Piezoelectric fast reflector angle control method based on improved terminal sliding mode controller

Abstract

The invention belongs to the technical field of control, and particularly relates to a piezoelectric fast reflector angle control method based on an improved terminal sliding mode controller. Comprising the following steps: S1, establishing a piezoelectric fast reflecting mirror dynamical model containing a hysteresis model and external disturbance; s2, obtaining a second-order kinetic model of the fast steering mirror by using the hysteresis inverse model; s3, taking the total disturbance of the second-order kinetic model of the fast steering mirror as an expansion variable, and establishing an expansion state observer based on the expansion variable; s4, designing an improved terminal sliding mode controller based on the non-singular fast terminal sliding mode surface and the improved adaptive reaching law; and S5, realizing high-precision control on the angle of the piezoelectric fast reflecting mirror based on the improved terminal sliding mode controller. According to the method, the adaptive function is introduced into the reaching law, so that the response speed of the system is dynamically changed, the robustness is improved, the buffeting of the system is effectively reduced, and the operation of the system is more stable and reliable.

Description

Technical Field

[0001] The present invention belongs to the field of control technology, and particularly relates to a piezoelectric fast steering mirror angle control method based on an improved terminal sliding mode controller. Background Art

[0002] As the core actuator of a precision optical system, the piezoelectric fast steering mirror (PFSM) plays an important role in fields such as laser communication, adaptive optics, and space target tracking due to its fast dynamic response and ultra-high positioning accuracy. However, the inherent hysteretic nonlinear characteristics of piezoelectric actuators severely restrict the performance improvement of the PFSM. Specifically, there is a complex rate-dependent hysteresis relationship between the driving voltage and the deflection angle, resulting in a non-one-to-one mapping between the system output and the control input, significantly reducing the control accuracy and stability. Especially in dynamic tracking tasks, the hysteresis effect will cause trajectory deviation, becoming the main bottleneck for achieving highly reliable beam control. To alleviate the influence of hysteretic nonlinearity on the system, researchers have explored from the aspect of hysteresis modeling. Classical modeling methods include the Preisach model based on operators, the Prandtl-Ishlinskii (P-I) model, and the Bouc-Wen model based on differential equations, etc. However, these models have problems such as insufficient accuracy or complex calculation when describing rate-dependent hysteresis. In recent years, by cascading the hysteresis into a static nonlinear link (such as the P-I model) and a linear dynamic link, the rate-dependent hysteresis behavior can be effectively characterized. However, in actual systems, the hysteresis curve drifts due to factors such as environmental temperature fluctuations and mechanical load changes. Relying solely on feedforward inverse model compensation is difficult to adapt to complex working conditions, and the tracking accuracy of the piezoelectric fast steering mirror will still decrease significantly. Therefore, the robust control strategy combining closed-loop feedback has become the key direction to break through this limitation. The sliding mode control method is widely used in piezoelectric drive systems due to its strong robustness to parameter uncertainties and external disturbances. However, the traditional sliding mode control method drives the system state to asymptotically converge to the equilibrium point by designing a linear sliding surface, but its convergence time is infinite, making it difficult to meet the requirements of high-dynamic scenarios. For this reason, terminal sliding mode control makes the system state converge within a finite time by introducing a nonlinear sliding surface. Although the non-singular terminal sliding mode avoids singularity by improving the sliding surface structure, its convergence rate is still limited by a fixed exponential parameter. In addition, due to the unknown actual disturbance boundary in the sliding mode control method, a high-gain switching term needs to be used, resulting in high-frequency chattering of the control signal, which not only reduces the tracking accuracy but also accelerates the mechanical fatigue of the piezoelectric actuator and shortens the service life of the device. Summary of the Invention

[0003] In view of this, the present invention aims to provide a piezoelectric fast steering mirror angle control method based on an improved terminal sliding mode controller, so as to solve the problems in existing traditional sliding mode control. In the method based on a linear sliding mode surface, it can only ensure the convergence of the system in infinite time. At the same time, in the traditional reaching law, the switching term relies on high gain to overcome the influence of disturbances, resulting in the system output switching back and forth on the sliding mode surface, thus generating a serious chattering phenomenon. In addition, the traditional method has the problem of a fixed convergence speed. To solve this problem, the present invention combines an extended state observer to estimate the disturbance in real time and feedback it to the control law to compensate for the influence caused by the disturbance. In addition, the present invention adopts an improved terminal sliding mode controller to achieve finite-time convergence, and by introducing an adaptive function in the reaching law, the system response speed is dynamically changed and the robustness is improved, effectively reducing the system chattering and making the system operation more stable and reliable.

[0004] To achieve the above object, the technical solution of the present invention is realized as follows: A piezoelectric fast steering mirror angle control method based on an improved terminal sliding mode controller specifically includes the following steps: S1: Establish a dynamic model of the piezoelectric fast steering mirror including a hysteresis model and external disturbances; S2: Design a hysteresis inverse model and obtain the second-order dynamic model of the fast steering mirror by using the hysteresis inverse model; S3: Take the total disturbance of the second-order dynamic model of the fast steering mirror as an extended variable and establish an extended state observer based on the extended variable; S4: Design an improved terminal sliding mode controller based on the estimated value of the position variable output by the extended state observer, a non-singular fast terminal sliding mode surface, and an improved adaptive reaching law; S5: Input the position signal of the piezoelectric fast steering mirror to be controlled into the improved terminal sliding mode controller for processing, and input the processing result of the improved terminal sliding mode controller into the hysteresis inverse model for processing to achieve high-precision control of the angle of the piezoelectric fast steering mirror.

[0005] Furthermore, in step S1, the expression of the dynamic model of the piezoelectric fast steering mirror is: ; Among them, , , and are all equivalent parameters related to the mechanical structure of the piezoelectric fast steering mirror, is the time variable, is the position output signal of the piezoelectric fast steering mirror, is the output of the hysteresis inverse model, is the concentrated effect of external disturbances, is the hysteresis model of the piezoelectric fast steering mirror, is the derivative of the position output signal.

[0006] Furthermore, the hysteresis model of the piezoelectric fast steering mirror is constructed using the OSP operator of the P-I model, and the expression of the hysteresis model of the piezoelectric fast steering mirror is: ; ; where is the initial value of the OSP operator of the hysteresis model, is the threshold coefficient of the OSP operator of the hysteresis model, and , is a constant, is the threshold of the i-th OSP operator of the hysteresis model, is the weight coefficient of the i-th OSP operator of the hysteresis model, and L is the total number of OSP operators to be identified in the hysteresis model.

[0007] Furthermore, step S2 specifically includes the following steps: S21: Based on the thresholds and weight coefficients of the OSP operators of the hysteresis model, use the P-I model to construct the expression of the hysteresis inverse model: ; ; where is the weight coefficient of the i-th OSP operator of the hysteresis inverse model, is the threshold of the i-th OSP operator of the hysteresis inverse model, L is the total number of OSP operators to be identified in the hysteresis inverse model, is the output value of the improved terminal sliding mode controller; S22: Use the hysteresis inverse model as a feedforward controller, and connect the piezoelectric fast steering mirror dynamics model in series with the feedforward controller to obtain the fast steering mirror second-order dynamics model: ; where is the position signal output by the fast steering mirror second-order dynamics model, is the velocity signal output by the fast steering mirror second-order dynamics model, is the displacement feedback signal of the fast steering mirror second-order dynamics model, is the disturbance caused by the uncompensated part of the hysteresis inverse model, is the lumped disturbance of the fast steering mirror second-order dynamics model, is the upper limit of the total disturbance of the fast steering mirror second-order dynamics model, , is the first derivative of the position signal output by the fast steering mirror second-order dynamics model, is the first derivative of the velocity signal output by the fast steering mirror second-order dynamics model.

[0008] Further, in step S3, the lumped disturbance d of the fast steering mirror second-order dynamic model is used as the expansion variable , and an extended state observer is constructed. The expression of the extended state observer is as follows: ; ; ; ; ; ; where A, B, and C are all intermediate parameters representing the extended state observer and have no physical meaning, is the gain matrix of the extended state observer, g is a positive number, g > 0, is the estimated value of the position variable ; is the estimated value of the displacement feedback signal of the fast steering mirror second-order dynamic model.

[0009] Further, step S4 specifically includes the following steps: S41: Set the reference position signal as , and construct a position error function: ; where, is the tracking error, is the first derivative of the tracking error, is the second derivative of the tracking error, is the first derivative of the reference position signal, is the second derivative of the reference position signal; S42: Based on the position error function, construct a non-singular fast terminal sliding mode surface : ; where, , and are positive numbers, , , and are all positive odd numbers, and , .

[0010] S43: Introduce an adaptive function into the traditional reaching law to obtain an improved adaptive reaching law: ; where both \(m\) and \(n\) are positive constants, is the coefficient of the exponential term, is the gain of the switching term, and are both positive constants; S44: Design an improved terminal sliding mode controller based on a nonsingular fast terminal sliding mode surface and an improved adaptive reaching law. The expression of the improved terminal sliding mode controller is: .

[0011] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) The piezoelectric fast steering mirror angle control method based on the improved terminal sliding mode controller of the present invention includes a nonsingular fast terminal sliding mode surface and an improved adaptive reaching law. At the same time, it also combines an extended state observer (ESO, i.e., an extended state observer) and a hysteresis inverse model feedforward compensation to solve the hysteretic nonlinearity and external disturbance problems in the PFSM system, providing an effective solution for the high-precision control of the piezoelectric drive system. The present invention can achieve high-precision control of the PFSM and improve the robustness of the PFSM system.

[0012] (2) The piezoelectric fast steering mirror angle control method based on the improved terminal sliding mode controller of the present invention can estimate the disturbance in real time and minimize the influence of the disturbance.

[0013] (3) Compared with the prior art, in the piezoelectric fast steering mirror angle control method based on the improved terminal sliding mode controller of the present invention, by introducing an adaptive function into the reaching law, when facing disturbances and the system is far from the sliding mode surface, the proposed improved terminal sliding mode controller can provide a faster convergence speed than the traditional sliding mode method. When approaching the sliding mode surface, it can reduce the system chattering. The proposed improved terminal sliding mode controller of the present invention exhibits better tracking performance, and its tracking trajectory can converge to the reference trajectory better, demonstrating stronger robustness and better disturbance rejection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 is a schematic flow chart of the piezoelectric fast steering mirror angle control method based on the improved terminal sliding mode controller according to the embodiment of the present invention; Figure 2 is a control block diagram of the improved terminal sliding mode controller according to the embodiment of the present invention; Figure 3 The hysteresis fitting graph of the P-I model using the OSP operator according to the embodiment of the present invention; Figure 4 The estimation effect diagram of the extended state observer for step disturbance according to the embodiment of the present invention; Figure 5 The effect comparison diagram of the present invention and the traditional sliding mode control method for tracking the sine position according to the embodiment of the present invention; Figure 6 The angle error comparison diagram of the present invention and the traditional sliding mode control method for tracking the sine position according to the embodiment of the present invention.

[0015] Explanation of reference numerals: 1. Improved terminal sliding mode controller; 2. Feedforward controller; 3. Piezoelectric fast steering mirror; 4. Extended state observer. Detailed implementation manners

[0016] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention.

[0017] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0018] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "plurality" is two or more.

[0019] In the description of the present invention, it should be noted that, unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0020] The present invention will be described in detail below with reference to the drawings and in conjunction with embodiments.

[0021] As Figure 1 shown, the piezoelectric fast steering mirror angle control method based on an improved terminal sliding mode controller proposed by the present invention specifically includes the following steps: S1: Establish a dynamic model of the piezoelectric fast steering mirror 3 including a hysteresis model and external disturbances; S2: Design a hysteresis inverse model and obtain a second-order dynamic model of the fast steering mirror using the hysteresis inverse model; S3: Use the total disturbance of the second-order dynamic model of the fast steering mirror as an extended variable and establish an extended state observer 4 based on the extended variable; S4: Design an improved terminal sliding mode controller 1 based on the position variable estimation value output by the extended state observer 4, a non-singular fast terminal sliding mode surface, and an improved adaptive reaching law; S5: Input the position signal of the piezoelectric fast steering mirror 3 to be controlled into the improved terminal sliding mode controller 1 for processing, and input the processing result of the improved terminal sliding mode controller 1 into the hysteresis inverse model for processing to achieve high-precision control of the angle of the piezoelectric fast steering mirror 3.

[0022] The present invention aims to solve the key technical problems of the piezoelectric fast steering mirror 3 (PFSM) in high-precision beam pointing and accurate tracking. Specifically, the inherent hysteresis characteristics of the piezoelectric actuator significantly affect the performance of the piezoelectric fast steering mirror 3, resulting in a strong non-linear hysteresis relationship between the deflection angle of the PFSM and the control voltage. This hysteresis effect is one of the main challenges in achieving high-precision and high-stability control. Traditional control methods often struggle to simultaneously achieve fast response, strong anti-disturbance ability, and high stability. The present invention proposes a novel non-singular fast terminal sliding mode controller. Specifically, a feed-forward compensation method based on the inverse hysteresis model is adopted to mitigate the adverse effects of hysteretic non-linearity on system performance. At the same time, an extended state observer is introduced to estimate system uncertainties and external disturbances in real time to ensure accurate disturbance compensation. In addition, the non-singular fast terminal sliding mode surface ensures convergence in finite time, and an adaptive function is added to the reaching law to optimize the convergence speed and reduce chattering, significantly improving the system's response time and robustness and effectively addressing problems that cannot be solved by traditional control methods. The present invention not only overcomes the influence of hysteretic non-linearity but also improves the anti-disturbance ability and position control accuracy of the system by compensating for lumped disturbances including the uncompensated part of the hysteresis inverse model and external disturbances, thus significantly enhancing the dynamic performance and tracking ability of the PFSM.

[0023] As Figure 2 shown, the improved terminal sliding mode controller 1 adopts a composite control strategy, and its working principle can be described as follows: A closed-loop feedback is constructed based on the error between the reference position signal and the displacement feedback signal y of the piezoelectric fast steering mirror 3, and feed-forward compensation is performed in combination with the disturbance estimation quantity output by the extended state observer 4 in real time to generate the control signal u(t); after this control signal is processed by the hysteresis inverse model, the precise control voltage v(t) is finally output to control the deflection of the piezoelectric fast steering mirror 3, forming a complete disturbance suppression and hysteresis compensation closed-loop control system.

[0024] In some embodiments, in step S1, the expression of the dynamic model of the piezoelectric fast steering mirror 3 is: ; where , , and are all equivalent parameters related to the mechanical structure of the piezoelectric fast steering mirror 3, is the time variable, is the position output signal of the piezoelectric fast steering mirror 3, is the output of the hysteresis inverse model, is the concentrated effect of external disturbances, is the hysteresis model of the piezoelectric fast steering mirror 3, is the derivative of the position output signal.

[0025] It should be noted that defines the concentrated effect of the disturbance, and at the same time considers the external disturbance and parameter uncertainty of the PFSM. represents the modeling hysteresis nonlinear term (i.e., the hysteresis model) of the piezoelectric fast steering mirror 3, and is expressed as a function of the input voltage of the PFSM .

[0026] In some embodiments, the OSP operator of the P-I model is used to construct the hysteresis model of the piezoelectric fast steering mirror 3, and the expression of the hysteresis model of the piezoelectric fast steering mirror 3 is: ; ; where is the initial value of the OSP operator of the hysteresis model, is the threshold coefficient of the OSP operator of the hysteresis model, and , is a constant, is the threshold of the i-th OSP operator of the hysteresis model, is the weight coefficient of the i-th OSP operator of the hysteresis model, and L is the total number of OSP operators to be identified in the hysteresis model.

[0027] It should be noted that the OSP operator is the unilateral play operator of the P-I model, and the unilateral play operator is expressed as . In practical applications, the P-I model is approximated by superimposing finite operators to obtain the hysteresis model of the piezoelectric fast steering mirror 3.

[0028] In some embodiments, step S2 specifically includes the following steps: S21: Based on the thresholds and weight coefficients of the OSP operators of the hysteresis model, use the P-I model to construct the expression of the hysteresis inverse model: ; where is the weight coefficient of the i-th OSP operator of the feedforward controller 2, is the threshold of the i-th OSP operator of the feedforward controller 2, L is the total number of OSP operators to be identified in the feedforward controller 2, is the output value of the improved terminal sliding mode controller 1; S22: Take the hysteresis inverse model as the feedforward controller 2, and connect the dynamic model of the piezoelectric fast steering mirror 3 in series with the feedforward controller 2 to obtain the second-order dynamic model of the fast steering mirror: ; where is the position signal output by the second-order dynamic model of the fast steering mirror, is the velocity signal output by the second-order dynamic model of the fast steering mirror, is the displacement feedback signal of the second-order dynamic model of the fast steering mirror, is the disturbance caused by the uncompensated part of the hysteresis inverse model, is the lumped disturbance of the second-order dynamic model of the fast steering mirror, is the upper limit of the total disturbance of the second-order dynamic model of the fast steering mirror, , is the first derivative of the position signal output by the second-order dynamic model of the fast steering mirror, is the first derivative of the velocity signal output by the second-order dynamic model of the fast steering mirror.

[0029] It should be noted that the second-order dynamic model of the fast steering mirror is established by using the anti-hysteresis compensation method. The main idea of anti-hysteresis compensation is to eliminate the hysteresis nonlinearity by cascading the anti-hysteresis model with the real hysteresis model. The weight coefficients and thresholds of the hysteresis inverse model are determined by the parameters of the P-I model, and their evolution relationship is as follows: ; Among them, and represent the thresholds and weight coefficients of each hysteresis inverse model operator; it should be noted that the number of hysteresis inverse model operators is the same as the number of hysteresis model operators.

[0030] Furthermore, in step S22, by connecting the dynamic model of the piezoelectric fast steering mirror 3 in series with the feedforward controller 2, the dynamic model of the piezoelectric fast steering mirror 3 can be simplified to obtain the second-order dynamic model of the fast steering mirror.

[0031] In some embodiments, in step S3, the lumped disturbance d of the second-order dynamic model of the fast steering mirror is used as the expansion variable , and an extended state observer 4 is constructed. The expression of the extended state observer 4 is: ; ; ; ; ; ; Among them, A, B, and C are all intermediate parameters representing the extended state observer 4 and have no physical meaning, is the gain matrix of the extended state observer 4, g is a positive number, is the estimated value of the state variable ; is the displacement feedback signal of the second-order dynamic model of the fast steering mirror Estimated value.

[0032] It should be noted that the extended state observer 4 is designed to estimate the states and lumped disturbances of the fast steering mirror second-order dynamic model.

[0033] In some embodiments, step S4 specifically includes the following steps: S41: Set the reference position signal to , and construct the position error function: ; Where is the tracking error, is the first derivative of the tracking error, is the second derivative of the tracking error, is the first derivative of the reference position signal, is the second derivative of the reference position signal; S42: Based on the position error function, construct a non-singular fast terminal sliding mode surface : ; Where , and are positive numbers, , , and are all positive odd numbers, and , .

[0034] S43: Introduce an adaptive function (i.e., and ) into the traditional reaching law to obtain an improved adaptive reaching law: ; Where m, n, k and are all positive constants, is the exponential term coefficient, is the switching term gain; S44: Design an improved terminal sliding mode controller 1 based on the non-singular fast terminal sliding mode surface and the improved adaptive reaching law. The expression of the improved terminal sliding mode controller 1 is:

[0035] It should be noted that the traditional sliding mode control method assumes the upper bound of the disturbance. By introducing a switching term with high gain, the system state converges to the preset sliding mode surface. In the present invention, an adaptive function is introduced into the traditional reaching law to complete the real-time adjustment of the gain, avoid chattering, and improve the convergence speed, so as to realize the position control of the piezoelectric fast steering mirror 3. On this basis, in order to suppress the influence of the disturbance on the piezoelectric fast steering mirror 3, the estimation of the ESO (extended state observer 4) is introduced to estimate the total disturbance of the piezoelectric fast steering mirror 3 in real time, and the total disturbance estimation is directly fed back to the control law (i.e., the improved terminal sliding mode controller 1), so that the control law (the improved terminal sliding mode controller 1) contains the estimated disturbance term to offset the influence of the disturbance on the piezoelectric fast steering mirror 3.

[0036] Further, in step S42, on the basis of obtaining the position error function, a nonsingular attractor is introduced into the traditional sliding mode surface to achieve the finite-time convergence of the system state and complete the design of the nonsingular fast terminal sliding mode surface.

[0037] In addition, the design of the improved adaptive reaching law can obtain a faster convergence speed and reduce system chattering.

[0038] It should be noted that: the traditional sliding mode reaching law can accelerate the speed of convergence to the sliding mode surface by increasing the coefficient. However, blindly increasing the parameters will cause strong chattering of the system (i.e., the piezoelectric fast steering mirror 3) and make the system unstable. Therefore, to avoid this problem, the present invention proposes an improved adaptive reaching law. On the basis of the traditional reaching law, an adaptive function is introduced into the sliding mode surface, so that the reaching law parameters can change with the change of the system state. Specifically, when the system is far from the sliding mode surface, that is increases, at this time, the exponential term coefficient also increases, and the switching term gain also increases, which can provide a faster convergence speed; conversely, when the system is close to the sliding mode surface, that is decreases, and the two coefficients (the exponential term coefficient and the switching term gain) decrease simultaneously. And when the system reaches the sliding mode surface, that is , the exponential term is 0, and the switching term gain gradually decreases to 0 as the error decreases, which can significantly reduce system chattering.

[0039] In addition, the control law (i.e., the improved terminal sliding mode controller 1) combines the ESO (extended state observer 4) estimation, and replaces the disturbance with the state variable to perform real-time compensation for the disturbance. At the same time, in order to avoid the influence of measurement noise, the system state variables (speed signal and position signal) in the control law (i.e., the improved terminal sliding mode controller 1) are replaced with estimated values.

[0040] In order to prove the stability of the improved sliding film controller, the Lyapunov function of the entire closed-loop system is considered ,right The derivative is: ; in, ,Depend on ,Pick , the above formula can be obtained: ; when hour, , the system is asymptotically stable. , based on the sliding surface, it can be ensured that the system error function also converges to 0.

[0041] In order to verify the effectiveness of the sliding mode control method proposed in the present invention, that is, it has stronger tracking ability and disturbance estimation ability, experiments are carried out under the same conditions using the traditional sliding mode control method and the improved sliding mode control method proposed in the present invention. Figure 3 The hysteresis effect modeled by the OSP operator in the present invention shows that the fitted model can well represent the actual model.

[0042] like Figure 4 As shown in the figure, after applying a 0.1mrad step disturbance at t=0.1s in the simulation, the estimated value of ESO can accurately converge to the actual disturbance value after a period of time, and its dynamic response process demonstrates the effectiveness of ESO.

[0043] In order to verify the effectiveness of the algorithm, Figure 5 The tracking effects of the traditional sliding mode control method and the present invention on the sinusoidal signal are compared. Figure 5 As shown in the figure, the present invention can control the tracking accuracy to about ±0.05 mrad, which is nearly 60% higher than the traditional algorithm. Figure 6 It can be seen from the angle error diagram that when disturbed, the error jitter is smaller and smoother, that is, the present invention exhibits better anti-disturbance capability.

[0044] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0045] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub - combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A piezoelectric fast mirror angle control method based on an improved terminal sliding mode controller, characterized in that: The specific steps include: S1: Establish a dynamic model of piezoelectric fast mirror including hysteresis model and external disturbance; S2: Design a hysteresis inverse model and use it to obtain the second-order dynamics model of the fast mirror; S3: The total disturbance of the second-order dynamics model of the fast mirror is used as an expansion variable, and an expansion state observer is established based on the expansion variable; S4: Design of an improved terminal sliding mode controller based on the position variable estimate output by the extended state observer, the non-singular fast terminal sliding surface and the improved adaptive reaching law; S5: inputting the position signal of the piezoelectric fast mirror to be controlled into the improved terminal sliding mode controller for processing, and inputting the processing result of the improved terminal sliding mode controller into the hysteresis inverse model for processing, so as to realize high-precision control of the angle of the piezoelectric fast mirror.

2. The piezoelectric fast-reflection mirror angle control method based on the improved terminal sliding mode controller according to claim 1 is characterized in that: In step S1, the expression of the piezoelectric fast mirror dynamic model is: ； in, , , and These are equivalent parameters related to the mechanical structure of the piezoelectric fast mirror. is the time variable, is the position output signal of the piezoelectric fast mirror, is the output of the hysteresis inverse model, is the concentrated effect of external disturbance, is the hysteresis model of the piezoelectric fast mirror, is the derivative of the position output signal.

3. The piezoelectric fast-reflection mirror angle control method based on the improved terminal sliding mode controller according to claim 2 is characterized in that: The hysteresis model of the piezoelectric fast mirror is constructed using the OSP operator of the PI model. The expression of the hysteresis model of the piezoelectric fast mirror is: ； ； in, is the initial value of the OSP operator of the hysteresis model, is the threshold coefficient of the OSP operator of the hysteresis model, and , is a constant, is the threshold of the ith OSP operator of the hysteresis model, is the weight coefficient of the i-th OSP operator of the hysteresis model, and L is the total number of OSP operators to be identified in the hysteresis model.

4. The piezoelectric fast-reflection mirror angle control method based on the improved terminal sliding mode controller according to claim 3 is characterized in that: Step S2 specifically includes the following steps: S21: Based on the thresholds and weight coefficients of each OSP operator of the hysteresis model, the PI model is used to construct the expression of the hysteresis inverse model: ； ； in, is the weight coefficient of the i-th OSP operator of the hysteresis inverse model, is the threshold of the i-th OSP operator of the hysteresis inverse model, L is the total number of OSP operators to be identified in the hysteresis inverse model, To improve the output value of the terminal sliding mode controller; S22: Using the hysteresis inverse model as a feedforward controller, connecting the piezoelectric fast-reflection mirror dynamics model and the feedforward controller in series, and obtaining a second-order dynamics model of the fast-reflection mirror: ； in, is the position signal output by the second-order dynamics model of the fast mirror, is the velocity signal output by the second-order dynamics model of the fast mirror, is the displacement feedback signal of the second-order dynamic model of the fast mirror, is the disturbance caused by the uncompensated part of the hysteresis inverse model, is the lumped perturbation of the second-order dynamics model of the fast mirror, is the upper limit of the total disturbance of the second-order dynamics model of the fast mirror, , is the first-order derivative of the position signal output by the second-order dynamic model of the fast mirror, It is the first derivative of the velocity signal output by the second-order dynamic model of the fast mirror.

5. The piezoelectric fast-reflection mirror angle control method based on the improved terminal sliding mode controller according to claim 4 is characterized in that: In step S3, the lumped disturbance d of the second-order dynamics model of the fast mirror is used as the expansion variable , construct an extended state observer, the expression of the extended state observer is: ； ； ； ； ； ； Among them, A, B and C are all intermediate parameters representing the extended state observer and have no physical meaning. is the gain matrix of the extended state observer, g is a positive number, g>0, For position variables An estimated value of is the displacement feedback signal of the second-order dynamics model of the fast mirror The estimated value of .

6. The piezoelectric fast-reflecting mirror angle control method based on the improved terminal sliding mode controller according to claim 5 is characterized in that: Step S4 specifically includes the following steps: S41: Set the reference position signal to , construct the position error function: ； in, is the tracking error, is the first-order derivative of the tracking error, is the second-order derivative of the tracking error, is the first-order derivative of the reference position signal, is the second-order derivative of the reference position signal; S42: Based on the position error function, construct a non-singular fast terminal sliding surface : ； in, , and is a positive number, , , and are all positive odd numbers, and , . S43: Introducing an adaptive function into the traditional reaching law, we obtain an improved adaptive reaching law: ； Among them, m and n are both positive constants, is the exponential term coefficient, is the switching term gain, and All are normal numbers; S44: Design an improved terminal sliding mode controller based on a non-singular fast terminal sliding mode surface and an improved adaptive reaching law, the improved terminal sliding mode controller The expression is: 。

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