A MEMS galvanometer scanning method based on adaptive law-based recursive terminal sliding mode control

Abstract

This invention belongs to the field of lidar scanning control technology and discloses a MEMS galvanometer scanning method based on adaptive law recursive terminal sliding mode control. The method first establishes a dynamic model of the MEMS galvanometer containing lumped uncertain disturbances. Then, based on the dynamic model of the MEMS galvanometer containing lumped uncertain disturbances, an adaptive recursive terminal sliding mode controller is constructed. The construction process includes fast non-singular terminal sliding mode design, recursive integral sliding mode design, and design of equivalent control laws and adaptive reaching laws. Finally, the adaptive recursive terminal sliding mode controller is used to achieve tracking control of the MEMS galvanometer. This invention proposes for the first time a state-dependent adaptive recursive terminal sliding mode control strategy and applies it to the precise control of MEMS galvanometers. It not only enables the system state to converge to the sliding surface within a certain time but also solves the problem that traditional control methods cannot guarantee convergence during high-frequency, large-range scanning.

Description

Technical Field

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

[0002] MEMS galvanometers have advantages such as simple structure, low power consumption, and fast response. As the core scanning execution device of the lidar system, they can achieve high-speed scanning of single or dual axes with the help of electrostatic drive.

[0003] However, the driving voltage and deflection angle of a MEMS galvanometer exhibit a nonlinear relationship, and are also significantly affected by factors such as mechanical damping, uncertainties in torsional spring stiffness, and manufacturing errors, resulting in significant model bias. In existing control technologies, electrostatically driven MEMS galvanometers, operating in open-loop mode, show a significant nonlinear relationship between their driving voltage and deflection angle, particularly pronounced during large-angle scanning. This nonlinearity makes it difficult for the MEMS galvanometer to accurately track the desired trajectory, easily causing laser beam pointing deviation, which directly affects the imaging quality and positioning accuracy of the lidar. Because lidar systems place extremely high demands on the scanning performance of MEMS galvanometers, conventional open-loop control of MEMS galvanometers results in large overshoot and long settling times, making it difficult to meet the requirements for high-precision scanning performance.

[0004] While traditional PID closed-loop control methods are simple in structure, the relationship between the driving voltage and torsional angle of MEMS mirrors is typically nonlinear. PID control struggles to handle the nonlinear dynamics of MEMS mirrors, especially during high-speed or large-range scanning, easily leading to response lag and decreased accuracy, and exhibiting poor robustness to external disturbances. It is evident that traditional PID closed-loop control methods are insufficient in dynamic performance and robustness when dealing with strong system nonlinearity, model parameter perturbations, and external disturbances, particularly prone to tracking errors during high-speed, large-range scanning, which can even affect system stability.

[0005] In actual lidar operation, the system also faces sudden disturbances such as external impacts and stiffness changes caused by temperature drift, as well as periodic disturbances such as structural resonance and power supply ripple. Traditional open-loop driving methods are difficult to effectively compensate for such nonlinearities and disturbances. Continuous sliding mode control (SMC) has good robustness, but it has the limitation of insufficient convergence capability within a finite time. Terminal sliding mode control (TSMC) can accelerate the convergence speed, but it faces the risks of singularity and chattering amplification.

[0006] In summary, existing MEMS galvanometer scanning control technology has the following shortcomings: First, under digital implementation, the convergence performance of traditional sliding mode deteriorates, and chattering becomes severe. Second, under large-scale, high-speed scanning, traditional control struggles to converge to the reference trajectory within a finite time. Third, its disturbance rejection capability is insufficient, especially against sudden and periodic combined disturbances, resulting in a significant decrease in scanning accuracy.

[0007] Therefore, there is an urgent need for a MEMS galvanometer closed-loop scanning control method that is suitable for continuous digital control platforms and has finite-time convergence, chatter suppression and strong anti-disturbance capabilities, so as to improve the scanning accuracy and stability of lidar systems under complex working conditions. Summary of the Invention

[0008] The purpose of this invention is to propose a recursive terminal sliding mode control method for MEMS galvanometer scanning based on adaptive laws. This method can achieve high-speed scanning trajectory tracking with convergence within a finite time while suppressing chattering in small error intervals, thereby improving the robustness of the system under strong nonlinearity and complex disturbances.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] The adaptive law-based recursive terminal sliding mode control method for MEMS galvanometer scanning includes the following steps:

[0011] Step 1. Establish a dynamic model of the MEMS galvanometer that includes lumped uncertainty perturbations;

[0012] Step 2. Based on the dynamic model of the MEMS galvanometer containing lumped uncertain disturbances, construct an adaptive recursive terminal sliding mode controller. The construction process includes fast non-singular terminal sliding mode design, recursive integral sliding mode design, and design of equivalent control law and adaptive reaching law.

[0013] Step 3. Use an adaptive recursive terminal sliding mode controller to achieve tracking control of the MEMS mirror.

[0014] Furthermore, based on the above-mentioned MEMS galvanometer scanning method based on adaptive law recursive terminal sliding mode control, this invention also proposes a lidar system, which includes a laser, a MEMS galvanometer, a controller, a position sensor, a driving circuit, and a receiver.

[0015] A reflector for adjusting the laser beam path is placed between the laser light source and the MEMS galvanometer.

[0016] The controller contains a readable storage medium, and when the readable storage medium is executed, it is used to implement the steps of the above-mentioned adaptive law-based recursive terminal sliding mode control MEMS galvanometer scanning method.

[0017] The position sensor inputs the detected mirror torsional position signal and the desired reference position signal to the controller in real time. After calculation according to the MEMS mirror scanning method based on the adaptive law recursive terminal sliding mode control, the controller outputs a voltage control signal. The driving voltage is amplified by the driving circuit and input to the bottom and side driving electrodes to drive the MEMS mirror to track the desired trajectory for scanning.

[0018] Furthermore, based on the aforementioned adaptive law-based recursive terminal sliding mode control MEMS galvanometer scanning method, this invention also proposes a computer-readable storage medium storing a program thereon; when executed by a processor, this program is used to implement the steps of the aforementioned adaptive law-based recursive terminal sliding mode control MEMS galvanometer scanning method.

[0019] The present invention has the following advantages:

[0020] As described above, this invention relates to a MEMS galvanometer scanning method based on an adaptive law for recursive terminal sliding mode control. Compared with existing technologies, this invention achieves a deep integration of the recursive terminal sliding mode structure and the adaptive approaching mechanism within the continuous control domain. By constructing the sliding surface through hierarchical recursion, the system state is positioned on the sliding manifold from the initial moment or enters sliding mode motion within a very short time. Theoretically, this completely eliminates the unavoidable approaching phase in traditional sliding mode control, ensuring that the system maintains its sliding mode robustness throughout the entire control process.

[0021] Based on this, the present invention introduces an improved type-1 symbolic integrator into the recursive integral sliding mode function. Through continuousization and integral recursion design, the control input is effectively smoothed, the discontinuity of the control signal is significantly reduced, and the robust and smooth control is unified from the system start-up stage to the steady-state convergence stage.

[0022] Meanwhile, the adaptive reaching law designed in this invention can adjust the control gain online based on sliding mode variables and system state information when the upper bound of the disturbance is unknown or changes over time. This achieves real-time adaptive compensation for complex uncertainties and external disturbances, significantly reducing the dependence on prior information about the disturbance and the selection of conservative parameters. The adaptive parameters are driven collaboratively by sliding mode variables and different state components, realizing the fractional adjustment of various uncertainties. Compared with traditional single adaptive gain or overall adjustment methods, the method of this invention can more accurately match the dynamic evolution characteristics of the system, making the disturbance compensation process more targeted and effective.

[0023] Without requiring precise knowledge of the maximum disturbance boundary, this invention significantly reduces the dependence on discontinuous switching terms. While ensuring finite-time convergence performance, it structurally suppresses steady-state chattering, achieving fast and smooth convergence throughout the entire process. This significantly improves the overall control performance of the system under conditions of strong nonlinearity, multi-source uncertainty, and complex disturbances. Attached Figure Description

[0024] Figure 1 This is a flowchart of the MEMS galvanometer scanning method based on adaptive law recursive terminal sliding mode control in an embodiment of the present invention.

[0025] Figure 2 This is a closed-loop control block diagram of the MEMS galvanometer scanning method based on adaptive law recursive terminal sliding mode control in an embodiment of the present invention.

[0026] Figure 3 The image shows a comparison of the scanning effects obtained by using PID control and the control method of this invention, namely ARTSM, when the scanning frequency is 200Hz.

[0027] in, Figure 3 (a) in the figure shows the tracking reference signal effect obtained by using PID and ARTSM control methods at 200Hz. Figure 3 (b) in the figure is a comparison of the tracking error values ​​obtained by using PID and ARTSM control methods at 200Hz.

[0028] Figure 4 The image shows a comparison of the scanning effects obtained by using PID control and the control method of this invention at a scanning frequency of 400Hz.

[0029] in, Figure 4 (a) shows the tracking reference signal effect obtained by using PID and ARTSM control methods at 400Hz. Figure 4 (b) in the figure is a comparison of the tracking error values ​​obtained by using PID and ARTSM control methods at 400Hz.

[0030] Figure 5 The image shows a comparison of the scanning effects obtained by using PID control and the control method of this invention at a scanning frequency of 600Hz.

[0031] in, Figure 5 (a) shows the tracking reference signal effect obtained by using PID and ARTSM control methods at 600Hz. Figure 5 (b) in the figure is a comparison of the tracking error values ​​obtained by using PID and ARTSM control methods at 600Hz.

[0032] Figure 6This is a schematic diagram of a lidar system in an embodiment of the present invention. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0034] Example 1

[0035] This invention proposes a galvanometer scanning method based on adaptive recursive terminal sliding mode control, specifically involving a high-precision closed-loop scanning control method for electrostatically driven MEMS galvanometers for lidar applications. This method combines fast nonsingular terminal sliding mode control, recursive integral sliding mode control, and adaptive reaching law. For systems with uncertain or time-varying upper boundaries of disturbances, it can automatically adjust to a suitable gain without precisely knowing the maximum boundary of the disturbance, thereby improving the system's convergence speed, chatter suppression capability, and disturbance rejection performance. Furthermore, it can significantly enhance the system's robustness and finite-time convergence.

[0036] This invention specifically provides an adaptive hierarchical finite-time recursive terminal sliding mode control scheme. This scheme eliminates the approaching phase of traditional sliding mode control by constructing a recursive sliding mode control structure and initializing the recursive sliding surface, ensuring that the system state is on the recursive sliding surface from the initial moment or enters the recursive sliding surface within a very short time. In the recursive sliding mode control structure, an improved symbolic integrator is introduced to continuously process the sliding mode control term, smoothing the control input and reducing chattering caused by discontinuous switching. Simultaneously, a state-dependent adaptive approaching law is introduced, enabling the control gain to adaptively adjust with the system's operating state. This achieves online compensation for system uncertainties and external disturbances without requiring prior knowledge of the maximum disturbance boundary, thus ensuring that the MEMS galvanometer can accurately track the predetermined trajectory even under high-frequency scanning and external disturbances.

[0037] like Figure 1 As shown, the recursive terminal sliding mode control MEMS galvanometer scanning method based on adaptive laws includes the following steps:

[0038] Step 1. Establish a dynamic model of the MEMS galvanometer that includes lumped uncertainty perturbations.

[0039] In this embodiment, step 1 specifically includes:

[0040] MEMS galvanometers consist of a mirror plate, a torsion bar, a frame, and driving electrodes. Their dynamic model is represented as follows:

[0041] .

[0042] in, and For rotational inertia, and These represent the rotation of the galvanometer. Axial direction and Angle of torsion in the axial direction, and The damping coefficient is... and Let be the spring constant of the torsion bar. and This refers to electrostatic torsional torque; and They are represented as follows:

[0043] .

[0044] .

[0045] 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:

[0046] .

[0047] .

[0048] 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; This refers to the control voltage applied to the driving electrode.

[0049] The driving method adopts differential drive, as shown below:

[0050] .

[0051] 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.

[0052] definition , , , , .

[0053] The dynamic model of the MEMS galvanometer is transformed into:

[0054] .

[0055] in, , , , , For system model parameters, , These represent the control mirrors along... , The driving voltage for angular torsion.

[0056] In this embodiment, the method is to... Taking angle control as an example, for Angle control is performed in a similar manner.

[0057] The dynamic model of a MEMS galvanometer containing lumped uncertainty perturbations is as follows:

[0058] .

[0059] in, Let be the state vector of the system. For the system's control input, For system output, , , , For the system matrix; For bounded lumped uncertainty disturbances, satisfying , The upper bound of the lumped uncertainty disturbance is:

[0060] .

[0061] in, For positive integers, . This represents an uncertain time-invariant disturbance. This represents the upper bound of the uncertainty related to the torsion angle. This represents the upper bound of the uncertainty related to angular velocity.

[0062] System Matrix , , , They are represented as follows:

[0063] , , , .

[0064] Under conditions of external disturbances and model uncertainties, the control objective of this invention is to design a corresponding control strategy that enables the system output to accurately track a preset reference trajectory within a finite time. Simultaneously, by introducing an adaptive reaching law, real-time compensation for system uncertainties and disturbances is achieved. This mechanism does not rely on precise knowledge of the upper bound of the disturbance and can automatically adjust the control gain, thereby improving system robustness while significantly suppressing high-frequency chattering in the control signal.

[0065] Step 2. Based on the dynamic model of the MEMS galvanometer containing lumped uncertainties, an adaptive recursive terminal sliding mode controller is constructed to ensure that the system output converges within a finite time. Simultaneously, an adaptive reaching law is introduced for real-time uncertainty compensation. The construction process of the adaptive recursive terminal sliding mode controller specifically includes fast nonsingular terminal sliding mode design, recursive integral sliding mode design, and design of equivalent control law and adaptive reaching law.

[0066] In step 2, the design process for fast nonsingular terminal sliding mode and recursive integral sliding mode is as follows:

[0067] Based on the dynamic model of the MEMS galvanometer containing lumped uncertainty perturbations established in step 1, the tracking error is defined. for:

[0068] .

[0069] in, This is a reference signal.

[0070] Based on the defined tracking error Construct an adaptive recursive terminal sliding mode controller.

[0071] Define a fast nonsingular terminal sliding mode function for:

[0072] .

[0073] in, For positive integers, and For sliding surface parameters, , .

[0074] when At that time, tracking error In a limited time It converges to zero.

[0075] For fast nonsingular terminal sliding mode functions Taking the derivative, we get:

[0076] .

[0077] Based on the designed fast nonsingular terminal sliding mode function, a signed integrator is designed within the sliding mode function. This integrator smooths the control signal, enabling the system to reach the sliding surface layer by layer and achieve finite-time convergence of the tracking error. By properly initializing the recursive sliding surface, the system can directly start on the sliding manifold, thereby eliminating the approach phase and accelerating the convergence process.

[0078] To further improve the robustness of the system, consider a second-order system whose differential-integral terminal sliding mode function is the recursive integral sliding mode function. Defined as:

[0079] ;

[0080] in, For sliding surface parameters, . This is the function to be designed.

[0081] To effectively smooth the control input and significantly reduce the discontinuity of the control signal, this embodiment also improves the symbolic integrator in the sliding mode function, that is, it introduces an improved type I symbolic integrator:

[0082] .

[0083] This equation constitutes a continuous function, which essentially avoids chattering. For parameters, .

[0084] By setting initial conditions ,in and They represent and Given the initial values, we get:

[0085] .

[0086] in, for The initial value.

[0087] This ensures sliding mode variables In a limited time Converging to zero in finite time Represented as:

[0088] .

[0089] In step 2, the design process of the equivalent control law is as follows:

[0090] Without considering system disturbances In this case, let ,get:

[0091] .

[0092] .

[0093] .

[0094] The equivalent control law is then obtained as follows:

[0095] .

[0096] In step 2, the design process of the adaptive reaching law is as follows:

[0097] To effectively compensate for matching perturbations with linear upper bounds, a state-dependent adaptive reaching law is introduced. This enables online compensation for system uncertainties and disturbances.

[0098] ;

[0099] in, For parameters, ; , , This indicates the estimated gain.

[0100] The update law for estimating the gain is:

[0101] .

[0102] .

[0103] .

[0104] in, It is a positive number.

[0105] Estimating parameters, i.e., estimating gain There exists an upper bound. , making It always holds true.

[0106] In step 2, the overall control law of the system is obtained by combining the equivalent control law and the adaptive reaching law. The final adaptive recursive terminal sliding mode controller is as follows:

[0107] .

[0108] in, This is the overall control law of the system.

[0109] In step 2 of this embodiment, after completing the design of the adaptive recursive terminal sliding mode controller, a stability analysis is also performed on the MEMS galvanometer system controlled by the adaptive recursive terminal sliding mode controller. That is, by proving the stability of the sliding surface, it is proved that the sliding surface converges to zero in a finite time.

[0110] First, let's introduce the theorems used in the stability analysis:

[0111] If there exists a continuous Lyapunov function satisfy:

[0112] .

[0113] in, It is about the state vector The positive definite Lyapunov function, and Indicates a parameter, and , Then for any initial conditions , In a limited time It converges to zero, and satisfy:

[0114] .

[0115] The specific process of stability analysis is described below:

[0116] For the equation The system described considers candidate Lyapunov functions. for: .

[0117] Lyapunov function along the system trajectory Taking the time derivative, we get:

[0118] .

[0119] in, .

[0120] Tracking error In a limited time It converges to zero, and satisfy:

[0121] .

[0122] in, Representing Lyapunov functions The initial value.

[0123] when Upon its establishment, there are , will with They converge to zero at the same convergence rate.

[0124] when , At that time, by get:

[0125] .

[0126] Limited time express From initial value The time required for convergence to zero is:

[0127] .

[0128] when , Then, using a similar derivation method, we obtain:

[0129] .

[0130] For any initial state , In a limited time It converges to zero, and satisfy:

[0131] .

[0132] Adaptive estimation error for: .

[0133] Choosing Lyapunov functions for:

[0134] .

[0135] in, It is a positive number.

[0136] For Lyapunov functions Taking the first derivative, we get:

[0137] .

[0138] in, ,get .

[0139] For any parameter If positive numbers exist ,satisfy , and The right side of the equation is negative definite, ensuring that the system meets the stability condition.

[0140] .

[0141] in:

[0142] , , , .

[0143] .

[0144] Lyapunov function From any initial state Depart, within a limited time It converges to zero, and satisfy:

[0145] .

[0146] in, Lyapunov function The initial value.

[0147] The sliding variable is the recursive integral sliding mode function. With estimation error All of them converge to zero within a finite amount of time.

[0148] according to The conditions can be guaranteed Established, among which express The initial value. This initialization method reduces the initial value. The amplitude, thereby ensuring the upper bound of the convergence time. Mainly affected by initial estimation error The impact.

[0149] In a MEMS galvanometer system controlled by an adaptive recursive terminal sliding mode controller, the tracking signal Starting from any initial conditions, it can converge to zero in a finite time, with a total settling time of [missing information]. for: This indicates that the system will converge within a finite time, and the convergence rate can be controlled by adjusting parameters. A recursive integral sliding surface, through proper initialization, allows the system to start directly on the sliding surface, thereby eliminating the approach phase and accelerating the convergence process.

[0150] Step 3. Use an adaptive recursive terminal sliding mode controller to achieve trajectory tracking control of the MEMS mirror.

[0151] like Figure 2 As shown, for a system model of a MEMS galvanometer, the control objective of this invention is to design an adaptive law-based hierarchical finite-time recursive sliding mode terminal sliding mode control scheme under controlled system conditions with model uncertainty and external disturbances. This involves constructing a recursive sliding mode control structure and initializing the recursive sliding surface so that the system state is on the recursive sliding surface from the initial moment or enters the recursive sliding surface within a very short time, thereby eliminating the approaching phase in traditional sliding mode control. Simultaneously, an improved symbolic integrator is introduced into the sliding mode function to continuously process the control terms related to the recursive sliding surface, smoothing the control input and reducing chattering caused by discontinuous switching. Subsequently, a state-related adaptive approaching law is introduced, enabling the control gain to adaptively change with the system operating state without prior knowledge of the maximum boundary of the disturbance. The adaptive parameters are driven by the recursive sliding surface variables and different state components, achieving fractional adjustment of various uncertainties, thereby improving the pertinence and effectiveness of disturbance compensation and reducing dependence on discontinuous switching control terms. Through the synergistic effect of recursive sliding mode control structure, adaptive reaching law and improved symbolic integrator, the tracking error of MEMS galvanometer can converge to zero in a finite time, ensuring that the system state accurately tracks the desired trajectory in a finite time.

[0152] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided:

[0153] To verify the effectiveness of the adaptive recursive terminal sliding mode control method proposed in this invention, sinusoidal reference trajectories of different frequencies were set for testing in this embodiment, and the results were compared with those of the traditional PID control method.

[0154] 1. Experimental setup.

[0155] Controlled object: electrostatically driven MEMS galvanometer.

[0156] Reference trajectory: a sine wave with an amplitude of 1°, tested at frequencies of 200Hz, 400Hz and 600Hz to evaluate the algorithm’s performance at different scan speeds.

[0157] Comparison of algorithms: Traditional PID control and the ARTSM control method proposed in this invention.

[0158] Performance metrics: These mainly examine tracking accuracy, convergence, overshoot, and the smoothness of the control output (chicking suppression effect).

[0159] Disturbance conditions: Introduce additional external disturbances to test the robustness of the system.

[0160] 2. Results and Analysis.

[0161] (1) 200Hz low-frequency scanning test.

[0162] Figure 3 The comparison chart shows the results of PID control and the method of this invention in a 200Hz low-frequency scan test. At 200Hz, PID control can basically track the reference trajectory, but there is significant phase lag and amplitude attenuation. The tracking error RMSE is relatively large, and the control output signal exhibits high-frequency fluctuations, indicating its limited disturbance rejection capability. At the same frequency, the method of this invention shows 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, proving its effectiveness and robustness under medium-speed scans.

[0163] (2) 400Hz intermediate frequency scanning test.

[0164] Figure 4 The graph shows a comparison between PID control and the method of this invention in a 400Hz intermediate frequency scanning test. As the frequency increases to 400Hz, the performance of PID control deteriorates further. Phase lag and amplitude attenuation worsen, overshoot becomes more pronounced, and settling time increases, making it difficult to meet the application requirements of high-precision scanning. The method of this invention maintains good tracking performance at 400Hz. Although the error increases slightly compared to 200Hz, it is still much smaller than that of PID control, effectively suppressing chattering at high frequencies. The system exhibits good stability and fast convergence.

[0165] (3) 600Hz high-frequency scanning test.

[0166] Figure 5 The graph shows a comparison between PID control and the method of this invention in a 600Hz high-frequency scanning test. At the 600Hz limiting frequency, PID control exhibits severe distortion, with a large 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 are ill-suited for high-speed scanning scenarios. The method of this invention, however, still achieves stable and accurate tracking under the stringent conditions of 600Hz. Although the error further increases, the system state converges to near the reference trajectory within a finite time without instability. This fully demonstrates the superior robustness and control accuracy of the method of this invention under nonlinear, strong disturbance, and high-speed conditions.

[0167] 3. Experimental conclusions.

[0168] comprehensive Figures 3 to 5The comparison results show that, at different scanning frequencies, the ARTSM control method proposed in this invention significantly outperforms the traditional PID control method in terms of tracking accuracy, response speed, anti-disturbance capability, and chatter suppression. Its performance advantages are particularly prominent at medium and high frequency scanning, 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.

[0169] Furthermore, in the method of this invention, the adaptive reaching law can be replaced by a power-law reaching law, which has a faster reaching speed than the linear term and can further reduce the width of the quasi-sliding mode band, thereby weakening chattering. However, the introduction of a nonlinear power-law term adds new design parameters, such as the power exponent. These parameters are sensitive to system performance, such as convergence time and chattering amplitude, but lack systematic adjustment rules.

[0170] The electrostatic drive method used in MEMS galvanometers can also be replaced by electromagnetic, piezoelectric, and other drive methods, each with its own advantages and disadvantages in response speed and power consumption. For example, piezoelectric drive mechanisms typically result in smaller displacements, making it difficult to achieve large-angle scanning, while electromagnetic drive mechanisms have more complex manufacturing processes, increase power consumption, and generate heat during the high current flow.

[0171] In the MEMS galvanometer scanning control of lidar, the core challenge lies in the inherent nonlinear relationship between the electrostatic drive voltage and the optical deflection angle. Traditional control algorithms, such as PID, heavily rely on accurate linearized models, which are difficult to effectively overcome in practical applications due to uncertainties in model parameters, manufacturing errors, and complex external disturbances such as mechanical shocks and temperature drift. This results in tracking errors, slow response, and decreased stability during high-frequency, large-area scanning.

[0172] To address the aforementioned problems, this invention proposes an adaptive recursive terminal sliding mode control strategy specifically designed for MEMS galvanometers, which dynamically adjusts with the system state. Its main advantages are reflected in the following three aspects:

[0173] This invention proposes for the first time a state-dependent adaptive recursive terminal sliding mode control strategy and applies it to the precise control of MEMS galvanometers. The control method of this invention enables the system state to converge to the sliding mode surface within a certain time, solving the problem that traditional control methods cannot guarantee convergence during high-frequency and large-range scanning.

[0174] Furthermore, this invention proposes an adaptive reaching law that dynamically adjusts with the system state to address situations where the upper bound of the disturbance is uncertain or time-varying. This reaching law dynamically adjusts its gain according to the system state, and its parameters are updated online through a set of decoupled adaptive reaching laws, asymptotically converging to the neighborhood of the true upper bound of the disturbance. This invention's method has a simple structure, low computational complexity, and the ability to dynamically suppress chattering, effectively compensating for matching disturbances with linear upper bounds. Theoretical analysis and experiments show that this invention significantly improves the robustness of the system under unknown and time-varying disturbances, ensuring high-precision trajectory tracking performance in complex environments.

[0175] Furthermore, this invention proposes a novel recursive terminal integral sliding mode method. It employs a hierarchical recursive structure to construct the sliding surface and improves the sign integrator in a type-one sliding mode function, resulting in a smoother control signal. Through the collaborative design of terminal sliding mode and recursive integral sliding mode, the system state is either already in or rapidly entering sliding mode motion from the initial moment, completely eliminating the approaching phase of traditional sliding mode control. This ensures robustness throughout the system and rigorously achieves convergence of the tracking error to zero within a finite time, fundamentally solving the problem of convergence not being guaranteed in high-dynamic scanning scenarios using traditional methods. Moreover, it is easily implemented on platforms such as FPGA, DSP, and MCU, making it suitable for large-scale deployment in industrial applications such as LiDAR.

[0176] Example 2

[0177] This embodiment 2 describes a lidar system, which is based on the same inventive concept as the adaptive law-based recursive terminal sliding mode control MEMS galvanometer scanning method in embodiment 1.

[0178] This invention employs a closed-loop controlled MEMS galvanometer scanning system for lidar applications. This system constructs a complete closed-loop chain from laser emission, optical path design, galvanometer scanning, drive control to position detection and signal feedback, achieving high-precision dynamic scanning. Specifically, the lidar system includes a laser, a MEMS galvanometer, a controller, a position sensor, a drive circuit, and a receiver.

[0179] A reflector is placed between the laser light source and the MEMS galvanometer to adjust the laser beam path.

[0180] The 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 adaptive law recursive terminal sliding mode control described in Example 1.

[0181] The position sensor inputs the detected mirror torsional position signal and the desired reference position signal to the controller in real time. After calculation according to the MEMS mirror scanning method based on the adaptive law recursive terminal sliding mode control, the controller outputs a voltage control signal. The driving voltage is amplified by the driving circuit and input to the bottom and side driving electrodes to drive the MEMS mirror to track the desired trajectory for scanning.

[0182] The lidar system in this embodiment is specifically as follows: Figure 6 As shown, the laser beam emitted by the laser emitter is calibrated by a reflector and then incident on the surface of the MEMS galvanometer. The laser reflected from the mirror is received in real time by a position-sensitive detector (PSD), i.e., a position sensor. A drive electrode is integrated at the bottom of the galvanometer. The controller, such as a microcontroller, outputs an analog drive voltage through its digital-to-analog converter (DAC). This voltage is amplified by an amplifier circuit and smoothed by a low-pass filter before being applied to the drive electrode, thereby controlling the mirror to twist to complete the scanning. Under the action of the drive voltage, the MEMS galvanometer twists, and the position of its reflected beam on the PSD photosensitive surface changes accordingly. The feedback voltage signal output by the PSD is conditioned by a sampling circuit and read by the controller's ADC. The controller calculates the actual scanning angle of the MEMS galvanometer based on this signal. Simultaneously, it receives the desired trajectory command from the host computer, compares the two to generate a tracking error, and processes this error in real time using the core control algorithm, ARTSM, to update the DAC output voltage, thereby driving the galvanometer to accurately track the target trajectory.

[0183] Example 3

[0184] This embodiment 3 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a MEMS galvanometer scanning method based on an adaptive law-based recursive terminal sliding mode control.

[0185] 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.

[0186] 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 adaptive law and recursive terminal sliding mode control, characterized in that, Includes the following steps: Step 1. Establish a dynamic model of the MEMS galvanometer that includes lumped uncertainty perturbations; Step 2. Based on the dynamic model of the MEMS galvanometer containing lumped uncertain disturbances, construct an adaptive recursive terminal sliding mode controller. The construction process includes fast non-singular terminal sliding mode design, recursive integral sliding mode design, and design of equivalent control law and adaptive reaching law. Step 3. Implement tracking control of the MEMS galvanometer using an adaptive recursive terminal sliding mode controller; Step 1 specifically involves: The dynamic model of the MEMS galvanometer is expressed as follows: ； in, and For rotational inertia, and These represent the rotation of the galvanometer. Axial direction and Angle of torsion in the axial direction, and The damping coefficient is... and Let be the spring constant of the torsion bar. and This refers to electrostatic torsional torque; 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; The dynamic model of a MEMS galvanometer containing lumped uncertainty perturbations is as follows: ； in, Let be the state vector of the system. For the system's control input, For system output, , , , For the system matrix; For bounded lumped uncertainty disturbances, satisfying , The upper bound of the lumped uncertainty disturbance is: ； in, For positive integers, ; System Matrix , , , They are represented as follows: ， ， ， ； In step 2, the design process for fast nonsingular terminal sliding mode and recursive integral sliding mode is as follows: Based on the dynamic model of the MEMS galvanometer containing lumped uncertainty perturbations established in step 1, the tracking error is defined. for: ； in, For reference signal; Define a fast nonsingular terminal sliding mode function for: ； in, For positive integers, and For sliding surface parameters, , ; when At that time, tracking error In a limited time Converging inward to zero; For fast nonsingular terminal sliding mode functions Taking the derivative, we get: ； Consider a second-order system, and the recursive integral sliding mode function Defined as: ； in, For sliding surface parameters, ; It is a function; Introducing an improved type I symbolic integrator: ； in, For parameters, ; By setting initial conditions ,in and They represent and Given the initial values, we get: ； in, for The initial value; In a limited time Converging to zero in finite time Represented as: ； In step 2, the design process of the equivalent control law is as follows: Without considering system disturbances In this case, let ,get: ； ； ； The equivalent control law is then obtained as follows: ； In step 2, the design process of the adaptive reaching law is as follows: Introducing a state-dependent adaptive reaching law This enables online compensation for system uncertainties and disturbances. ； in, For parameters, ; , , Indicates the estimated gain; The update law for estimating the gain is: ； ； ； in, , , It is a positive number; Estimating parameters, i.e., estimating gain There exists an upper bound. , making Always true; In step 2, the overall control law of the system is obtained by combining the equivalent control law and the adaptive approach law, that is, the construction of the adaptive recursive terminal sliding mode controller is specifically as follows: ； in, This is the overall control law of the system.

2. The MEMS galvanometer scanning method based on adaptive law and recursive terminal sliding mode control as described in claim 1, characterized in that, In step 2, after completing the design of the adaptive recursive terminal sliding mode controller, a stability analysis is also performed on the MEMS galvanometer system controlled by the adaptive recursive terminal sliding mode controller.

3. The MEMS galvanometer scanning method based on adaptive law and recursive terminal sliding mode control as described in claim 2, characterized in that, In step 2, the process of performing stability analysis on the MEMS galvanometer system controlled by the adaptive recursive terminal sliding mode controller is as follows: For the equation The system described considers candidate Lyapunov functions. for: ; Lyapunov function along the system trajectory Taking the time derivative, we get: ； in, ; Tracking error In a limited time It converges to zero, and satisfy: ； in, Representing Lyapunov functions The initial value; when Upon its establishment, there are , will with They converge to zero at the same rate of convergence. when , At that time, by get: ； Limited time express From initial value The time required for convergence to zero is: ； when , At that time, we obtained: ； For any initial state , In a limited time It converges to zero, and satisfy: ； Adaptive estimation error for: ; Choosing Lyapunov functions for: ； in, It is a positive number; For Lyapunov functions Taking the first derivative, we get: ； in, ,get ; For any parameter If positive numbers exist ,satisfy , and To ensure the system meets stability requirements; ； in: ， ， ， ； ； Lyapunov function From any initial state Depart, within a limited time It converges to zero, and satisfy: ； in, Lyapunov function The initial value; The sliding variable is the recursive integral sliding mode function. With estimation error All converge to zero within a finite amount of time; according to The conditions can be guaranteed Established, among which express The initial value; In a MEMS galvanometer system controlled by an adaptive recursive terminal sliding mode controller, the tracking signal Starting from any initial conditions, it can converge to zero in a finite time, with a total settling time of [missing information]. for: .

4. A lidar system, comprising a laser, a MEMS galvanometer, a controller, a position sensor, a driving circuit, and a receiver; characterized in that, A reflector for adjusting the laser beam path is placed between the laser light source and the MEMS galvanometer. The 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 the adaptive law recursive terminal sliding mode control according to any one of claims 1 to 3. The position sensor inputs the detected mirror torsional position signal and the desired reference position signal to the controller in real time. After calculation according to the MEMS mirror scanning method based on the adaptive law recursive terminal sliding mode control, the controller outputs a voltage control signal. The driving voltage is amplified by the driving circuit and input to the bottom and side driving electrodes to drive the MEMS mirror to track the desired trajectory for scanning.

5. A computer-readable storage medium having a program stored thereon; characterized in that, When executed by a processor, the program is used to implement the steps of the adaptive law-based recursive terminal sliding mode control MEMS galvanometer scanning method as described in any one of claims 1 to 3.

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