

[0022] like Figure 1 As shown, the MEMS galvanometer scanning method based on integral terminal sliding mode control specifically includes the following steps: Step 1. Construct a dynamic model of the MEMS galvanometer and discretize it to obtain a discretized model.

[0023] In step 1 of this embodiment, a continuous-time nonlinear dynamic model of the MEMS galvanometer is first established based on its mechanical structure and electrostatic drive principle, i.e., the dynamic model of the MEMS galvanometer is constructed. Then, to adapt to the implementation of the digital controller, the continuous model of the MEMS galvanometer's dynamic model is precisely discretized using the zero-order hold method, resulting in a discrete state-space equation suitable for algorithm design, i.e., the discretized model.

[0024] The electrostatically driven MEMS mirror consists of a mirror plate, two pairs of torsion bars, a support frame, a frame, a bottom electrode, and side electrodes. By applying a driving voltage to the bottom and side electrodes, the MEMS mirror can be twisted around the X and Y axes. The parameters of the electrostatically driven MEMS mirror in this embodiment are shown in Table 1.

[0025] Table 1 Parameters of Electrostatically Driven MEMS Galvanometer

[0026] The following is a detailed explanation of step 1.

[0027] The dynamic model of the MEMS galvanometer is expressed as follows: .

[0028] in, and These represent the galvanometer along... Axial direction and Angle of torsion in the axial direction, and For rotational inertia, and The damping coefficient is... and Let be the spring constant of the torsion bar. and This is the electrostatic torsional torque.

[0029] and They are represented as follows: .

[0030] .

[0031] in, Indicates silicon density, Indicates the thickness of the mirror. Indicates the width and length of the mirror. Indicates the outer width of the frame. Indicates the outer length of the frame. Indicates the internal width of the frame. Indicates the internal length of the frame.

[0032] and They are represented as follows: .

[0033] .

[0034] in, , and This indicates the electrostatic torque generated by the bottom drive electrode attracting the mirror surface. , and This indicates the electrostatic torque generated by the side drive electrode attracting the mirror surface. This indicates the electrostatic torque generated by the bottom drive electrode attracting the frame. and It has the following forms: .

[0035] .

[0036] in, Indicates the dielectric constant of air. and These represent the integration regions of the bottom driving electrode and the side driving electrode, respectively. , This indicates the distance between the bottom driving electrode and the mirror surface. This refers to the control voltage applied to the driving electrode.

[0037] The driving method adopts differential drive, as shown below: .

[0038] in, This is the bias voltage. and These represent the control voltages of the electrostatically driven MEMS galvanometer in the X and Y axes, respectively.

[0039] definition , , , , The dynamic model of the MEMS galvanometer is transformed into: .

[0040] in, , , , , For system model parameters, , These represent the control mirrors along... , The driving voltage for angular torsion.

[0041] This invention primarily focuses on the control of the α angle in a MEMS galvanometer. The control of the β angle can be achieved using a similar but independent control architecture. To facilitate controller design and considering external disturbances, the dynamic model of the MEMS galvanometer is rewritten from a continuous-time system model to a state-space form: .

[0042] in, Let be the state vector of the system. For the system's control input, For system output, For a bounded perturbation, satisfying , It represents the upper bound of unknown external disturbances. , , , For a continuous system matrix, , , , They are represented as follows: , , , .

[0043] To implement the algorithm on a digital controller such as an FPGA, the continuous-time model needs to be converted into a discrete-time model, i.e., the dynamic model of the MEMS mirror needs to be discretized. This embodiment employs the zero-order hold method, within a fixed sampling period. The continuous system is then precisely discretized. The discretization process involves integrating the continuous state equations of the MEMS galvanometer's dynamic model over the sampling period to obtain the discretized model, whose standard form is as follows: .

[0044] in, Indicates that the system is in The state vector at time t, Indicates that the system is in The state vector at time t. for System control input at any given time. for The system output at any given time. for External disturbances at all times, and satisfying . , , , The system matrix represents the discretized model. , , , These are the matrices of continuous systems. , , , During the sampling period Discretized form below, , , , They are represented as follows: , , , .

[0045] The control objective of this invention is to design a controller that enables the system output to accurately track the reference signal within a finite time, even in the presence of disturbances. Simultaneously, by employing a designed minimum operator reaching law, system disturbances are effectively suppressed and chattering is significantly reduced without overestimating the controller gain.

[0046] Step 2. Based on the discretized model obtained in Step 1, design a disturbance observer to estimate unknown disturbances in the system in real time. Combine the disturbance estimates to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

[0047] In step 2 of this embodiment, a disturbance observer and a discrete minimum operator integrator terminal sliding mode controller based on disturbance observer compensation are designed and theoretically proven. For systems with disturbances, a disturbance observer is designed based on the discretized model obtained in step 1 to estimate unknown disturbances in the system in real time. Subsequently, the disturbance estimates from the disturbance observer are combined to construct a discrete minimum operator integrator terminal sliding mode controller based on disturbance observer compensation. Step 2 also includes a rigorous proof of the estimation effectiveness of the disturbance observer and the stability of the closed-loop control system to ensure that the system converges within a finite time.

[0048] This invention designs a discrete disturbance observer to estimate unknown disturbances in a system, thereby achieving accurate compensation. The specific process of designing the disturbance observer is as follows: The purpose of the disturbance observer is to estimate the disturbance through the system's state error. Let the estimated state of the interference observer at time k be... The perturbation at time k is estimated as follows: The discrete state equation of the disturbance observer is: The discrete state equation of the disturbance observer is: .

[0049] .

[0050] in, For interference observer Estimated state at time [time] for Perturbation estimation at any given time. This is the state estimation gain matrix, used to ensure the stability and speed of state estimation. This is the disturbance estimation gain, used to adjust the convergence speed of the disturbance estimation. The disturbance observer measures the system's output error. Feedback is provided to continuously update the estimates of system state and disturbances.

[0051] To analyze the performance of the disturbance observer, the disturbance estimation error at time k is defined. for: The design goal of the disturbance observer is to achieve [something] through feedback control. It converges to zero or a sufficiently small neighborhood within a finite time, thereby achieving accurate compensation for the perturbation.

[0052] This invention combines the disturbance estimate provided by a discrete disturbance observer to construct a discrete minimum operator integrator terminal sliding mode controller based on disturbance observer compensation. This enables the system state output to quickly and accurately track the reference signal within a finite time. The specific process of constructing the discrete minimum operator integrator terminal sliding mode controller based on disturbance observer compensation is as follows: definition Tracking error at time for: .

[0053] in, for The desired output signal at time.

[0054] definition The integral variable at time t is The discrete update rule for the integral variable is as follows: .

[0055] in, express The integral variable at time step (in time). Within each sampling period, the discrete update of the integral variable is achieved by adjusting the error... Accumulation is achieved.

[0056] The terminal sliding surface of discrete integral is designed based on the minimum operator reaching law: .

[0057] in, express The discrete integral terminal sliding surface at time t. Indicates the weight of the terminal item. . The terminal sliding mode index, . Represents a symbolic function. Indicates integral gain. The nonlinear term is a term that exists in the sliding surface. The nonlinear part is used to achieve finite-time convergence characteristics.

[0058] Calculate the predicted output error, i.e. Tracking error at time for: .

[0059] in, for The system output at any given time, for The desired output signal at time.

[0060] The predicted output error Substituting the discrete integral terminal sliding surface designed based on the minimum operator reaching law, we obtain the system in The predicted sliding surface at time, i.e. Discrete integral terminal sliding surface at time step for: .

[0061] To obtain an explicit control law, a standard one-step explicit method is used to process the nonlinear terminal terms. Perform valuation, define for: .

[0062] Constructing the nominal part of the predicted sliding surface for: .

[0063] Predict the sliding surface of the nominal part of the structure. Adding the actual effects of the input and disturbance, we get: .

[0064] The actual disturbances in the system are replaced with the disturbance estimates from the disturbance observer. Simultaneously, the incompletely compensated residuals from the disturbance observer are merged into the original disturbance term for unified processing, resulting in: .

[0065] .

[0066] in, This is an additional term caused by factors such as disturbances, and it has an upper bound. It can be effectively compressed by improving the estimation accuracy of the interference observer or reducing the step size.

[0067] The minimum operator convergence law is designed as follows: .

[0068] in, It is a contractile factor. . For bandwidth parameters, .

[0069] when hour, Limited steps to enter the sliding mode belt .like If it gradually approaches 0, then it reaches [the desired value] within a finite number of steps. ,get: .

[0070] The discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is constructed as follows: .

[0071] After completing the design of the discrete minimum operator integrator terminal sliding mode controller based on disturbance observer compensation, this embodiment also performs a stability analysis on the MEMS galvanometer system controlled by the disturbance observer-compensated discrete minimum operator integrator terminal sliding mode controller. The stability analysis includes the stability analysis of the disturbance observer and the stability analysis of the closed-loop control system. By rigorously proving the stability of the disturbance observer and the closed-loop control system, it is theoretically guaranteed that the system can converge in a finite time and has the expected robust performance.

[0072] The process of stability analysis for interference observers is as follows: To demonstrate the stability of the interference observer designed in this invention, a Lyapunov function is introduced to analyze the interference observer.

[0073] Define the state estimation error of the disturbance observer at time k. for: .

[0074] Define the disturbance estimation error at time k for the disturbance observer. for: .

[0075] Error in state estimation of the observer at time k+1 The recursion is as follows: .

[0076] Perturbation estimation error of the observer at time k+1 The recursion is as follows: .

[0077] in, for External disturbances at all times, and satisfying . Indicates changes in disturbances. .

[0078] Introducing Lyapunov functions Stability analysis of the interference observer: .

[0079] in, Representing Lyapunov functions At any moment The value of . R represents a positive definite matrix. , .

[0080] By calculating the Lyapunov function Increment To demonstrate that the MEMS galvanometer system controlled by a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is stable under disturbance observer compensation: .

[0081] in, Representing Lyapunov functions At any moment The value of . .

[0082] The two types of errors, namely the disturbance estimation error and the disturbance estimation error, are combined, and the following variables are defined: , , , .

[0083] Where 0 represents the zero matrix of the corresponding dimension. Denotes an identity matrix of appropriate order, whose dimensions are related to the perturbation estimation error. Same. Then: .

[0084] Define Lyapunov functions for: .

[0085] in, Representing Lyapunov functions At any moment The value of .

[0086] Calculate the Lyapunov function Increment for: .

[0087] in, Representing Lyapunov functions At any moment The value of .

[0088] exist Make .make ,in This represents the smallest eigenvalue of the matrix.

[0089] Under the condition of no perturbation increment, we obtain: .

[0090] Able to draw conclusions That is, the disturbance estimation error It will converge to a compact set containing the origin, exhibiting uniform eventual boundedness.

[0091] The process of stability analysis for a closed-loop control system is as follows: Define Lyapunov functions for: .

[0092] in, Representing Lyapunov functions At any moment The value of .

[0093] Lyapunov function Increment for: .

[0094] in, Representing Lyapunov functions At any moment The value of .

[0095] To analyze the sign characteristics of the Lyapunov function increment, it is necessary to compare... and The numerical relationship. According to the properties of the minimum operator approach law, it can be known that when... When the value is large, the smallest operator term has a weaker impact on the system dynamics. However, when... When it is small, this approach term will dominate the system's behavior and drive it. It converges rapidly to zero. Based on the above analysis, the upper bound expression for the Lyapunov function increment can be derived as follows: Lyapunov function Increment The upper bound expression is: .

[0096] in, for The upper bound of the function reflects the error range caused by uncompensated disturbances and system uncertainties. In each iteration, the Lyapunov function... The value will continue to decrease until... Entering a small bandwidth of the sliding surface Furthermore, the system state will converge within a finite number of steps.

[0097] To estimate the upper bound of the convergence steps, the Lyapunov function needs to be calculated. Less than The number of steps required. First, based on the Lyapunov function. Increment By analyzing the inequalities, we obtain: .

[0098] By studying the Lyapunov function Increment By summing the expressions, we get: .

[0099] If Lyapunov function The initial value is Then after After one iteration, its function value satisfies: .

[0100] when When the system enters the convergence zone, the number of convergence steps of the system is... The upper bound expression for the number of convergence steps is obtained by satisfying the following upper bound estimate: .

[0101] In particular, when there is no disturbance in the system... At this time, the number of convergence steps is minimized, and the number of convergence steps at this time is: .

[0102] The above results demonstrate that the MEMS galvanometer system controlled by the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation can converge within a finite number of steps, and that the system can be further improved by adjusting the parameters. and Lyapunov functions initial value It can control the convergence speed of the system. The tracking error of the system can reach the sliding surface of the integrator terminal in a finite time, maintain its motion state on the sliding surface of the integrator terminal, and finally converge to zero along the sliding surface of the integrator terminal in a finite time.

[0103] Step 3. Implement trajectory tracking control of the MEMS galvanometer using a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

[0104] like Figure 2 As shown, in step 3 of this implementation, the discrete reference signal is first compared with the actual angle position signal detected by the feedback loop to generate a tracking error signal. The tracking error signal is input to the disturbance observer (DO) to estimate unknown disturbances in the system in real time and generate feedforward compensation. It is also used to calculate the sliding surface combining the integral term and the terminal attractor. The core of the control method of this invention is to use a minimum operator reaching law with "faster at distant points and slower at near points" characteristics, integrating the tracking error, sliding surface state, and feedforward compensation to synthesize the final digital control quantity, thereby effectively suppressing chattering while ensuring finite-step convergence of the system. The final digital control quantity is amplified by the driving circuit and used to drive the MEMS galvanometer to perform scanning motion. The actual deflection angle of the galvanometer is detected in real time by the position sensor and fed back to the input, thus forming a closed-loop control system capable of achieving high-precision and robust trajectory tracking control.

[0105] Step 3 will be described in detail below.

[0106] The discrete reference signal is the desired output signal. The actual angular position signal detected by the feedback loop is the system output. Compare and generate tracking error signals .

[0107] Tracking error signal The input is fed into the disturbance observer to estimate unknown disturbances in the system in real time, thus obtaining a disturbance estimate. And based on perturbation estimation Generate feedforward compensation, i.e., extra term .

[0108] Based on tracking error signal Calculate the terminal sliding surface of discrete integral .

[0109] By employing the least operator reaching law and combining the tracking error signal, sliding surface state, and feedforward compensation, the final digital control quantity, i.e., the system control input, is obtained. This is to ensure that the sliding surface variables converge and suppress chattering, thereby suppressing chattering while guaranteeing finite-step convergence of the system.

[0110] Final digital control quantity The voltage is amplified by the driving circuit and used to drive the MEMS galvanometer to perform scanning motion.

[0111] The actual deflection angle of the galvanometer is detected in real time by the position sensor and fed back to the input, forming a closed-loop control.

[0112] Furthermore, the discrete integral terminal sliding mode control in the method of this invention can be replaced by robust output regulation control. Robust output regulation control has the advantage of strong robustness, but its algorithm is more complex and difficult to implement. The electrostatic driving method used in MEMS galvanometers can be replaced by electromagnetic, piezoelectric, or other driving methods. Different driving methods have their own advantages and disadvantages in response speed and power consumption. For example, under the piezoelectric driving mechanism, the displacement is usually small, making it difficult to achieve large-angle scanning. Under the electromagnetic driving mechanism, the process design is more complex and increases power consumption. The high current during the driving process generates heat.

[0113] This embodiment also includes simulation verification and performance analysis.

[0114] Based on the discrete minimum operator integral terminal sliding mode controller with disturbance observer compensation designed in step 2, a simulation model of the MEMS galvanometer system was built in the MATLAB environment. The effectiveness of the proposed control method was verified through simulation experiments. In the simulation, the controller calculates the control quantity in real time to drive the galvanometer to twist, and its tracking performance under reference trajectories of different frequencies and amplitudes is tested, thereby evaluating the actual effect of the system in suppressing chattering and improving tracking accuracy while ensuring robustness.

[0115] To verify the effectiveness of the proposed Discrete Minimum Operator Integral Terminal Sliding Mode Control (DO+DM-ITSM) method based on disturbance observer compensation, sinusoidal reference trajectories of different frequencies were set up for testing, and the results were compared with those of the traditional PID control method.

[0116] 1. Experimental setup.

[0117] Experimental subject: electrostatically driven MEMS galvanometer.

[0118] Reference trajectory: a sinusoidal signal with an amplitude of 1.5°, tested at frequencies of 200 Hz, 400 Hz and 600 Hz to evaluate the performance of the control method at different scan rates.

[0119] Comparison method: Traditional PID control method and the DO+DM-ITSM control method proposed in this invention.

[0120] Performance indicators: mainly examine tracking accuracy, convergence, overshoot, and the smoothness of control output, i.e., chatter suppression effect.

[0121] Disturbance conditions: Additional external disturbances were introduced in the simulation experiments to test the robustness of the system.

[0122] 2. Experimental Results and Analysis.

[0123] (1) 200 Hz low-frequency scanning test.

[0124] Figure 4 This is a scan tracking effect diagram of the traditional PID control method at 200Hz and 1.5° amplitude.

[0125] The horizontal axis represents time, and the vertical axis represents angle. The solid line represents the reference trajectory, i.e., the desired trajectory, while the dashed line represents the actual tracking trajectory obtained using the PID control method. It can be seen that the PID control exhibits significant phase lag and tracking error.

[0126] according to Figure 4 It can be seen that at 200 Hz, the PID control can basically track the reference trajectory, but there is obvious phase lag and amplitude attenuation. The tracking error RMSE is large, and the control output signal has high-frequency fluctuations, indicating that its disturbance rejection capability is limited.

[0127] Figure 5 This is a scanning and tracking effect diagram of the method proposed in this invention at 200Hz and 1.5° amplitude.

[0128] The solid line represents the reference trajectory, and the dashed line represents the actual tracking trajectory obtained using the method of this invention. The method of this invention offers high tracking accuracy, almost perfectly coinciding with the reference trajectory, and exhibits significant chatter suppression.

[0129] according to Figure 5 As can be seen, at the same frequency, the method of this invention exhibits excellent tracking performance, with the actual trajectory almost overlapping the reference trajectory. The error is significantly reduced, the control output is smooth, and there is no significant chattering. The disturbance observer effectively estimates and compensates for system disturbances, demonstrating its effectiveness and robustness.

[0130] (2) 400 Hz intermediate frequency scanning test.

[0131] Figure 6 This is a scan tracking effect diagram of the traditional PID control method at 400Hz and 1.5° amplitude.

[0132] As the frequency increases, the overshoot of PID control increases, the settling time is prolonged, and the tracking performance deteriorates further.

[0133] according to Figure 6 It can be seen that as the frequency increases to 400 Hz, the performance of PID control deteriorates further. Phase lag and amplitude attenuation intensify, overshoot becomes more pronounced, and settling time becomes longer, making it difficult to meet the application requirements of high-precision scanning.

[0134] Figure 7 This is a scanning and tracking effect diagram of the method proposed in this invention at 400Hz and 1.5° amplitude.

[0135] The method of this invention still maintains good tracking performance, with no obvious distortion or chattering.

[0136] according to Figure 7 As can be seen, the method of this invention still maintains good tracking performance at 400 Hz. Although the error increases slightly compared to 200 Hz, it is still much smaller than that of PID control. The minimum operator reaching law effectively suppresses chattering at high frequencies, and the system exhibits good stability and fast convergence.

[0137] (3) 600 Hz high frequency scanning test.

[0138] Figure 8 This is a scan tracking effect diagram of the traditional PID control method at 600Hz and 1.5° amplitude.

[0139] PID control exhibits severe distortion at extremely high frequencies, failing to meet the requirements for high-precision scanning.

[0140] according to Figure 8 It is evident that at the 600 Hz limiting frequency, PID control exhibits severe distortion, with a significant deviation between the tracked trajectory and the reference trajectory, resulting in a sluggish system response and near-complete loss of tracking capability. This demonstrates that traditional linear control methods, i.e., PID control, are ill-suited for high-speed scanning scenarios.

[0141] Figure 9 This is a scanning and tracking effect diagram of the method proposed in this invention at 600Hz and 1.5° amplitude.

[0142] The method of this invention can still maintain high tracking accuracy and stability, verifying its superiority under high-speed scanning.

[0143] according to Figure 9 It is evident that the method of this invention can still achieve stable and accurate tracking under the harsh condition of 600 Hz. Although the error further increases, the system state still converges to the vicinity of the reference trajectory within a finite number of steps, without any instability. This fully demonstrates the excellent robustness and control accuracy of the proposed method under nonlinear, strong disturbance, and high-speed conditions.

[0144] 3. Experimental conclusions.

[0145] comprehensive Figures 4 to 9Experimental results show that, at different scanning frequencies, the control method proposed in this invention significantly outperforms traditional PID control in terms of tracking accuracy, response speed, anti-disturbance capability, and chatter suppression. Its performance advantages are particularly pronounced at medium- and high-frequency scanning frequencies, effectively solving the control problems caused by external disturbances in MEMS mirrors and fully meeting the stringent requirements of lidar for high-speed, high-precision scanning control.

[0146] In the scanning control of MEMS galvanometers in lidar systems, there is a significant nonlinear relationship between the driving voltage and the deflection angle. Traditional control methods heavily rely on accurate system models and struggle to overcome the effects of external disturbances, resulting in limited control accuracy. To address this issue, this invention proposes a discrete nonlinear robust control strategy for lidar applications, which can significantly improve the scanning accuracy and disturbance rejection capability of MEMS galvanometers.

[0147] The method of this invention is a discrete nonlinear scanning control method. It uses a disturbance observer to estimate and compensate for unknown disturbances in the system in real time, and combines a discrete minimum operator integral terminal sliding mode control strategy. It uses the minimum operator reaching law to effectively suppress control signal jitter, thereby ensuring that the MEMS galvanometer can still track the predetermined trajectory with high precision under high frequency scanning and external disturbances.

[0148] First, the method of this invention is the first to apply discrete minimum operator integral terminal sliding mode control to MEMS galvanometer control. The control method of this invention enables the system state to converge to the sliding surface within a finite number of steps, effectively solving the problem of insufficient convergence of traditional control methods in high-frequency and large-range scanning.

[0149] Secondly, the method of this invention designs an interference observer that can estimate and compensate for external disturbances to the system in real time, greatly enhancing the robustness of the system in complex disturbance environments, thereby maintaining high-precision trajectory tracking performance.

[0150] Furthermore, the method of this invention proposes a minimum operator approach law, which can automatically reduce the approach speed in the small error region, and achieve an effective balance between chatter suppression and convergence speed. This can avoid chattering caused by excessively high approach speed, while ensuring that the system converges quickly.

[0151] Finally, the discrete control algorithm proposed in this invention has a clear structure, high computational efficiency, and is easy to implement in embedded platforms such as FPGA and DSP, supporting large-scale deployment in industrial applications such as LiDAR.

[0152] Compared with existing technologies, this invention is based on discrete minimum operator integral terminal sliding mode control, which combines a disturbance observer and a minimum operator reaching law in the discrete control domain, and has the following advantages: The disturbance observer can estimate and compensate for external disturbances in real time, effectively reducing the gain required for switching terms in sliding mode control. Combined with the minimum operator reaching law, it achieves "faster at distant points and slower at near points" approach, automatically reducing speed within a small error range, thus significantly suppressing chattering without sacrificing response speed. This control structure maintains good overall performance under quantization, sampling, and zero-order hold conditions, balancing control accuracy in both the arrival and steady-state phases.

[0153] By constructing an integral terminal sliding surface and introducing the minimum operator arrival law, i.e. the minimum operator approach law, the system state can converge to the sliding surface in a finite number of steps, and the tracking error reaches the preset bandwidth in a finite number of steps. Even under large angle and high speed scanning conditions, high-precision trajectory tracking can still be achieved, and there is no obvious distortion at the edges.

[0154] Furthermore, the discrete disturbance observer designed using the method of this invention can perform online estimation and dynamic compensation for sudden and periodic disturbances, maintaining small steady-state errors and phase stability. In complex scenarios such as combined disturbances, this invention can significantly improve the scanning accuracy and stability of MEMS galvanometers.

[0155] Example 2 This embodiment 2 proposes a lidar system, which is based on the same inventive concept as the MEMS galvanometer scanning method based on integral terminal sliding mode control in embodiment 1. The lidar system includes a laser, a MEMS galvanometer, a position sensor, an analog-to-digital converter, an FPGA-based controller, and a driving circuit.

[0156] The laser, as a laser source, emits laser light that is incident on the mirror surface of the MEMS galvanometer.

[0157] The position sensor is used to receive the laser reflected from the mirror surface of the MEMS galvanometer and convert it into an electrical signal.

[0158] An analog-to-digital converter is used to convert the electrical signals output by a position sensor into digital signals, which are then fed into an FPGA-based controller.

[0159] The FPGA-based controller stores a readable storage medium, and when the readable storage medium is executed, it is used to implement the steps of the MEMS galvanometer scanning method based on integral terminal sliding mode control described in Example 1.

[0160] The scanning method of MEMS galvanometer based on integral terminal sliding mode control is calculated and then the voltage control signal is output by the FPGA-based controller. The driving voltage is amplified by the voltage amplifier of the driving circuit and input to the bottom and side driving electrodes of the MEMS galvanometer to drive the MEMS galvanometer to track the desired trajectory for scanning.

[0161] The method of this invention constructs a closed-loop controlled MEMS galvanometer scanning system. This closed-loop system of "laser emission - optical path - galvanometer scanning - position detection - control calculation - drive output" is beneficial for realizing high-speed scanning lidar applications.

[0162] like Figure 3 As shown, the MEMS galvanometer driving circuit in this embodiment specifically includes a digital-to-analog converter (DAC), a low-pass filter, and an amplifier circuit. The lidar system in this embodiment also includes a host computer.

[0163] The laser emitted by the laser is incident on the surface of the MEMS galvanometer. The reflected laser light passes through the receiving mirror and is received by the position sensor, which converts it into an electrical signal. This electrical signal is then converted into a digital signal by an analog-to-digital converter (ADC) and sent to the FPGA-based controller. The bottom of the MEMS galvanometer has driving electrodes. The digital control output from the controller is amplified and converted into a corresponding voltage driving signal, which is applied to the driving electrodes to control the mirror surface to achieve a specific angle of rotation, thus realizing precise scanning of a preset trajectory.

[0164] When the galvanometer deflects under the driving voltage, the position of the reflected laser beam on the position sensor changes accordingly. By detecting and calculating this position signal, the scanning angle of the MEMS galvanometer can be obtained in real time. The position sensor signal is obtained in real time through an FPGA high-speed data acquisition card, compared with the desired reference trajectory signal to obtain an error signal, and then processed by the control method of this invention to generate a control signal, which is used to drive the MEMS galvanometer to complete closed-loop trajectory tracking adjustment.

[0165] Example 3 This embodiment 3 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the MEMS galvanometer scanning method based on integral terminal sliding mode control in embodiment 1 above.

[0166] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0167] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A MEMS galvanometer scanning method based on integral terminal sliding mode control, characterized in that, Includes the following steps: Step 1. Construct a dynamic model of the MEMS galvanometer and discretize it to obtain a discretized model; Step 2. Based on the discretized model obtained in Step 1, design a disturbance observer to estimate unknown disturbances in the system in real time. Combine the disturbance estimates to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation. Step 3. Implement trajectory tracking control of the MEMS galvanometer using a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

2. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 1, characterized in that, Step 1 specifically involves: The dynamic model of the MEMS galvanometer is expressed as follows: ； in, and These represent the galvanometer along... Axial direction and Angle of torsion in the axial direction, and For rotational inertia, and The damping coefficient is... and Let be the spring constant of the torsion bar. and This is the electrostatic torsional torque; and They are represented as follows: ； ； in, Indicates silicon density, Indicates the thickness of the mirror. Indicates the width and length of the mirror. Indicates the outer width of the frame. Indicates the outer length of the frame. Indicates the internal width of the frame. Indicates the internal length of the frame; and They are represented as follows: ； ； in, , and This indicates the electrostatic torque generated by the bottom drive electrode attracting the mirror surface. , and This indicates the electrostatic torque generated by the side drive electrode attracting the mirror surface; This indicates the electrostatic torque generated by the bottom drive electrode attracting the frame; and It has the following forms: ； ； in, Indicates the dielectric constant of air. and These represent the integration regions of the bottom driving electrode and the side driving electrode, respectively. , Indicates the distance between the bottom driving electrode and the mirror surface; The control voltage applied to the driving electrode; The driving method adopts differential drive, as shown below: ； in, This is the bias voltage. and These represent the control voltages of the electrostatically driven MEMS galvanometer in the X and Y axes, respectively. definition , , , , The dynamic model of the MEMS galvanometer is transformed into: ； in, , , , , For system model parameters, , These represent the control mirrors along... , The driving voltage for angular torsion; Considering external disturbances, the dynamic model of the MEMS galvanometer is rewritten from a continuous-time system model to a state-space form: ； in, Let be the state vector of the system. For the system's control input, For system output, For a bounded perturbation, satisfying , It represents the upper bound of unknown external disturbances; , , , For a continuous system matrix, , , , They are represented as follows: ， ， ， ； Using the zero-order hold method, during the sampling period The dynamic model of the MEMS galvanometer is discretized below, where The discretized model is obtained as follows: ； in, Indicates that the system is in The state vector at time t, Indicates that the system is in The state vector at any given time; for System control input at any given time; for The system output at that moment; for External disturbances at all times, and satisfying ; , , The system matrix represents the discretized model. , , These are the matrices of continuous systems. , , During the sampling period Discretized form below, , , They are represented as follows: ， ， 。 3. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 2, characterized in that, In step 2, the process of designing the interference observer is as follows: Let the estimated state of the interference observer at time k be: The perturbation at time k is estimated as follows: ; The discrete state equation of the disturbance observer is: ； ； in, For interference observer Estimated state at time [time] for Perturbation estimation at any given time; The gain matrix is ​​used for state estimation; Estimate the gain for the disturbance.

4. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 3, characterized in that, In step 2, the process of constructing a discrete minimum operator integral terminal sliding mode controller based on interference observer compensation is as follows: definition Tracking error at time for: ； in, for The expected output signal at time; definition The integral variable at time t is The discrete update rule for the integral variable is as follows: ； in, express The integral variable at time step; The terminal sliding surface of discrete integral is designed based on the minimum operator reaching law: ； in, express The discrete integral terminal sliding surface at time t. Indicates the weight of the terminal item. ; The terminal sliding mode index, ; Represents a symbolic function; Indicates integral gain. ; Calculate the predicted output error, i.e. Tracking error at time for: ； in, for The system output at any given time, for The expected output signal at time; The predicted output error Substituting the discrete integral terminal sliding surface designed based on the minimum operator reaching law, we obtain the system in The predicted sliding surface at time, i.e. Discrete integral terminal sliding surface at time step for: ； The standard one-step explicit method is used to process the nonlinear terminal terms. Perform valuation, define for: ； Constructing the nominal part of the predicted sliding surface for: ； Predict the sliding surface of the nominal part of the structure. Adding the actual effects of the input and disturbance, we get: ； The actual disturbances in the system are replaced with the disturbance estimates from the disturbance observer. Simultaneously, the incompletely compensated residuals from the disturbance observer are merged into the original disturbance term for unified processing, resulting in: ； ； in, For additional terms with an upper bound; The minimum operator convergence law is designed as follows: ； in, It is a contractile factor. ; For bandwidth parameters, ; when hour, Limited steps to enter the sliding mode belt ;like If it gradually approaches 0, then it reaches [the desired value] within a finite number of steps. ,get: ； The discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is constructed as follows: 。 5. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 4, characterized in that, In step 2, after completing the design of the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation, a stability analysis is also performed on the MEMS galvanometer system controlled by the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation. The stability analysis includes the stability analysis of the disturbance observer and the stability analysis of the closed-loop control system.

6. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 5, characterized in that, In step 2, the process of stability analysis of the interference observer is as follows: Define the state estimation error of the disturbance observer at time k. for: ； Define the disturbance estimation error at time k for the disturbance observer. for: ； Error in state estimation of the observer at time k+1 The recursion is as follows: ； Perturbation estimation error of the observer at time k+1 The recursion is as follows: ； in, for External disturbances at all times, and satisfying ; Indicates changes in disturbances. ; Introducing Lyapunov functions Stability analysis of the interference observer: ； in, Representing Lyapunov functions At any moment The value; R represents a positive definite matrix. , ; Calculate the Lyapunov function Increment To demonstrate that the MEMS galvanometer system controlled by a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is stable under disturbance observer compensation: ； in, Representing Lyapunov functions At any moment The value; ; The disturbance estimation error and the disturbance estimation error are combined, and the following variables are defined: ， ， ， ； in, Let the identity matrix be represented; then: ； Define Lyapunov functions for: ； in, Representing Lyapunov functions At any moment The value; Calculate the Lyapunov function Increment for: ； in, Representing Lyapunov functions At any moment The value; exist Make ;make ,in Represents the smallest eigenvalue of the matrix; Under the condition of no perturbation increment, we obtain: ； And thus obtain Perturbation estimation error Converging to a compact set containing the origin, which manifests as the perturbation estimation error. Consistency is ultimately bounded.

7. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 6, characterized in that, In step 2, the stability analysis process of the closed-loop control system is specifically as follows: Define Lyapunov functions for: ； in, Representing Lyapunov functions At any moment The value; Lyapunov function Increment for: ； in, Representing Lyapunov functions At any moment The value; Lyapunov function Increment The upper bound expression is: ； in, for The upper bound; Based on Lyapunov functions Increment Analyzing the inequalities, we obtain: ； By studying the Lyapunov function Increment By summing the expressions, we get: ； If Lyapunov function The initial value is Then after After one iteration, its function value satisfies: ； when When the system enters the convergence zone, the number of convergence steps of the system is... Satisfies the following upper bound estimate: ； When the system has no disturbances, At time, the number of convergence steps for: ； The MEMS galvanometer system controlled by a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation can converge within a finite number of steps, and can be further improved by adjusting parameters. and Lyapunov functions initial value It can control the convergence speed of the system; the tracking error of the system can reach the sliding surface of the integrator terminal in a finite time and maintain its motion state on the sliding surface of the integrator terminal, and finally converge to zero along the sliding surface of the integrator terminal in a finite time.

8. The MEMS galvanometer scanning method based on integral terminal sliding mode control according to claim 7, characterized in that, Step 3 specifically involves: The discrete reference signal is the desired output signal. The actual angular position signal detected by the feedback loop is the system output. Compare and generate tracking error signals ; Tracking error signal The input is fed into the disturbance observer to estimate unknown disturbances in the system in real time, thus obtaining a disturbance estimate. And based on perturbation estimation Generate feedforward compensation, i.e., extra term ; Based on tracking error signal Calculate the terminal sliding surface of discrete integral ; By employing the least operator reaching law and combining the tracking error signal, sliding surface state, and feedforward compensation, the final digital control quantity, i.e., the system control input, is obtained. ; Final digital control quantity The voltage is amplified by the driving circuit and used to drive the MEMS galvanometer to perform scanning motion. The actual deflection angle of the galvanometer is detected in real time by the position sensor and fed back to the input, forming a closed-loop control.

9. A lidar system, comprising a laser, a MEMS galvanometer, a position sensor, an analog-to-digital converter, an FPGA-based controller, and a driving circuit; characterized in that, The laser, as a laser source, emits laser light that is incident on the mirror surface of the MEMS galvanometer. The position sensor is used to receive the laser light reflected from the mirror surface of the MEMS galvanometer and convert it into an electrical signal; An analog-to-digital converter is used to convert the electrical signals output by the position sensor into digital signals, which are then sent to an FPGA-based controller. The FPGA-based controller stores a readable storage medium, and when the readable storage medium is executed, it is used to implement the steps of the MEMS galvanometer scanning method based on integral terminal sliding mode control as described in any one of claims 1 to 8. The scanning method of MEMS galvanometer based on integral terminal sliding mode control is calculated and then the voltage control signal is output by the FPGA-based controller. The driving voltage is amplified by the voltage amplifier of the driving circuit and input to the bottom and side driving electrodes of the MEMS galvanometer to drive the MEMS galvanometer to track the desired trajectory for scanning.

10. A computer-readable storage medium having a program stored thereon; characterized in that, When executed by the processor, the program is used to implement the steps of the MEMS galvanometer scanning method based on integral terminal sliding mode control as described in any one of claims 1 to 8.

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