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

Abstract

The application belongs to the technical field of laser radar scanning control, and discloses a MEMS galvanometer scanning method and system based on integral terminal sliding mode control. The method constructs an integral terminal sliding surface and introduces a minimum operator reaching law, so that the system state can converge to the sliding surface within a limited step, and the tracking error reaches a preset bandwidth within a limited step. Even under large-angle and high-speed scanning conditions, high-precision trajectory tracking can still be achieved, and there is no obvious distortion on the edge. In addition, the method estimates and compensates external disturbances in real time through an interference observer to reduce the gain required by the switching term in the sliding mode control. The interference observer estimates and dynamically compensates the sudden disturbance and the periodic disturbance online, thereby maintaining small steady-state error and phase stability. Under complex scenes such as compound disturbance, the control method can significantly improve the scanning accuracy and stability of the MEMS galvanometer.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser radar scanning control, and particularly relates to a MEMS galvanometer scanning method and system based on integral terminal sliding mode control. BACKGROUND

[0002] As a core scanning actuator of a laser radar system, a MEMS galvanometer realizes high-speed scanning in single-axis or double-axis by electrostatic driving. The galvanometer has simple structure, low power consumption and fast response, but there is a nonlinear relationship between the driving voltage and the deflection angle, and the system model has deviations due to the influence of factors such as mechanical damping, torsional spring stiffness uncertainty and manufacturing errors. The laser radar system has high requirements for the scanning performance of the MEMS galvanometer, and the existing control methods have many shortcomings.

[0003] Under conventional open-loop control, the system has large overshoot and long regulation time, and it is difficult to realize high-precision scanning. Under open-loop control, the electrostatically driven MEMS galvanometer has a significant nonlinear relationship between the driving voltage and the deflection angle, especially at large deflection angles, which makes it difficult for the MEMS galvanometer to accurately track the desired trajectory required by the laser radar system, thereby causing the reflected laser beam to deviate and affecting the imaging quality. Moreover, in actual operation, the laser radar will also be affected by sudden disturbances such as external impact, spring stiffness changes caused by temperature drift, and periodic disturbances such as structural resonance and driving power ripple. The traditional open-loop driving strategy cannot effectively compensate for such nonlinearities and disturbances.

[0004] As a traditional closed-loop method, PID control is easy to implement, but the driving voltage of the MEMS galvanometer has a significant nonlinear relationship with the deflection angle, and the robustness of PID control for nonlinear systems is poor. Moreover, the dynamic response of traditional PID control is lagging and the precision is limited when scanning at high speed and over a large range. Model parameter perturbations and external disturbances can easily cause significant trajectory tracking errors, even jeopardizing system stability. Since PID control has problems such as large overshoot and long regulation time in large-amplitude fast scanning, and the robustness of PID control to external disturbances is poor, PID control cannot meet the performance requirements of laser radar in high-frequency and large-range scanning applications.

[0005] Sliding mode control (SMC) has strong robustness, but it has chattering when discretized on digital platforms such as FPGA and DSP. Terminal sliding mode control (TSMC) can speed up convergence, but it has singularity problems and the risk of amplifying chattering. In digital control platforms, sliding mode control and terminal sliding mode control have reduced convergence performance and severe chattering, making it difficult to achieve accurate trajectory tracking for large-range high-speed scanning in a limited number of steps. Moreover, sliding mode control and terminal sliding mode control have insufficient suppression ability for sudden and periodic combined disturbances, resulting in a significant decrease in scanning accuracy.

[0006] Therefore, it is urgent to design a MEMS galvanometer closed-loop scanning control method suitable for discrete digital control platform, which has limited step convergence, chattering suppression and anti-disturbance ability. SUMMARY

[0007] The purpose of the present application is to propose a MEMS galvanometer scanning method based on integral terminal sliding mode control, which combines integral terminal sliding surface, minimum operator reaching law and disturbance observer dynamic compensation, can effectively suppress small error interval chattering while achieving limited step convergence and high-speed scanning trajectory tracking, thereby significantly improving the robust performance of the laser radar system under strong nonlinearity and composite disturbance.

[0008] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0009] A MEMS galvanometer scanning method based on integral terminal sliding mode control, comprising the following steps:

[0010] Step 1. Construct the dynamic model of the MEMS galvanometer and discretize it to obtain a discretized model;

[0011] Step 2. Based on the discretized model obtained in step 1, design a disturbance observer to estimate the unknown disturbance in the system in real time, and combine the disturbance estimate to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation;

[0012] Step 3. Use the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation to realize trajectory tracking control of the MEMS galvanometer.

[0013] In addition, on the basis of the above-mentioned MEMS galvanometer scanning method based on integral terminal sliding mode control, the present application also proposes a laser radar system, which comprises a laser, a MEMS galvanometer, a position sensor, an analog-to-digital converter, a FPGA-based controller and a driving circuit;

[0014] The laser serves as a laser light source, and the laser emitted thereby is incident to the mirror surface of the MEMS galvanometer;

[0015] The position sensor is used to receive the laser reflected by the mirror surface of the MEMS galvanometer and convert it into an electrical signal;

[0016] The analog-to-digital converter is used to convert the electrical signal output by the position sensor into a digital signal and send it to the FPGA-based controller;

[0017] The FPGA-based controller stores a readable storage medium, and when the readable storage medium is executed, it is used to realize the steps of the above-mentioned MEMS galvanometer scanning method based on integral terminal sliding mode control;

[0018] The voltage control signal output by the FPGA-based controller according to the integral terminal sliding mode control-based MEMS mirror scanning method is amplified by a voltage amplifier of a driving circuit and then input into the bottom and side driving electrodes of the MEMS mirror, so as to drive the MEMS mirror to track a desired trajectory and perform scanning.

[0019] In addition, based on the integral terminal sliding mode control-based MEMS mirror scanning method, the application further provides a computer readable storage medium, which stores a program; when the program is executed by a processor, the steps of the integral terminal sliding mode control-based MEMS mirror scanning method are implemented.

[0020] The application has the following advantages:

[0021] As described above, the application provides an integral terminal sliding mode control-based MEMS mirror scanning method, which first uses a discrete minimum operator integral terminal sliding mode control in the control of the MEMS mirror, and realizes the convergence of the system state to a sliding mode surface within a limited step through the control method, thereby effectively solving the problem of insufficient convergence of the traditional control method in high-frequency and large-range scanning. The application further provides a minimum operator reaching law, which can automatically reduce the reaching speed in a small error area, thereby realizing the effective balance between chattering suppression and convergence speed, avoiding the chattering phenomenon caused by excessively high reaching speed, and ensuring the rapid convergence of the system. In addition, the application further designs an interference observer, which can estimate and compensate external disturbances of the system in real time, thereby greatly enhancing the robustness of the system in a complex disturbance environment, and maintaining high-precision trajectory tracking performance. In addition, the discrete control method provided by the application has a clear structure and high calculation efficiency, and is easy to implement on an embedded platform such as FPGA and DSP, and supports large-scale deployment of industrial applications such as laser radars. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The flowchart of the integral terminal sliding mode control-based MEMS mirror scanning method in the embodiment of the application.

[0023] Figure 2 The closed-loop control block diagram of the integral terminal sliding mode control-based MEMS mirror scanning method in the embodiment of the application.

[0024] Figure 3 The schematic diagram of the laser radar system in the embodiment of the application.

[0025] Figure 4 The scanning tracking effect diagram obtained by using the traditional PID control method at f = 200 Hz and an amplitude of 1.5°.

[0026] Figure 5 A scanning tracking effect diagram obtained by using the control method proposed in the application at f = 200 Hz and an amplitude of 1.5°.

[0027] Figure 6 A scanning tracking effect diagram obtained by using the traditional PID control method at f = 400 Hz and an amplitude of 1.5°.

[0028] Figure 7 A scanning tracking effect diagram obtained by using the control method proposed in the application at f = 400 Hz and an amplitude of 1.5°.

[0029] Figure 8 A scanning tracking effect diagram obtained by using the traditional PID control method at f = 600 Hz and an amplitude of 1.5°.

[0030] Figure 9 A scanning tracking effect diagram obtained by using the control method proposed in the application at f = 600 Hz and an amplitude of 1.5°. DETAILED DESCRIPTION

[0031] The application will be further described in detail below in combination with the accompanying drawings and specific embodiments:

[0032] Embodiment 1

[0033] The application is directed to laser radar application, and proposes a MEMS mirror scanning method based on integral terminal sliding mode control for high-precision closed-loop scanning control of electrostatically driven MEMS mirrors. The method is a discrete minimum operator integral terminal sliding mode control method based on disturbance observer compensation. The method constructs a discrete integral terminal sliding surface, designs a minimum operator reaching law, and introduces a disturbance observer to estimate and compensate system disturbances in real time, so as to improve the finite step convergence, chattering suppression ability and anti-disturbance performance of the system, and significantly improve the robustness and finite time convergence performance of the system under complex conditions.

[0034] As shown in Figure 1 The MEMS mirror scanning method based on integral terminal sliding mode control specifically includes the following steps:

[0035] Step 1. Build a dynamic model of the MEMS mirror and discretize it to obtain a discretized model.

[0036] The embodiment first establishes a nonlinear dynamic model of the MEMS mirror in step 1 according to the mechanical structure and electrostatic driving principle of the MEMS mirror, that is, a dynamic model of the MEMS mirror is constructed. Then, in order to adapt to the implementation of the digital controller, the zero-order holder method is used to accurately discretize the dynamic model of the MEMS mirror, that is, the continuous model, to obtain a discrete state space equation suitable for algorithm design, that is, a discretized model.

[0037] The electrostatically driven MEMS mirror is composed of a mirror plate, two pairs of torsion rods, a support frame, a frame, a bottom electrode and a side electrode. By applying a driving voltage to the bottom electrode and the side electrode, the MEMS mirror can be twisted around the X and Y axes. The parameters of the electrostatically driven MEMS mirror in the embodiment are shown in Table 1.

[0038] Table 1 Parameters of the electrostatically driven MEMS mirror

[0039]

[0040] The step 1 will be specifically introduced as follows.

[0041] The dynamic model of the MEMS mirror is expressed as:

[0042] .

[0043] wherein, and represent the torsion angles of the mirror along the axis direction and the axis direction, and are the moments of inertia, and are the damping coefficients, and are the spring coefficients of the torsion rods, and are the electrostatic torsion moments.

[0044] and are respectively expressed as:

[0045] .

[0046] .

[0047] wherein, represents the silicon density, represents the mirror thickness, represents the width and length of the mirror, represents the frame external width, represents the frame external length, represents the inner width of the frame, represents the inner length of the frame.

[0048] represents the inner width of the frame, represents the inner length of the frame.

[0049] .

[0050] .

[0051] represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame.

[0052] .

[0053] .

[0054] represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame.

[0055] represents the inner width of the frame, represents the inner length of the frame.

[0056] represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame,

[0057] represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame.

[0058] represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame. represents the inner width of the frame, represents the inner length of the frame.

[0059] .

[0060] wherein, , , , , are system model parameters, , respectively represent the driving voltage of the galvanometer along the , angle twist.

[0061] The design of the present application is mainly described for the control of the angle a in the MEMS galvanometer, and the control of the angle b can be realized by a similar but independent control architecture. For the convenience of the controller design, considering the external disturbance, the dynamic model of the MEMS galvanometer is rewritten from the continuous-time system model to the state space form:

[0062] .

[0063] wherein, is the state vector of the system, is the control input of the system, is the output of the system, is the bounded disturbance, satisfying , represents the upper bound of the unknown external disturbance. , , , is the continuous system matrix, , , , respectively represent:

[0064] , , , .

[0065] In order to realize the algorithm on a digital controller such as FPGA, the above continuous-time model needs to be converted into a discrete-time model, that is, the dynamic model of the MEMS galvanometer is discretized. In the present embodiment, the zero-order holder method is used to accurately discretize the continuous system at a fixed sampling period . The discretization process obtains the discretization model by integrating the continuous state equation of the dynamic model of the MEMS galvanometer within the sampling period, and the standard form is as follows:

[0066] .

[0067] wherein, represents the state vector of the system at time, represents the state vector of the system the state vector at time t. is the system control input at time t. is the system output at time t. is the external disturbance at time t, and satisfies . , , , denotes the system matrix of the discretized model, , , , denotes the continuous system matrix , , , the discretized form under the sampling period , , , , denotes:

[0068] , , , .

[0069] The control objective of the method is to design a controller to enable the system output to accurately track the reference signal in a limited time in the presence of disturbances. At the same time, with the help of the designed minimum operator approach law, the system disturbance is effectively suppressed and the chattering phenomenon is significantly reduced without overestimating the controller gain.

[0070] Step 2. Based on the discretized model obtained in step 1, design a disturbance observer to estimate the unknown disturbance in the system in real time, and combine the disturbance estimation value to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

[0071] In step 2, the disturbance observer and the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation are designed, and the theoretical proof is completed. In the presence of system disturbance, based on the discretized model obtained in step 1, a disturbance observer is designed to estimate the unknown disturbance in the system in real time. Then, combined with the disturbance estimation value of the disturbance observer, a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is constructed. In step 2, the estimation effectiveness of the disturbance observer and the stability of the closed-loop control system are strictly proved to ensure that the system can converge in a limited time.

[0072] 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:

[0073] 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:

[0074] The discrete state equation of the disturbance observer is:

[0075] .

[0076] .

[0077] 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.

[0078] 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.

[0079] 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:

[0080] definition Tracking error at time for:

[0081] .

[0082] in, for The desired output signal at time.

[0083] definition The integral variable at time t is The discrete update rule for the integral variable is as follows:

[0084] .

[0085] in, express The integral variable at time step. Within each sampling period, the discrete update of the integral variable is achieved by adjusting the error... Accumulation is achieved.

[0086] The terminal sliding surface of discrete integral is designed based on the minimum operator reaching law:

[0087] .

[0088] 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.

[0089] Calculate the predicted output error, i.e. Tracking error at time for:

[0090] .

[0091] in, for The system output at any given time, for The desired output signal at time.

[0092] 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:

[0093] .

[0094] To obtain an explicit control law, a standard one-step explicit method is used to process the nonlinear terminal terms. Estimation, definition is:

[0095] .

[0096] Constructing nominal partial prediction sliding surface is:

[0097] .

[0098] For the constructed nominal partial prediction sliding surface Adding the true effects of inputs and disturbances, we get:

[0099] .

[0100] Replace the actual disturbance in the system with the disturbance estimation value of the disturbance observer, and combine the residual part that the disturbance observer does not fully compensate into the original disturbance term for unified processing, to get:

[0101] .

[0102] .

[0103] wherein, is an additional term caused by disturbances and other factors, and has an upper bound, It can be effectively compressed by improving the estimation accuracy of the disturbance observer or reducing the step size.

[0104] Design the minimum operator reaching law as:

[0105] .

[0106] wherein, is a contraction factor, . is a bandwidth parameter, .

[0107] When , Limited steps into the sliding mode band . If gradually approaches 0, then is reached within a finite number of steps, to get:

[0108] .

[0109] Construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation as:

[0110] .

[0111] After completing the design of the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation, the stability of the MEMS mirror system controlled by the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is analyzed in this embodiment, and the stability analysis includes the stability analysis of the disturbance observer and the stability analysis of the closed-loop control system. By strictly proving the stability of the disturbance observer and the closed-loop control system, it is theoretically ensured that the system can converge in a finite time and has the expected robust performance.

[0112] The process of the stability analysis of the disturbance observer is specifically:

[0113] To prove the stability of the disturbance observer designed in the application, Lyapunov function is introduced to analyze the disturbance observer.

[0114] The state estimation error of the disturbance observer at time k is defined as .

[0115] .

[0116] The disturbance estimation error of the disturbance observer at time k is defined as .

[0117] .

[0118] The state estimation error of the disturbance observer at time k+1 is recursively defined as .

[0119] .

[0120] The disturbance estimation error of the disturbance observer at time k+1 is recursively defined as .

[0121] .

[0122] wherein, is the external disturbance at time , and satisfies . represents the change of the disturbance, .

[0123] Lyapunov function is introduced to analyze the stability of the disturbance observer:

[0124] .

[0125] wherein, represents the value of Lyapunov function at time . and R represent positive definite matrices, , .

[0126] By calculating the increment of the Lyapunov function , it is proved that the MEMS mirror system controlled by the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is stable under disturbance observer compensation:

[0127] .

[0128] wherein, represents the value of the Lyapunov function at the time . .

[0129] Two types of errors, i.e., disturbance estimation error and disturbance estimation error, are combined, and the following variables are defined:

[0130] , , , .

[0131] wherein, 0 represents a zero matrix of the corresponding dimension. represents a unit matrix of a proper order, and the dimension thereof is the same as that of the disturbance estimation error . Then:

[0132] .

[0133] The Lyapunov function is defined as:

[0134] .

[0135] wherein, represents the value of the Lyapunov function at the time .

[0136] The increment of the Lyapunov function is calculated as:

[0137] .

[0138] wherein, represents the value of the Lyapunov function at the time .

[0139] There exists such that . Let , wherein denotes the minimum eigenvalue of the matrix.

[0140] Under the disturbance increment, we have

[0141] .

[0142] It can be concluded that the disturbance estimation error will converge to a compact set containing the origin, which is uniformly ultimately bounded.

[0143] The process of stability analysis of closed-loop control system is as follows:

[0144] The Lyapunov function is defined as

[0145] .

[0146] where denotes the value of the Lyapunov function at time .

[0147] The increment of the Lyapunov function is .

[0148] .

[0149] where denotes the value of the Lyapunov function at time .

[0150] To analyze the sign characteristics of the Lyapunov function increment, we need to compare the numerical relationship between and . According to the characteristics of the minimum operator approach law, when is large, the minimum operator term has a weak influence on the system dynamics. When is small, the approach term will dominate the system behavior and drive to converge to zero quickly. Based on the above analysis, the upper bound expression of the Lyapunov function increment can be derived as follows:

[0151] The upper bound expression of the increment of the Lyapunov function is .

[0152] .

[0153] where is ​the upper bound of the Lyapunov function reflects the error range caused by uncompensated disturbance and system uncertainty. In each iteration step, the value of the Lyapunov function will continue to decrease until enters a small bandwidth , and the system state will converge within a finite number of steps.

[0154] To estimate the upper bound of the convergence step number, the step number required when the Lyapunov function is less than needs to be calculated. First, based on the inequality of the increment of the Lyapunov function , the following is obtained:

[0155] .

[0156] By accumulating the expression of the increment of the Lyapunov function , the following is obtained:

[0157] .

[0158] If the initial value of the Lyapunov function is , then after iteration steps, the function value satisfies:

[0159] .

[0160] When , the system enters the convergence band, and the convergence step number of the system satisfies the following upper bound estimate, and the upper bound expression of the convergence step number is:

[0161] .

[0162] In particular, when the system does not have disturbance, i.e. , the convergence step number is the smallest, and at this time the convergence step number is:

[0163] .

[0164] The above results show that the MEMS mirror 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 by adjusting the parameters and the initial value of the Lyapunov function , the convergence speed of the system can be controlled. The tracking error of the system can reach the integral terminal sliding surface within a finite time, and maintain its motion state on the integral terminal sliding surface, and finally converge to zero along the integral terminal sliding surface within a finite time.

[0165] Step 3. Trajectory tracking control of MEMS mirror is realized by using discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation.

[0166] As shown in Figure 2 , in step 3, first, the discrete reference signal is 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 on one hand, for real-time estimation of unknown disturbances in the system and generation of a feedforward compensation. On the other hand, the tracking error signal is also used to calculate the sliding mode surface combined with the integral term and the terminal attractor. The control core of the method of the present application is to use the minimum operator reaching law with the characteristics of "fast far and slow near", to synthesize the tracking error, the sliding mode surface state and the feedforward compensation, to synthesize the final digital control quantity, so as to ensure the finite step convergence of the system while effectively suppressing chattering. The final digital control quantity is used to drive the MEMS mirror to perform scanning motion through the driving circuit and voltage amplification.

[0167] Step 3 is described in detail below.

[0168] The discrete reference signal, i.e. the expected output signal , is compared with the actual angle position signal detected by the feedback loop, i.e. the system output , to generate a tracking error signal .

[0169] The tracking error signal is input to the disturbance observer for real-time estimation of unknown disturbances in the system, to obtain disturbance estimation , and based on the disturbance estimation , a feedforward compensation, i.e. an additional term is generated.

[0170] Based on the tracking error signal , a discrete integral terminal sliding mode surface is calculated .

[0171] The minimum operator reaching law is used to synthesize the tracking error signal, the sliding mode surface state and the feedforward compensation, to obtain the final digital control quantity, i.e. the system control input , so that the sliding mode surface variable converges and chattering is suppressed, while ensuring the finite step convergence of the system.

[0172] The final digital control quantity is used to drive the MEMS mirror to perform scanning motion through the driving circuit and voltage amplification.

[0173] The actual deflection angle of the galvanometer is detected in real time by the position sensor and fed back to the input end, forming a closed-loop control.

[0174] In addition, the discrete integral terminal sliding mode control in the method of the application can be replaced by a robust output regulation control, which has the advantage of strong robustness, but its algorithm is more complex and not easy to implement. The electrostatic driving mode adopted by the MEMS galvanometer can be replaced by electromagnetic, piezoelectric and other driving modes. Different driving modes have their own advantages and disadvantages in response speed and power consumption. For example, under the piezoelectric driving mechanism, the displacement is usually small, and it is difficult to realize large-angle scanning. Under the electromagnetic driving mechanism, the process design is more complex, and the power consumption is increased. High current during driving can generate heat.

[0175] The simulation verification and performance analysis are also included in the embodiment.

[0176] The discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation designed based on step 2 is used to build a simulation model of the MEMS galvanometer system in the MATLAB environment, and the effectiveness of the control method is verified through simulation experiments. In the simulation, the controller calculates the control quantity in real time to drive the galvanometer to twist, tests its tracking performance under different frequency and amplitude reference trajectories, and evaluates the actual effect of the system in suppressing chattering, improving tracking accuracy while ensuring robustness.

[0177] To verify the effectiveness of the discrete minimum operator integral terminal sliding mode control method based on disturbance observer compensation DO+DM-ITSM proposed in the application, different frequency sinusoidal reference trajectories are set for testing, and the method is compared with the traditional PID control method.

[0178] 1. Experimental setup.

[0179] Experimental object: electrostatically driven MEMS galvanometer.

[0180] Reference trajectory: a sinusoidal signal with an amplitude of 1.5°, and the test frequencies are 200 Hz, 400 Hz and 600 Hz, to evaluate the performance of the control method at different scanning speeds.

[0181] Comparison method: traditional PID control method and DO+DM-ITSM control method proposed in the application.

[0182] Performance index: mainly investigates the tracking accuracy, convergence, overshoot and smoothness of the control output, i.e. the chattering suppression effect.

[0183] Disturbance condition: additional external disturbance is introduced in the simulation experiment to test the robustness of the system.

[0184] 2. Experimental results and analysis.

[0185] (1) 200 Hz low frequency scan test.

[0186] Figure 4 The scan tracking effect diagram of the traditional PID control method under 200 Hz, 1.5° amplitude.

[0187] The horizontal coordinate is time, and the vertical coordinate is angle. The solid line is the reference trajectory, and the dashed line is the actual tracking trajectory obtained by using the PID control method. It can be seen that the PID control has obvious phase lag and tracking error.

[0188] According to Figure 4 It can be seen that under 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 anti-disturbance ability is limited.

[0189] Figure 5 The scan tracking effect diagram of the method proposed in the application under 200 Hz, 1.5° amplitude.

[0190] The solid line is the reference trajectory, and the dashed line is the actual tracking trajectory obtained by using the method of the application. The method of the application has high tracking accuracy and almost coincides with the reference trajectory, and the chattering suppression effect is significant.

[0191] According to Figure 5 It can be seen that under the same frequency, the method of the application shows excellent tracking performance, and the actual trajectory almost coincides with 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 the system disturbance, proving its effectiveness and robustness.

[0192] (2) 400 Hz medium frequency scan test.

[0193] Figure 6 The scan tracking effect diagram of the traditional PID control method under 400 Hz, 1.5° amplitude.

[0194] As the frequency increases, the PID control overshoot increases, the regulation time is prolonged, and the tracking performance is further deteriorated.

[0195] According to Figure 6 It can be seen that as the frequency increases to 400 Hz, the performance of the PID control is further deteriorated. The phase lag and amplitude attenuation are intensified, the overshoot phenomenon becomes obvious, the regulation time is lengthened, and it is difficult to meet the application requirements of high-precision scanning.

[0196] Figure 7 The scan tracking effect diagram of the method proposed in the application under 400 Hz, 1.5° amplitude.

[0197] The method of the application still maintains good tracking performance without obvious distortion or chattering.

[0198] According to Figure 7 It can be seen that the method of the application still maintains good tracking performance at 400 Hz. Although the error increases slightly compared with 200 Hz, it is still much smaller than that of PID control. The minimum operator approach law effectively suppresses chattering at high frequencies, and the system exhibits good stability and rapid convergence.

[0199] (3) 600 Hz high-frequency scanning test.

[0200] Figure 8 The scanning tracking effect diagram of the traditional PID control method at 600 Hz and 1.5° amplitude.

[0201] PID control appears serious distortion at very high frequency, which cannot meet the requirements of high-precision scanning.

[0202] According to Figure 8 It can be seen that at the limit frequency of 600 Hz, PID control appears serious distortion, the tracking trajectory deviates greatly from the reference trajectory, the system response is slow, and the tracking ability is almost lost. This shows that the traditional linear control method, i.e. PID control, is difficult to cope with high-speed scanning scenarios.

[0203] Figure 9 The scanning tracking effect diagram of the method of the application at 600 Hz and 1.5° amplitude.

[0204] The method of the application still maintains high tracking precision and stability, which verifies its superiority under high-speed scanning.

[0205] According to Figure 9 It can be seen that under the severe condition of 600 Hz, the method of the application can still achieve stable and accurate tracking. Although the error further increases, the system state still converges to the vicinity of the reference trajectory within a limited number of steps, and there is no instability phenomenon. This fully proves the excellent robustness and control precision of the method of the application under nonlinear, strong disturbance and high-speed working conditions.

[0206] 3. Experimental conclusion.

[0207] According to the experimental results Figures 4 to 9 It can be seen that under different scanning frequencies, the control method proposed in the application is significantly superior to the traditional PID control in tracking precision, response speed, disturbance rejection ability and chattering suppression. Especially under medium and high frequency scanning, its performance advantage is more prominent, which can effectively solve the control problems of MEMS galvanometer caused by external disturbance, and fully meets the harsh requirements of laser radar on high-speed and high-precision scanning control.

[0208] In the MEMS mirror scanning control of laser radar, there is a significant nonlinear relationship between the driving voltage and the deflection angle, and the traditional control method is severely dependent on the accurate system model, and it is difficult to overcome the influence of external disturbance, resulting in limited control accuracy. In view of the problem, the present application proposes a discrete nonlinear robust control strategy for laser radar application, which can significantly improve the scanning accuracy and anti-interference ability of MEMS mirror.

[0209] The method of the present application is a discrete nonlinear scanning control method, which estimates and compensates the unknown disturbance in the system in real time through the disturbance observer, and combines the discrete minimum operator integral terminal sliding mode control strategy, effectively suppresses the chattering of the control signal by using the minimum operator reaching law, so as to ensure that the MEMS mirror can still track the predetermined trajectory with high precision under the condition of high frequency scanning and external disturbance.

[0210] Firstly, the method of the present application first uses the discrete minimum operator integral terminal sliding mode control in the MEMS mirror control, and realizes the convergence of the system state to the sliding mode surface in a limited step through the control method of the present application, effectively solving the problem of insufficient convergence of the traditional control method in high frequency and large range scanning.

[0211] Secondly, the method of the present application designs a disturbance observer, which can estimate and compensate the external disturbance of the system in real time, greatly enhancing the robustness of the system in a complex disturbance environment, thereby maintaining high-precision trajectory tracking performance.

[0212] Further, the method of the present application proposes a minimum operator reaching law, which can automatically reduce the reaching speed in the small error zone, realize the effective balance of chattering suppression and convergence speed, avoid the chattering phenomenon caused by too high reaching speed, and ensure the rapid convergence of the system.

[0213] Finally, the discrete control algorithm proposed by the method of the present application has clear structure and high efficiency, and is easy to realize in FPGA, DSP and other embedded platforms, supporting large-scale deployment of industrial applications such as laser radar.

[0214] Compared with the prior art, the present application is based on the discrete minimum operator integral terminal sliding mode control, and combines the disturbance observer and the minimum operator reaching law in the discrete control domain, which has the following advantages:

[0215] The disturbance observer can estimate and compensate the external disturbance in real time, effectively reducing the gain required by the switching term in the sliding mode control. Combined with the minimum operator reaching law, the "fast far and slow near" reaching is realized, and the speed is automatically reduced in the small error interval, so as to significantly suppress the chattering without sacrificing the response speed. The control structure still has good comprehensive performance under the conditions of quantization, sampling and zero-order hold, and takes into account the control accuracy of the reaching stage and the steady state stage.

[0216] By constructing an integral terminal sliding mode surface and introducing a minimum operator reaching law, i.e., a minimum operator approaching law, the system state can converge to the sliding mode surface in a finite step, and the tracking error reaches a preset bandwidth in a finite step, so that high-precision trajectory tracking can be achieved even in a large-angle and high-speed scanning condition, and no obvious distortion occurs at the edge.

[0217] In addition, the discrete disturbance observer designed in the method can estimate and dynamically compensate the sudden disturbance and the periodic disturbance online, so that small steady-state error and phase stability can be maintained.

[0218] Embodiment 2

[0219] Embodiment 2 provides a laser radar system based on the same inventive concept as the MEMS mirror scanning method based on integral terminal sliding mode control in embodiment 1, and the laser radar system comprises a laser, a MEMS mirror, a position sensor, an analog-to-digital converter, an FPGA-based controller, and a driving circuit.

[0220] The laser serves as a laser light source, and the laser emitted by the laser is incident on the mirror surface of the MEMS mirror.

[0221] The position sensor is configured to receive the laser reflected by the mirror surface of the MEMS mirror and convert the laser into an electrical signal.

[0222] The analog-to-digital converter is configured to convert the electrical signal output by the position sensor into a digital signal and send the digital signal to the FPGA-based controller.

[0223] The FPGA-based controller stores a readable storage medium, and when the readable storage medium is executed, the FPGA-based controller is configured to implement the steps of the MEMS mirror scanning method based on integral terminal sliding mode control in embodiment 1.

[0224] The FPGA-based controller outputs a voltage control signal according to the MEMS mirror scanning method based on integral terminal sliding mode control, and the voltage control signal is amplified by a voltage amplifier of the driving circuit and then input into the bottom and side driving electrodes of the MEMS mirror, so as to drive the MEMS mirror to track a desired trajectory and perform scanning.

[0225] The method constructs a closed-loop MEMS mirror scanning system, and the closed-loop system of “laser emission-optical path-mirror scanning-position detection-control calculation-driving output” is conducive to realizing high-speed scanning of a laser radar.

[0226] As shown in FIG. 1, Figure 3 the MEMS mirror driving circuit in this embodiment specifically comprises a digital-to-analog converter DAC, a low-pass filter, and an amplification circuit, and the laser radar system in this embodiment further comprises an upper computer.

[0227] The laser emitted by the laser is incident on the MEMS mirror, the reflected laser passes through the receiving mirror, is received by the position sensor and converted into an electric signal, the electric signal is converted into a digital signal by an analog-to-digital converter ADC and then sent to the FPGA-based controller. The MEMS mirror is provided with a driving electrode, and the digital control quantity output by the controller is converted into a corresponding voltage driving signal by an amplification circuit and applied to the driving electrode for controlling the mirror to achieve a specific angle of twist and realize accurate scanning of the preset trajectory.

[0228] When the mirror is deflected under the action of the driving voltage, the position of the reflected laser beam on the position sensor will change accordingly, and by detecting the position signal and performing conversion, the scanning angle of the MEMS mirror can be obtained in real time. The position sensor signal is obtained in real time by the FPGA high-speed data acquisition card, compared with the expected reference trajectory signal to obtain an error signal, and the control signal is generated by the control method of the application for driving the MEMS mirror to complete the closed-loop trajectory tracking adjustment.

[0229] Embodiment 3

[0230] This embodiment 3 describes a computer readable storage medium, which stores a program, the program is executed by a processor, and is used to realize the steps of the MEMS mirror scanning method based on integral terminal sliding mode control in the above embodiment 1.

[0231] The computer readable storage medium can be an internal storage unit of any device or apparatus with data processing capability, such as a hard disk or memory, or an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc.

[0232] Of course, the above description is only for the preferred embodiments of the present application, and the present application is not limited to the above-mentioned embodiments. It should be noted that any skilled person in the art can make all equivalent substitutions and obvious modifications under the teaching of the present application, which are within the scope of the present application, and should be protected by the present application.

Claims

1. A MEMS galvanometer scanning method based on integral terminal sliding mode control, characterized in that, Comprising the following steps: Step 1. Constructing a dynamic model of the MEMS mirror and discretizing it to obtain a discretized model; Step 2. Based on the discretized model obtained in step 1, designing a disturbance observer for real-time estimation of unknown disturbances in the system, and combining the disturbance estimation value to construct a discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation; Step 3. Using the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation to realize trajectory tracking control of the MEMS mirror; Said step 1 is specifically: The dynamic model of the MEMS mirror is represented as: ； wherein, and denote the torsion angle of the galvanometer along the axis direction and the axis direction, respectively, and are the moments of inertia, and are the damping coefficients, and are the spring coefficients of the torsion bar, and are the electrostatic torsion moments; with respectively ； ； wherein, represents the silicon density, represents the mirror thickness, represents the width and length of the mirror, represents the frame outer width, represents the frame outer length, represents the frame inner width, represents the frame inner length; with respectively: ； ； wherein, , and denote the electrostatic torques generated by the mirror surface attracted by the bottom drive electrodes, , and denote the electrostatic torques generated by the mirror surface attracted by the side drive electrodes; denote the electrostatic torques generated by the frame attracted by the bottom drive electrodes; and have the form: ； ； wherein, represents the air permittivity, and denote the integral area of the bottom and side driving electrodes, respectively, , denotes the distance of the bottom driving electrode from the mirror; is the control voltage applied to the driving electrode; The driving mode adopts differential driving, and the driving mode is as follows: ； wherein, is a bias voltage, and Vxand Vydenote the control voltages of the electrostatically driven MEMS mirror in the X-axis and Y-axis directions, respectively. Definitions , , , , ; the dynamic model of the MEMS mirror is transformed into: ； wherein, , , , , are system model parameters, , represent the driving voltage for controlling the galvanometer to twist along the , angle respectively. Considering external disturbances, the dynamic model of the MEMS mirror is rewritten from a continuous-time system model to a state space form: ； where is the state vector of the system, is the control input of the system, is the output of the system, is the bounded disturbance satisfying , denotes the upper bound of the unknown external disturbance; , , , is the continuous system matrix, , , , respectively denote ， ， ， ； Using the zero-order holder method, the sampling period The dynamics model of MEMS mirror is discretized as follows The discretized model is obtained as ； wherein, denotes the state vector of the system at time , denotes the state vector of the system at time ; is the system control input at time ; is the system output at time ; is the external disturbance at time , and satisfies ; , , denotes the system matrix of the discretized model, , , is the continuous system matrix , , in the discretized form at the sampling period , , , denotes respectively: ， ， ； In step 2, the process of designing the disturbance observer is specifically: Let the estimated state of the disturbance observer at time k be , and the disturbance estimate at time k be ; The discrete state equation of the disturbance observer is: ； ； wherein, is an interference observer is an estimated state at time instant is is a disturbance estimate at time instant is a state estimation gain matrix is a disturbance estimation gain In step 2, the process of constructing the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is specifically: Definitions Tracking error of the time is: ； wherein is the desired output signal at the instant Definitions The integral variable of time is The discrete update rule for the integral variable is ； wherein represents the integration variable of time; The discrete integral terminal sliding surface is designed based on the minimum operator reaching law as: ； wherein represents discrete integral terminal sliding mode surface at time instant represents terminal term weight ; is terminal sliding mode exponent ; represents sign function represents integral gain ; The output error of the computation prediction, i.e. the tracking error at the time instant is: ； wherein is the system output at time is the desired output signal at time the predicted output error Substituting the discrete integral terminal sliding surface designed based on the minimum operator reaching law, the predicted sliding surface of the system at time t + k is obtained, that is, the discrete integral terminal sliding surface of time t + k is ​​​ ； The nonlinear terminal terms are evaluated using a standard one-step explicit method defined as ​ ； Constructing nominal partial predicted sliding surface is: ； Predicting a sliding surface for a structure for a nominal portion Adding the true impact of the input and the disturbance, we get: ； The actual disturbance in the system is replaced by the disturbance estimation value of the disturbance observer, and the residual part not completely compensated by the disturbance observer is combined into the original disturbance term for unified processing, obtaining: ； ； wherein is an additional term with an upper bound; The minimum operator reaching law is designed as: ； wherein is a shrinkage factor, ; is a bandwidth parameter, ; When time, finite step into the sliding mode band ; if gradually approach 0, reach , we get: ； The discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is constructed as: 。 2. The MEMS mirror scanning method based on integral terminal sliding mode control according to claim 1, 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, the MEMS mirror system controlled by the discrete minimum operator integral terminal sliding mode controller based on disturbance observer compensation is also analyzed for stability, and the stability analysis includes disturbance observer stability analysis and closed-loop control system stability analysis.

3. The integral terminal sliding mode control based MEMS galvanometer scanning method according to claim 2, wherein, In step 2, the process of disturbance observer stability analysis is specifically: Define the state estimation error at time k for the disturbance observer is: ； Defining the disturbance estimation error of the disturbance observer at time k is: ； interfering observer of the state estimation error at time k+1 is recursively given by ； interfering observer disturbance estimation error at time k+1 is recursively given by ； wherein is external disturbances at the moment in time, and satisfies ; denotes a change in the disturbance, ; Introducing Lyapunov function Stability analysis on disturbance observer: ； wherein represents a Lyapunov function at time the value of and R represents a positive definite matrix, , ; Increment of a Lyapunov function to prove that the MEMS mirror system controlled by the discrete minimum operator integral terminal sliding mode controller with disturbance observer compensation is stable under disturbance observer compensation:​ ； wherein represents a Lyapunov function at time the value of ; The disturbance estimation error and the disturbance estimation error are combined to define the following variables: ， ， ， ； wherein denotes the identity matrix; then: ； Defining a Lyapunov function is: ； wherein represents a Lyapunov function at time the value of The increment of the Lyapunov function is given by: ​ ； wherein represents a Lyapunov function at time the value of there is such that ; let wherein denotes the smallest eigenvalue of the matrix; Under the condition of no disturbance increment, it is obtained that: ； Further, we obtain , the perturbation estimation error converges to a compact set containing the origin, which is represented as the perturbation estimation error is uniformly ultimately bounded.

4. The integral terminal sliding mode control based MEMS galvanometer scanning method according to claim 3, wherein, In step 2, the process of closed-loop control system stability analysis is specifically: Defining a Lyapunov function is: ； wherein represents a Lyapunov function at time the value of the increment of the lyapunov function is: is: ； wherein represents a Lyapunov function at time the value of lyapunov function increment of the upper bound expression is ； wherein is an upper bound of Based on the Lyapunov function of the increment of the inequality analysis, get: ； 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 the system enters the convergence zone, the number of steps of convergence of the system satisfies the following upper bound estimate: ； When the system is free from disturbances, i.e. the number of steps to convergence is: ​ ； 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.

5. The integral terminal sliding mode control based MEMS galvanometer scanning method according to claim 4, wherein, Said step 3 is specifically: The discrete reference signal, i.e. the desired output signal is compared to the actual angle position signal, i.e. the system output detected by the feedback loop, to generate a tracking error signal ; The tracking error signal is input to a disturbance observer for estimating unknown disturbances in the system in real time to obtain a disturbance estimate , and a feedforward compensation amount, i.e., an extra term is generated based on the disturbance estimate ; Based on tracking error signal Computing a discrete integral terminal sliding surface ; By using the minimum operator approach law, the final digital control quantity, i.e. the system control input, is obtained by synthesizing the tracking error signal, the state of the sliding mode surface and the feedforward compensation quantity ; Final digital control quantity Through the driving circuit, after voltage amplification, it is used to drive the MEMS scanner to perform scanning motion; The actual deflection angle of the mirror is detected by the position sensor in real time and fed back to the input end to form a closed-loop control.

6. A laser radar system comprising a laser, a MEMS mirror, a position sensor, an analog-to-digital converter, an FPGA-based controller, and a driving circuit; characterized in that, The laser serves as a laser light source, and the laser emitted thereby is incident on the mirror surface of the MEMS mirror; The position sensor is used to receive the laser reflected by the mirror surface of the MEMS mirror and convert it into an electrical signal; The analog-to-digital converter is used to convert the electrical signal output by the position sensor into a digital signal and send it to the FPGA-based controller; The FPGA-based controller has a readable storage medium stored therein, and when the readable storage medium is executed, it is used to realize the steps of the MEMS mirror scanning method based on integral terminal sliding mode control according to any one of claims 1 to 5. According to the MEMS scanner scanning method based on integral terminal sliding mode control, a voltage control signal is output by a controller based on FPGA, amplified by a voltage amplifier of a driving circuit, and input into bottom and side driving electrodes of the MEMS scanner, so as to drive the MEMS scanner to track a desired trajectory and scan.

7. A computer readable storage medium having stored thereon a program; characterized in that, The program is executed by the processor, and is used for implementing the steps of the MEMS scanner scanning method based on integral terminal sliding mode control in any one of claims 1 to 5.

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