阅读说明：本技术 一种两轴音圈快速反射镜的神经网络滑模控制方法 (Neural network sliding mode control method of two-axis voice coil fast reflector ) 是由 郭会军 林遂芳 于 2021-05-19 设计创作，主要内容包括：本发明公开了一种两轴音圈快速反射镜的神经网络滑模控制方法,具体按照以下步骤实施：步骤1、进行音圈电机快反镜系统建模与简化；步骤2、利用步骤1建立的音圈电机快反镜系统模型,计算音圈电机快速反射镜的滑模控制函数；步骤3、采用神经网络对步骤2得到的滑模控制函数进行优化,完成神经网络滑模控制；解决了现有技术中存在的对模型参数扰动鲁棒性差的问题。(The invention discloses a neural network sliding mode control method of a two-axis voice coil fast reflector, which is implemented according to the following steps: step 1, modeling and simplifying a voice coil motor fast reflecting mirror system; step 2, calculating a sliding mode control function of the voice coil motor fast reflecting mirror by using the voice coil motor fast reflecting mirror system model established in the step 1; step 3, optimizing the sliding mode control function obtained in the step 2 by adopting a neural network to complete sliding mode control of the neural network; the problem of poor robustness to model parameter disturbance in the prior art is solved.)

1. A neural network sliding mode control method of a two-axis voice coil fast reflector is characterized by comprising the following steps:

step 1, modeling and simplifying a voice coil motor fast reflecting mirror system;

step 2, calculating a sliding mode control function of the voice coil motor fast reflecting mirror by using the voice coil motor fast reflecting mirror system model established in the step 1;

and 3, optimizing the sliding mode control function obtained in the step 2 by adopting a neural network to complete the sliding mode control of the neural network.

2. The neural network sliding-mode control method of the two-axis voice coil fast reflector according to claim 1, wherein the step 1 is implemented specifically according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; for the part of the reflecting mirror mechanism which can move in two-dimensional directions except for the voice coil motor, the part of the reflecting mirror mechanism is decoupled into two independent torsional vibration systems with single degree of freedom, and a moment balance equation is established as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andthe angular velocity and the angular acceleration are adopted, C is an equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil;

let J₁＝J+2mL²，C₁＝2CL²Then, equation (4) is expressed as:

substituting equations (1), (2) and (3) into equation (5) yields a transfer function between output angular velocity and voltage as:

the reflector driven by the voice coil motor is a second-order oscillation link obtained by the formula, and the corresponding differential equation is as follows:

if neglectedThe influence of the term, the above equation can be:

wherein:

f(ω)＝(R_aC₁+C_eC_m)ω/C_m

this time order x₁＝θ_m，Equation (8) can be converted to an equation of state:

equations (9) and (10) constitute the decoupled state equation.

3. The neural network sliding-mode control method of the two-axis voice coil fast reflector according to claim 2, wherein the step 2 is implemented specifically according to the following steps:

θ_dand theta_mRespectively setting and actual positions of the reflector;

defining the position error as e ═ x₁-θ_dWherein theta_dFor a position given signal, a sliding mode switching function is defined as:

wherein the constant c > 0, is definedThen:

s＝x₂-x_q (12)

deriving s on both sides and bringing into formula (10):

adopting an equal approach rate:

the parameter λ > 0 controls the speed at which the system motion point approaches the switching plane s ═ 0, and the value is small, the approach speed is slow, and conversely, the approach speed is fast, and further the following ideal control quantity can be obtained by the equations (13) and (14):

4. the neural network sliding-mode control method of the two-axis voice coil fast reflector according to claim 3, wherein the step 3 is implemented specifically according to the following steps:

due to the fact that the parameters J and f (x) in the formula (15) are actually equivalent₂) Is time-varying, ideally controlled quantity u_rIs an unknown nonlinear function, and takes a sliding mode variable s as a unique input approximation u of a radial basis function neural network_rNamely:

wherein epsilon₁For approximation error, n is the number of neurons, phi_i(x) For Sigmoid basis function, W ═ W₁…w_n]^TAs a weight vector, [ phi ] is defined as₁,...,φ_n]^TIs a vector of basis functions;

for any positive number xi and a continuous function f X → R in neural networksⁿThere is a sufficiently large positive integerN > v for any integer^*Always find an ideal n-dimensional weight vector W ═ W^*And a suitable set of basis functions phi such that the output of the neural network with n hidden elements satisfies:

whereinIs a neural network model;

find a set of weights W such that the approximation error satisfies | ∈₁Xi is less than or equal to | and the optimal weight W is generally unknown and needs on-line estimation; therefore, define the current weight estimate asThen the actual control inputs at this time are:

according to the sliding mode control theory, only when the sliding mode control is adopted, the condition that the sliding mode can be achieved is metAt all times, in u_r(t) the state of the controlled system converges to the origin; on-line approximation of u by neural network_r(t), the weight of the network needs to be updated on line under the condition that the sliding mode can be met, and the corresponding weight updating strategy is as follows:

wherein the parameter gamma > 0 represents the learning rate, and the weight estimation error is defined asThen:

defining the Lyapunov function as:

the first derivative with respect to time is found as:

and because ofThe following are easy to know:

it can be seen that when | s | ≧ xi/J^*At λ, thenThen satisfyWhen the sliding mode variable s converges to the curve s near 0 +/-xi/J^*Lambda, and the system error decreases with the improvement of the approximation precision of the neural network; meanwhile, in the neighborhood of s-0, V is positive,negative semi-definite, and the closed loop system can be known to be stable according to the Lyapunov stability theorem; as can be seen from equation (11), the position tracking error e converges bounded; in practical application, the position of the control input control reflector is obtained through the formula (18) according to the formula (11) and the formula (14), and the weight coefficient of the sliding mode neural network controller is updated in real time through the formula (19); and completing the sliding mode control of the neural network.

5. The neural network sliding-mode control method of the two-axis voice coil fast reflector according to claim 1, wherein the step 1 is implemented specifically according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; for the part of the reflecting mirror mechanism which can move in two-dimensional directions except for the voice coil motor, the part of the reflecting mirror mechanism is decoupled into two independent torsional vibration systems with single degree of freedom, and a moment balance equation is established as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andc is the equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil.

Let J₁＝J+2mL²，C₁＝2CL²Then, equation (4) is expressed as:

from equation (5), the transfer function between the electromagnetic torque and the output position is:

substituting equations (1), (2) and (3) into the above equation can result:

then:

in view ofThe above formula can be converted into:

if neglectedThe influence of the term, the above equation can be:

wherein:

this time order x₁＝θ_m，Then (28) can be converted to an equation of state:

equations (29) and (30) constitute the decoupled state equation.

Technical Field

The invention belongs to the technical field of fast reflector control, and relates to a neural network sliding mode control method of a two-axis voice coil fast reflector.

Background

In the fields of laser communication, laser radar, laser processing, large-caliber astronomical telescopes, space detection and the like, stable control of light beams in two-dimensional directions is one of core technologies restricting system performance. Within a specified rotation angle range, the fast reflector can fast and accurately direct the light beam with high precision and high dynamic.

The two-axis fast reflector adopts a flexible supporting structure capable of reducing friction and is arranged in a composite shaft structure. The driving method of the fast reflecting mirror can be divided into a piezoelectric ceramic type and a voice coil motor type. Compared with the piezoelectric ceramic driving method, the voice coil motor driving has the advantages of large movement stroke, low driving voltage and simple driving circuit, but is inferior to the piezoelectric ceramic method in the aspect of disturbance suppression. However, in the practical application of the voice coil motor fast reflecting mirror, the flexible supporting structure friction torque and the mass unbalance torque loaded in the system in a disturbance mode, including a nonlinear link, system parameter variation caused by environmental factors and an unmodeled link, may cause instability of the mirror system, thereby affecting the precise and fast pointing and precise positioning performance of the fast reflecting mirror on the light beam. Under the conditions of the manufacturing capability of the existing structure and the measurement accuracy of the sensor, the improvement of the anti-interference performance of the system and the robustness to the parameter perturbation become one of the difficulties restricting the performance of the fast reflection mirror of the voice coil motor. The main methods adopted at present are a disturbance observer method, active disturbance rejection control and adaptive robust control: the disturbance observer method and the active disturbance rejection control are designed based on a linear model, accurate observation and inhibition of nonlinear friction torque are difficult to carry out, and the sign function adopted by the adaptive robust control easily causes state buffeting to influence the control precision.

Disclosure of Invention

The invention aims to provide a neural network sliding mode control method of a two-axis voice coil fast reflector, which solves the problem of poor robustness to model parameter disturbance in the prior art.

The technical scheme adopted by the invention is that a neural network sliding mode control method of a two-axis voice coil fast reflector is implemented according to the following steps:

step 1, modeling and simplifying a voice coil motor fast reflecting mirror system;

step 2, calculating a sliding mode control function of the voice coil motor fast reflecting mirror by using the voice coil motor fast reflecting mirror system model established in the step 1;

and 3, optimizing the sliding mode control function obtained in the step 2 by adopting a neural network to complete the sliding mode control of the neural network.

The invention is also characterized in that:

the step 1 is implemented according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; for the part of the reflecting mirror mechanism which can move in two-dimensional directions except for the voice coil motor, the part of the reflecting mirror mechanism is decoupled into two independent torsional vibration systems with single degree of freedom, and a moment balance equation is established as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andthe angular velocity and the angular acceleration are adopted, C is an equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil;

let J₁＝J+2mL²，C₁＝2CL²Then, equation (4) is expressed as:

substituting equations (1), (2) and (3) into equation (5) yields a transfer function between output angular velocity and voltage as:

the reflector driven by the voice coil motor is a second-order oscillation link obtained by the formula, and the corresponding differential equation is as follows:

if neglectedThe influence of the term, the above equation can be:

wherein:

f(ω)＝(R_aC₁+C_eC_m)ω/C_m

this time order x₁＝θ_m，Equation (8) can be converted to an equation of state:

equations (9) and (10) constitute the decoupled state equation.

The step 2 is implemented according to the following steps:

θ_dand theta_mRespectively setting and actual positions of the reflector;

defining the position error as e ═ x₁-θ_dWherein theta_dFor a position given signal, a sliding mode switching function is defined as:

wherein the constant c > 0, is definedThen:

s＝x₂-x_q (12)

deriving s on both sides and bringing into formula (10):

adopting an equal approach rate:

the parameter λ > 0 controls the speed at which the system motion point approaches the switching plane s ═ 0, and the value is small, the approach speed is slow, and conversely, the approach speed is fast, and further the following ideal control quantity can be obtained by the equations (13) and (14):

step 3 is specifically implemented according to the following steps:

due to the fact that the parameters J and f (x) in the formula (15) are actually equivalent₂) Is time-varying, ideally controlled quantity u_rIs an unknown nonlinear function, and takes a sliding mode variable s as a unique input approximation u of a radial basis function neural network_rNamely:

wherein epsilon₁For approximation error, n is the number of neurons, phi_i(x) For Sigmoid basis function, W ═ W₁ … w_n]^TAs a weight vector, [ phi ] is defined as₁,...,φ_n]^TIs a vector of basis functions;

for any positive number xi and a continuous function f X → R in neural networksⁿThere is a sufficiently large positive integerN > v for any integer^*Always find an ideal n-dimensional weight vector W ═ W^*And a suitable set of basis functions phi such that the output of the neural network with n hidden elements satisfies:

whereinIs a neural network model;

find a set of weights W such that the approximation error satisfies | ∈₁Xi is less than or equal to | and the optimal weight W is generally unknown and needs on-line estimation; therefore, define the current weight estimate asThen the actual control inputs at this time are:

according to the sliding mode control theory, only when the sliding mode control is adopted, the condition that the sliding mode can be achieved is metWhen is at u_r(t) the state of the controlled system converges to the origin; on-line approximation of u by neural network_r(t), the weight of the network needs to be updated on line under the condition that the sliding mode can be met, and the corresponding weight updating strategy is as follows:

wherein the parameter gamma > 0 represents the learning rate, and the weight estimation error is defined asThen:

defining the Lyapunov function as:

the first derivative with respect to time is found as:

and because ofThe following are easy to know:

it can be seen that when | s | ≧ xi/J^*At λ, thenThen satisfyWhen the sliding mode variable s converges to the curve s near 0 +/-xi/J^*Lambda, and the system error decreases with the improvement of the approximation precision of the neural network; meanwhile, in the neighborhood of s-0, V is positive,negative semi-definite, and the closed loop system can be known to be stable according to the Lyapunov stability theorem; as can be seen from equation (11), the position tracking error e converges bounded; in practical application, the position of the control input control reflector is obtained through the formula (18) according to the formula (11) and the formula (14), and the weight coefficient of the sliding mode neural network controller is updated in real time through the formula (19); and completing the sliding mode control of the neural network.

The step 1 is implemented according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; decoupling a part of a mirror mechanism, which is movable in two dimensions, other than a voice coil motor into two independent single-degree-of-freedom torquesThe vibration system is established with a moment balance equation as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andc is the equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil.

Let J₁＝J+2mL²，C₁＝2CL²Then, equation (4) is expressed as:

from equation (5), the transfer function between the electromagnetic torque and the output position is:

substituting equations (1), (2) and (3) into the above equation can result:

then:

in view ofThe above formula can be converted into:

if neglectedThe influence of the term, the above equation can be:

wherein:

this time order x₁＝θ_m，Then (28) can be converted to an equation of state:

equations (29) and (30) constitute the decoupled state equation.

The invention has the beneficial effects that: the invention discloses a neural network sliding mode control method of a two-axis voice coil fast reflector, which solves the problems of poor robustness to model parameter disturbance and weak external disturbance resistance in the prior art. The voice coil motor is converted into a torque controller equivalent to an available proportional link by constructing a current loop, so that the output torque of the voice coil motor and the control current are in a linear relation, the quick reflection mirror mechanical part is decoupled into two independent single-degree-of-freedom second-order torsional vibration systems, and the second-order systems are converted into a state equation; position errors are defined, and a sliding mode controller of constant speed approach rate is designed to restrain the problems caused by disturbance and parameter perturbation; and then designing a neural network to carry out online estimation on the sliding mode controller, wherein the output voltage of the neural network is used as the given value of the torque controller. On the basis of not changing the existing system and sensor, the method has robustness on parameter perturbation and system external disturbance, can meet the performance requirement of the voice coil motor reflector, does not adopt a sign function to design a sliding mode controller, and has higher practicability.

Drawings

FIG. 1 is a sliding mode neural network position control frame in the neural network sliding mode control method of the two-axis voice coil fast reflector of the present invention;

FIG. 2 is a schematic structural diagram of a two-axis voice coil motor fast reflector in a neural network sliding mode control method of the two-axis voice coil fast reflector according to the present invention;

FIG. 3 is a diagram of excitation response of 1Hz 17.4mrad sinusoidal signals under parameter mutation in the neural network sliding mode control method of the two-axis voice coil fast reflector of the present invention;

FIG. 4 is an excitation response diagram of a 1Hz 17.4mrad sinusoidal signal under the disturbance condition in the neural network sliding mode control method of the two-axis voice coil fast reflector of the present invention.

In the figure: 1. the device comprises a reflector, 2 a reflector bracket, 3 a flexible supporting structure, 4 a voice coil motor, 5 a micro-displacement sensor, 6 a base and 7 a controller.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The invention discloses a neural network sliding mode control method of a two-axis voice coil fast reflector, which is implemented according to the following steps:

step 1, modeling and simplifying a voice coil motor fast reflecting mirror system;

the step 1 is implemented according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; for the part of the reflecting mirror mechanism which can move in two-dimensional directions except for the voice coil motor, the part of the reflecting mirror mechanism is decoupled into two independent torsional vibration systems with single degree of freedom, and a moment balance equation is established as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andthe angular velocity and the angular acceleration are adopted, C is an equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil;

let J₁＝J+2mL²，C₁＝2CL²Then, thenFormula (4) is represented as:

substituting equations (1), (2) and (3) into equation (5) yields a transfer function between output angular velocity and voltage as:

the reflector driven by the voice coil motor is a second-order oscillation link obtained by the formula, and the corresponding differential equation is as follows:

if neglectedThe influence of the term, the above equation can be:

wherein:

f(ω)＝(R_aC₁+C_eC_m)ω/C_m

this time order x₁＝θ_m，Equation (8) can be converted to an equation of state:

equations (9) and (10) constitute the decoupled state equation.

Step 1 can also be carried out according to the following steps:

the equivalent mathematical model of the voice coil motor as the driver in the two-axis voice coil motor fast reflector is as follows:

M_e＝C_mi_a (2)

E_a＝C_eω (3)

wherein i_aIs armature current, R_aIs armature resistance, L_aIs an armature inductance, E_aTo counter-potential, U_aIs armature voltage, M_eIs an electromagnetic torque, C_mIs an electromagnetic torque constant, C_eIs an electromotive constant, and omega is the angular velocity of the coil; for the part of the reflecting mirror mechanism which can move in two-dimensional directions except for the voice coil motor, the part of the reflecting mirror mechanism is decoupled into two independent torsional vibration systems with single degree of freedom, and a moment balance equation is established as follows:

wherein M is_eResultant moment applied by two coaxial series-connected voice coil motors together, J₁Is the moment of inertia of the tilting mirror, theta_mIn order to tilt the deflection angle of the mirror,andis angular velocityAnd angular acceleration, C is an equivalent damping coefficient, L is the distance from the action point of the driver to the rotating shaft, and m is the mass of the voice coil.

Let J₁＝J+2mL²，C₁＝2CL²Then, equation (4) is expressed as:

from equation (5), the transfer function between the electromagnetic torque and the output position is:

substituting equations (1), (2) and (3) into the above equation can result:

then:

in view ofThe above formula can be converted into:

if neglectedThe influence of the term, the above equation can be:

wherein:

this time order x₁＝θ_m，Then (28) can be converted to an equation of state:

equations (29) and (30) constitute the decoupled state equation.

Step 2, calculating a sliding mode control function of the voice coil motor fast reflecting mirror by using the voice coil motor fast reflecting mirror system model established in the step 1;

the step 2 is implemented according to the following steps:

the voice coil motor fast reflecting mirror position ring mainly realizes the functions of directing and tracking scanning of the fast reflecting mirror, and adopts a sliding mode neural network position control block diagram, as shown in figure 1. In the figure, G(s) is a mathematical model of the controlled object, namely, a part of the reflecting mirror mechanism including the voice coil motor shown in formula (6), and theta_dAnd theta_mRespectively setting and actual positions of the reflector;

defining the position error as e ═ x₁-θ_dWherein theta_dFor a position given signal, a sliding mode switching function is defined as:

wherein the constant c > 0, is definedThen:

s＝x₂-x_q (12)

deriving s on both sides and bringing into formula (10):

adopting an equal approach rate:

the parameter λ > 0 controls the speed at which the system motion point approaches the switching plane s ═ 0, and the value is small, the approach speed is slow, and conversely, the approach speed is fast, and further the following ideal control quantity can be obtained by the equations (13) and (14):

however, the ideal control quantity of the above formula is a multivariable function and is complex to implement.

And 3, optimizing the sliding mode control function obtained in the step 2 by adopting a neural network to complete the sliding mode control of the neural network.

Step 3 is specifically implemented according to the following steps:

due to the fact that the parameters J and f (x) in the formula (15) are actually equivalent₂) Is time-varying, so that the desired control quantity u_rIs an unknown non-linear function and therefore requires an estimate of the ideal manipulated variable u_r. For facilitating practical control, the sliding mode variable s is taken as the only input approximation u of the radial basis function neural network_rNamely:

wherein epsilon₁For approximation error, n is the number of neurons, phi_i(x) For Sigmoid basis function, W ═ W₁ … w_n]^TAs a weight vector, [ phi ] is defined as₁,...,φ_n]^TIs a vector of basis functions;

for any positive number xi and a continuous function f X → R in neural networksⁿThere is a sufficiently large positive integerN > v for any integer^*Always find an ideal n-dimensional weight vector W ═ W^*And a suitable set of basis functions phi such that the output of the neural network with n hidden elements satisfies:

whereinIs a neural network model;

find a set of weights W such that the approximation error satisfies | ∈₁Xi is less than or equal to | and the optimal weight W is generally unknown and needs on-line estimation; therefore, define the current weight estimate asThen the actual control inputs at this time are:

according to the sliding mode control theory, only when the sliding mode control is adopted, the condition that the sliding mode can be achieved is metWhen is at u_r(t) the state of the controlled system converges to the origin; on-line approximation of u by neural network_r(t), the weight of the network needs to be updated on line under the condition that the sliding mode can be met, and the corresponding weight updating strategy is as follows:

wherein the parameter gamma > 0 represents the learning rate, and the weight estimation error is defined asThen:

defining the Lyapunov function as:

the first derivative with respect to time is found as:

and because ofThe following are easy to know:

it can be seen that when | s | ≧ xi/J^*At λ, thenThen satisfyWhen the sliding mode variable s converges to the curve s near 0 +/-xi/J^*Lambda, and the system error decreases with the improvement of the approximation precision of the neural network; meanwhile, in the neighborhood of s-0, V is positive,negative semi-definite, and the closed loop system can be known to be stable according to the Lyapunov stability theorem; as can be seen from equation (11), the position tracking error e converges bounded; in practical application, the position of the control input control reflector is obtained through the formula (18) according to the formula (11) and the formula (14), and the weight coefficient of the sliding mode neural network controller is updated in real time through the formula (19); and completing the sliding mode control of the neural network.

In the neural network sliding mode control method of the two-axis voice coil quick reflector, the two-axis voice coil motor quick reflector can adopt the following structure: the device comprises a reflector 1, a reflector bracket 2, a flexible supporting structure 3, a voice coil motor 4, a micro-displacement sensor 5, a base 6 and a controller 7. The method comprises the steps of establishing an x axis and a y axis by taking the circle center of a circular reflector as an origin of coordinates, installing a reflector 1 on a reflector support 2, installing a flexible supporting structure 3 and a voice coil motor 4 between the reflector support 2 and a base 6, installing two voice coil motors 4 between the reflector support 2 and the base 6 along the x axis and the y axis respectively, installing two differential measurement micro-displacement sensors 5 on the base 6 along the x axis and the y axis respectively, and controlling a fast-reflecting mirror by a controller 7.

When the voice coil motor fast reflector sliding mode neural network controller 7 works, according to a received position instruction, a difference is made between the received position instruction and a position measurement signal of the micro displacement sensor 5 to obtain a position error, the sliding mode neural network controller serving as a position ring generates corresponding output according to the position error to drive the voice coil motor 4, and the reflector is adjusted to rotate around an x axis and a y axis until a specified position is reached.

According to the neural network sliding mode control method of the two-axis voice coil quick reflector, the two-axis voice coil motor quick reflector is decoupled, the voice coil motors arranged on the two axes are in the same specification, namely the rotation of the mirror surface around the x axis and the rotation of the mirror surface around the y axis can be independently controlled and do not influence each other, so that the control on the two axes is completely the same. Thus, the example selects control about the x-axis to illustrate the method.

The neural network sliding mode control method of the two-axis voice coil fast reflector can calculate the sliding mode variable by using the position error and the differential of the position error on the basis of not needing a system model, and constructs the neural network based on the basis of the basis function by taking the sliding mode variable as input, and the output of the neural network controls the voice coil motor fast reflector mechanism. And the neural network has simple structure, and the weight value is updated on line only according to the sliding mode reachable condition. The method integrates robustness of sliding mode control and self-adaptive learning capability of a neural network, can effectively inhibit adverse effects caused by sudden change of system parameters and external disturbance, and improves the control performance of the voice coil motor fast-response mirror.

When the two-axis voice coil motor fast reflection mirror actually works, the fast reflection mirror faces the influence of environmental factors such as temperature, electromagnetic interference, vibration, dust, wind resistance and the like, and the factors can cause the parameter change of a system model or act in a system in an external interference mode, so that the performance of the system is reduced, and even the system is unstable. The neural network sliding mode control method of the two-axis voice coil fast reflector not only can utilize sliding mode control to deal with output change caused by external interference, but also can utilize the online learning capacity of the neural network to deal with performance reduction caused by model parameter change, and can ensure the stability of the system. The neural network sliding mode control method of the two-axis voice coil fast reflector solves the problems that an existing voice coil motor reflector control method is poor in model parameter disturbance robustness and weak in external disturbance resistance.

In order to quantitatively illustrate the control effect of the neural network sliding mode control method of the two-axis voice coil fast reflector, the root mean square error is defined as

Where N is the number of sample points. It is desirable to track the input signal x in the experiment_d17.4sin (6.28t), i.e. a sinusoidal signal with amplitude of 17.4mrad and frequency of 1Hz, and then experiments were performed with the neural network sliding mode controller shown in equation (16-17). FIG. 3 shows the tracking effect of the method of the present invention when the analog controller tracks the input command signal and the equivalent moment of inertia J has a sudden change. The first 4 seconds in fig. 3 are the case of tracking command signals, and it can be seen from the figure that the output reaches the designated value quickly after a short deviation, the moment of inertia J suddenly increases by 10% at the 4 th time, and the condition of sudden change of the simulation parameter, and it can be seen from fig. 3 that after a short fluctuation with a large amplitude, the output stably tracks the input command signal again, and the tracking error x is_RMS0.1351mrad, while the tracking error is x using the conventional PID method_RMS0.8634 mrad. FIG. 4 is a graph illustrating the tracking effect of the method of the present invention when applied disturbance is received under simulated steady state. In fig. 4, the first 4 seconds are steady-state conditions, the 4 th second sudden interference d is 0.05cos (502.4t), t is greater than or equal to 4s, it can be seen from the figure that after a short small oscillation, the output can still stably track the command signal, and the tracking error is x_RMS0.0699mrad, while the tracking error is x using the conventional PID method_RMS0.2383 mrad. Therefore, by adopting the neural network sliding mode control method, the output of the fast reflecting mirror still has a tracking effect far superior to that of the traditional PID method under the conditions of parameter disturbance and external disturbance.

Parameters of the voice coil motor in the simulation process are as follows: armature resistor R of voice coil motor_a5 omega, voice coil motor armature inductance L_a0.08 muH, 0.005Ns/m, 35mm distance L between the action point of driver and rotary shaft, and mass m of voice coil load_c60.21g, torque coefficient C_m8.1, back emf coefficient C_e8.1, moment of inertia J161.215 × 10^-6kg·m². The controller parameters were taken as: n is 7, λ is 10, γ is 10, and the initial weight of the neural network is taken as the interval [0, 0.01%]Inner random number, perturbation d ═ 0.005sin (502.4 t).

The invention discloses a neural network sliding mode control method of a two-axis voice coil fast reflector, which solves the problems of poor robustness to model parameter disturbance and weak external disturbance resistance in the prior art. The voice coil motor is converted into a torque controller equivalent to an available proportional link by constructing a current loop, so that the output torque of the voice coil motor and the control current are in a linear relation, the quick reflection mirror mechanical part is decoupled into two independent single-degree-of-freedom second-order torsional vibration systems, and the second-order systems are converted into a state equation; position errors are defined, and a sliding mode controller of constant speed approach rate is designed to restrain the problems caused by disturbance and parameter perturbation; and then designing a neural network to carry out online estimation on the sliding mode controller, wherein the output voltage of the neural network is used as the given value of the torque controller. On the basis of not changing the existing system and sensor, the method has robustness on parameter perturbation and system external disturbance, can meet the performance requirement of the voice coil motor reflector, does not adopt a sign function to design a sliding mode controller, and has higher practicability.