CN111025915B - Z-axis gyroscope neural network sliding mode control method based on disturbance observer - Google Patents

Abstract

The application discloses a Z-axis gyroscope neural network sliding mode control method based on a disturbance observer. In this method, on the basis of obtaining the tracking error of the micro-gyroscope and the designed sliding surface, the RBF neural network is used to estimate the time-varying angular velocity parameter matrix. Variable angular velocity parameter matrix and disturbance observer design micro-gyroscope control law. Finally, the continuously changing angular velocity signal and unknown external disturbances are correctly estimated. The method of the invention can use the neural network to estimate the time-varying angular velocity under the condition that the angular velocity changes continuously, and complete the self-adaptive adjustment of the weight by designing the self-adaptive law of the weight of the neural network. At the same time, when the external interference of the system is unknown, the interference observer is used to estimate the external interference, which can effectively reduce the chattering of the system and improve the measurement accuracy of the MEMS gyroscope.

Description

A Neural Network Sliding Mode Control Method for Z-axis Gyroscope Based on Disturbance Observer

technical field

The invention relates to the field of automatic control systems, in particular to a Z-axis gyroscope neural network sliding mode control method based on disturbance observers.

Background technique

MEMS gyroscope is a sensor produced by micro-electromechanical system processing technology, which is used to measure angular velocity. MEMS gyroscopes can be divided into vibration type, microfluidic type, solid type and suspended rotor type. The most common of these is the vibrating MEMS gyroscope. The MEMS gyroscope uses the Coriolis theorem to convert the angular velocity of a rotating object into a DC voltage signal proportional to the angular velocity, thereby calculating the angular velocity. MEMS gyroscopes have the advantages of small size, low power consumption, and low cost, and have broad application prospects in inertial navigation, consumer electronics, and modern defense. Due to defects in manufacturing technology, the structure of the gyroscope is not completely symmetrical. This asymmetric structure will cause unnecessary mechanical coupling and reduce the measurement accuracy of the gyroscope. At the same time, the parameter uncertainty caused by processing errors and the external disturbance of the system will also degrade the performance of the MEMS gyroscope.

In the gyroscope control system, the adaptive sliding mode control is usually used to realize the desired trajectory tracking and the estimation of the angular velocity signal is completed through the adaptive algorithm. However, traditional adaptive algorithms are only suitable for long-term constant angular velocity signals. However, in actual situations, the angular velocity of the object's rotation changes, which makes the traditional adaptive algorithm unable to accurately estimate the time-varying angular velocity. Considering that the neural network has the ability to approximate any function, the RBF neural network is used to estimate the angular velocity signal.

The external interference of the gyroscope system is the main source of system chattering. Conventional sliding mode control is derived when the external disturbance is known. However, in practical situations, the upper bound of external interference is unknown. At this time, a larger switching gain needs to be selected, which will cause stronger chattering. Therefore, the disturbance observer is used to observe and estimate the external disturbance, so as to ensure the stability and trajectory tracking performance of the system.

Since the RBF neural network can approximate any continuous function, it can also be applied to the measurement of time-varying angular velocity signals. For unknown external interference, the interference observer can be used for observation and estimation. Compared with the traditional adaptive algorithm, the RBF neural network can correctly estimate the continuously changing angular velocity signal and effectively reduce control chattering.

Contents of the invention

In view of this, the object of the present invention is to provide a Z-axis gyroscope neural network sliding mode control method based on a disturbance observer, aiming at estimating the time-varying angular velocity by using a neural network, and using the disturbance observer to estimate the unknown external disturbance. Observation and estimation reduce system chattering and ensure system stability.

In order to solve the above-mentioned technical problems, the invention provides a Z-axis gyroscope neural network sliding mode control method based on a disturbance observer, comprising the following steps:

1) set up micro-gyroscope dynamics model, output micro-gyroscope motion track according to said model;

The model is shown in the following formula:

In the above formula,

Among them, q is the trajectory of the gyroscope, u is the control input of the gyroscope, D is the damping parameter matrix, K is the spring parameter matrix, Ω is the time-varying angular velocity parameter matrix, and d is the external disturbance;

2) Calculate the tracking error according to the micro-gyroscope motion trajectory obtained in step 1), and set up the sliding mode surface according to the tracking error;

The tracking error is shown in the following formula:

e=q _d -q (2)

Among them, e is the tracking error, and q _d is the reference trajectory of the micro-gyroscope movement;

The sliding mode surface is established according to the following formula:

Among them, S is the sliding mode surface, and λ is the parameter of the sliding mode surface;

3) using the RBF neural network to take the tracking error as an input vector, and output an estimated time-varying angular velocity parameter matrix;

The estimated time-varying angular velocity parameter matrix is:

为估计时变角速度参数矩阵，

分别为对应的RBF神经网络权值，φ₁，φ₂为高斯基函数；in,

To estimate the time-varying angular velocity parameter matrix,

are the corresponding RBF neural network weights, φ ₁ and φ ₂ are Gaussian functions;

4) According to the micro-gyroscope trajectory obtained in step 1), the estimated time-varying angular velocity parameter matrix obtained in step 3) and the control law design disturbance observer of the micro-gyroscope;

The disturbance observer is:

为对干扰d的估计，

为

的一阶导数，

为q的一阶导数，

为对

的估计，k₁、k₂为常数，并且k₁＞0，k₂＞0；in,

is an estimate of the disturbance d,

for

The first derivative of ,

is the first derivative of q,

for right

The estimation of , k ₁ and k ₂ are constants, and k ₁ >0, k ₂ >0;

5) according to described sliding mode surface, step 3) the estimated time-varying angular velocity parameter matrix that obtains and step 4) obtain the disturbance observer design the control law of micro-gyroscope;

The control law of the micro gyroscope is:

为q的一阶导数，

为q_d的一阶导数，ρ为切换增益，sgn()为符号函数；Among them, u is the control law of the micro gyroscope,

is the first derivative of q,

is the first derivative of _qd , ρ is the switching gain, and sgn() is the sign function;

6) Based on the Lyapunov stability theory, design the Lyapunov function, design the update algorithm of the RBF neural network weight according to the Lyapunov function, and apply the update algorithm to the RBF neural network to ensure that the tracking error converges to zero and guarantees system stability;

The Lyapunov function is:

为外界干扰估计误差，

为微陀螺仪速度的估计误差，

为权值估计误差，

为神经网络理想权值；Wherein, η ₁ and η ₂ are RBF neural network weight adaptive law gain parameters, which are taken as positive numbers,

is the estimation error of the external disturbance,

is the estimation error of the micro-gyroscope velocity,

is the weight estimation error,

is the ideal weight of the neural network;

The update algorithm is:

为微陀螺仪在X，Y轴上的速度，S₁，S₂为滑模面S在X，Y轴上的分量，

为微陀螺仪速度的估计误差

在X，Y轴上的分量。in,

is the speed of the micro gyroscope on the X and Y axes, S ₁ and S ₂ are the components of the sliding surface S on the X and Y axes,

is the estimation error of the micro-gyroscope velocity

Components on the X,Y axes.

Compared with the prior art, the present invention discloses a Z-axis gyroscope neural network sliding mode control method based on a disturbance observer. The method is based on obtaining the tracking error of the micro gyroscope and the designed sliding mode surface, based on For the tracking error and sliding mode surface, the RBF neural network is used to estimate the time-varying angular velocity parameter matrix, and the disturbance observer is designed according to the motion trajectory, the micro-gyroscope control law and the estimated time-varying angular velocity parameter matrix, and according to the The sliding mode surface, the estimated time-varying angular velocity parameter matrix and the disturbance observer design micro-gyroscope control law. Finally, the continuously changing angular velocity signal and unknown external disturbances are correctly estimated. It can be seen that the application of the method of the present invention can effectively compensate system parameter errors and external disturbances, effectively improve the control effect and parameter estimation effect, and further improve the measurement accuracy of the micro gyroscope.

The method of the invention can use the RBF neural network to estimate the time-varying angular velocity under the condition that the angular velocity changes continuously and the external disturbance is unknown, and completes the adaptive adjustment of the weight by designing the neural network weight adaptive law, so as to realize the time-varying angular velocity estimate. At the same time, a disturbance observer is used to estimate the unknown disturbance of the system to ensure the stability of the system and improve the measurement accuracy of the gyroscope. Compared with the traditional self-adaptive algorithm, the present invention can use the disturbance observer to estimate the external disturbance and use the neural network to estimate the time-varying angular velocity under the condition that the gyro system measures the time-varying angular velocity and the external disturbance is unknown, so as to avoid inaccurate estimation of the angular velocity and system chattering to ensure system stability.

The adaptive laws designed in the present invention are all based on the Lyapunov stability theory, so the stability of the system can be guaranteed.

Description of drawings

Fig. 1 is the schematic diagram of the Z-axis gyroscope neural network sliding mode control method based on disturbance observer provided by the present invention;

Fig. 2 is X, Y axis position tracking curve in the specific embodiment of the present invention;

Fig. 3 is X, Y axis position tracking error curve in the specific embodiment of the present invention;

Fig. 4 is the time-varying angular velocity identification curve of the Z-axis gyroscope in a specific embodiment of the present invention;

FIG. 5 is an estimation curve of external interference of a Z-axis gyroscope in a specific embodiment of the present invention.

Detailed ways

In order to further understand the present invention, the preferred embodiments of the present invention are described below in conjunction with the examples, but it should be understood that these descriptions are only to further illustrate the features and advantages of the present invention, rather than limiting the claims of the present invention.

Please refer to Fig. 1, the present invention provides a kind of Z-axis gyroscope neural network sliding mode control method based on disturbance observer, comprises the following steps:

1) Establish a micro-gyroscope dynamics model, output the micro-gyroscope motion track according to the model:

The mathematical model of the micro gyroscope is:

Among them, x, y are the displacement of the micro gyroscope in the direction of X, Y axis, u _x , u _y are the control input of the micro gyroscope in the direction of X, Y axis, d _xx , d _yy are the direction of X, Y axis The elastic coefficient of the spring, ω _xx and ω _yy are the damping coefficients in the X and Y axis directions, d _xy , d _yx , ω _xy , ω _yx are the coupling parameters caused by machining errors, etc., Ω _z is the angular velocity of the mass block’s rotation.

The mathematical model of the micro gyroscope shown in formula (9) is written as a state space expression:

In the above formula, q ₁ =q,

Among them, q is the trajectory of the gyroscope, u is the control input of the gyroscope, D is the damping parameter matrix, K is the spring parameter matrix, and Ω is the angular velocity parameter matrix.

Considering the external disturbance, the dynamic model of the micro gyroscope can be written as:

In formula (11), d is external disturbance.

2) Calculate the tracking error according to the motion trajectory of the micro-gyroscope obtained in step 1), and establish the sliding mode surface according to the tracking error:

Define the tracking error of the micro gyroscope as:

e=q _d -q (12)

为理想振动轨迹，

为实际振动轨迹。In formula (12),

is the ideal vibration trajectory,

is the actual vibration trajectory.

According to the tracking error, the sliding mode surface is designed as:

In formula (13), λ is the sliding mode surface parameter, which is taken as a second-order diagonal matrix, and its diagonal elements are positive numbers.

3) using the RBF neural network to take the tracking error as an input vector, and output an estimated time-varying angular velocity parameter matrix;

The unknown angular velocity of the system will lead to the decline of control performance, therefore, it is necessary to estimate the angular velocity of the system. In actual situations, the angular velocity is not constant for a long time, but changes continuously. The RBF neural network can be used to approximate the time-varying angular velocity parameter matrix of the micro-gyroscope.

满足

σ₁，σ₂为逼近误差，并且逼近误差是有界的，即满足|σ₁|＜σ_1d，|σ₂|＜σ_2d，σ_1d，σ_2d为逼近误差的上界，理论上神经网络的逼近误差可以使得逼近误差上界σ_1d，σ_2d趋近于0。Use the RBF neural network to estimate all the parameters in the time-varying angular velocity parameter matrix of the micro-gyroscope, and when using the neural network to approximate the time-varying angular velocity of the system, there is an optimal weight

Satisfy

σ ₁ , σ ₂ are the approximation errors, and the approximation errors are bounded, that is, |σ ₁ |<σ _1d , |σ ₂ |<σ _2d , σ _1d , σ _2d are the upper bounds of the approximation errors. In theory, neural The approximation error of the network can make the upper bounds of the approximation error σ _1d , σ _2d close to 0.

可以表示为：Time-varying angular velocity parameter matrix

It can be expressed as:

为估计时变角速度参数矩阵，

分别为所对应的RBF神经网络权值，φ₁，φ₂为高斯基函数；In formula (14),

To estimate the time-varying angular velocity parameter matrix,

are the corresponding RBF neural network weights, φ ₁ and φ ₂ are Gaussian functions;

4) According to the micro-gyroscope trajectory obtained in step 1), the estimated time-varying angular velocity parameter matrix obtained in step 3) and the control law design disturbance observer of the micro-gyroscope;

In practical situations, the external interference of the system is unknown. Therefore, a relatively large switching gain is generally set to deal with interference. At this time, the influence caused by relatively large switching gain is chattering of the control force signal. Therefore, the robust term needs to be improved. Since the external disturbance is generally difficult to determine, the disturbance observer can be used to estimate the external disturbance, and the robust item can be determined according to the estimated external disturbance, so as to ensure the stability and trajectory tracking performance of the system.

The disturbance observer is:

为对干扰d的估计，

为

的一阶导数，

为q的一阶导数，

为对

的估计，k₁、k₂为常数，并且k₁＞0，k₂＞0。In formula (15),

is an estimate of the disturbance d,

for

The first derivative of ,

is the first derivative of q,

for right

The estimation of , k ₁ and k ₂ are constants, and k ₁ >0, k ₂ >0.

5) according to described sliding mode surface, step 3) the estimated time-varying angular velocity parameter matrix that obtains and step 4) obtain the disturbance observer design the control law of micro-gyroscope;

可以得到等效控制律为Regardless of external interference and parameter uncertainty, the sliding mode surface is derived and the sliding mode surface derivative

The equivalent control law can be obtained as

为q的导数，

为q_d的导数。In formula (16), u _eq is the equivalent control law of the micro gyroscope,

is the derivative of q,

is the derivative of q _d .

According to the sliding surface S, the robust term of the designed control law is:

u _s = ρsgn(S) (17)

Among them, u _s is the robust term of micro-gyroscope control law, ρ is the switching gain, and sgn() is the sign function.

When the system model and external disturbances are completely known, the final control law can be designed as

Among them, u is the control law of the micro gyroscope.

Since the control law contains the angular velocity matrix Ω of the system, in actual situations the angular velocity Ω is not a constant value, but time-varying. Therefore, the designed control law is difficult to implement in practical situations. The neural network can be used to estimate the time-varying angular velocity, and the estimated value of the angular velocity can be used to replace its real value to complete the control law signal design, and the neural network weight update algorithm can be designed to update the estimated value of the system parameters online.

Due to the actual situation, external interference is unknown. The disturbance observer is used to observe and estimate the external disturbance, and the estimated output of the disturbance observer is brought into the control law to improve the control performance of the existing controller.

Use the estimated value of the time-varying angular velocity parameter matrix instead of its real value to design the control law, and at the same time bring the estimated value of the disturbance observer into it, the control law is designed as

为微陀螺仪外界干扰的估计值，估计偏差为

in,

is the estimated value of the external disturbance of the micro gyroscope, and the estimated deviation is

6) Based on the Lyapunov stability theory, design the Lyapunov function, design the update algorithm of the RBF neural network weight according to the Lyapunov function, and apply the update algorithm to the RBF neural network to ensure that the tracking error converges to zero and guarantees system stability;

The Lyapunov function is:

为外界干扰估计误差，

为微陀螺仪速度的估计误差，

为权值估计误差，

为神经网络理想权值；Wherein, η ₁ and η ₂ are RBF neural network weight adaptive law gain parameters, which are taken as positive numbers,

is the estimation error of the external disturbance,

is the estimation error of the micro-gyroscope velocity,

is the weight estimation error,

is the ideal weight of the neural network;

Induce it, get

趋近于零，当k₁取较大值时，可认为：For the external disturbance d, it is assumed that its change is very slow, so,

tends to zero, when k ₁ takes a larger value, it can be considered as:

Substituting the control law, the disturbance observer and equation (22) into equation (21), we get

设计所述更新算法为in order to get

The update algorithm is designed as

为微陀螺仪在X，Y轴上的速度，S₁，S₂为X，Y轴上的滑模面，

为X，Y轴上微陀螺仪速度的估计误差。in,

is the speed of the micro gyroscope on the X and Y axes, S ₁ and S ₂ are the sliding surface on the X and Y axes,

is the estimation error of the micro-gyroscope velocity on the X and Y axes.

Bringing the Lyapunov stability theory update algorithm into (23), we get

The property of the matrix trace is used in the proof

Take the switching gain slightly greater than the upper bound of the external interference estimation error, that is,

σ₃为正数，

σ ₃ is a positive number,

From hypothesis 2 we know

Stability is proven.

5) Computer simulation experiment

According to the Z-axis gyroscope neural network sliding mode control method based on the disturbance observer, a computer simulation experiment is carried out on the control method of the present invention in MATLAB/SIMULINK. The parameters of the micro gyroscope in the simulation experiment are as follows:

m = 1.8×10 ^-7 kg, k _xx = 63.955N/m, k _yy = 95.92N/m, k _xy = 12.779N/m,

d _xx = 1.8×10 ^-6 N·s/m, d _yy = 1.8×10 ^-6 N·s/m, d _xy = 3.6×10 ^-7 N·s/m

The unknown input angular velocity is assumed to be Ω _z =10000 sin(0.3t)rad/s. The reference length is selected as q ₀ =1μm, and the reference frequency ω ₀ =1000Hz. After non-dimensionalization, the parameters of the micro gyroscope are as follows:

ω_xy＝70.99，d_xx＝0.01，d_yy＝0.01，d_xy＝0.002，Ω＝10sin(0.3t)

ω _xy =70.99, d _xx =0.01, d _yy =0.01, d _xy =0.002, Ω=10sin(0.3t)

干扰取为

The initial state of the controlled object is taken as X ₀ =[0.1 0 0.1 0], the reference trajectory

Interference is taken as

Sliding mode surface coefficient

Neural network parameter identification part parameters are taken as: η ₁ =0.5, η ₂ =0.5

The robust gain value of fixed robust gain is set as: ρ=80

Some parameters of the disturbance observer are taken as: k ₁ =100, k ₂ =20

Fig. 2 is the X, Y-axis position tracking performance curve in the specific implementation example of the present invention; wherein the dotted line is the actual track, and the solid line is the ideal track. It can be seen from the figure that the trajectory of the micro-gyroscope can track the ideal trajectory very well by adopting the Z-axis gyroscope neural network sliding mode control based on the disturbance observer.

Fig. 3 is the X, Y axis position tracking error curves in the embodiment of the present invention; As can be seen from the figure, the tracking error can quickly converge to 0, and the convergence speed is very fast, which shows that the control effect of the present invention is very ideal.

Fig. 4 is the time-varying angular velocity identification curve of the Z-axis gyroscope in the specific implementation example of the present invention; Wherein, the solid line is the true value of the time-varying angular velocity parameter, and the dotted line is the approximation value of the neural network to the time-varying angular velocity; as can be seen from the figure , the neural network can approximate the time-varying angular velocity well in real time.

Fig. 5 is the Z-axis gyroscope external interference estimation curve in the concrete implementation example of the present invention; Wherein, solid line is the true value of external interference, and dotted line is the estimated value of interference observer to external interference; As can be seen from the figure, interference observation The device can quickly converge to the true value of the external disturbance, realizing the compensation for the external disturbance of the system.

It can be seen from the above simulation diagram that the control method proposed by the present invention can realize trajectory tracking well, and can effectively estimate the time-varying angular velocity and unknown external disturbances in the face of unknown external disturbances of angular velocity, ensuring system stability.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above-mentioned exemplary embodiments, and without departing from the spirit or basic principles of the present invention. The present invention can be implemented in other specific forms without any specific features. Accordingly, the embodiments should be regarded in all points of view as exemplary and not restrictive, the scope of the invention being defined by the appended claims rather than the foregoing description, and it is therefore intended that the scope of the invention be defined by the appended claims rather than by the foregoing description. All changes within the meaning and range of equivalents of the elements are embraced in the present invention. Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications and substitutions can be made to these embodiments without departing from the principle and spirit of the present invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.

Claims (1)

1. a Z-axis gyroscope neural network sliding mode control method based on disturbance observer, is characterized in that, comprises the following steps: 1) set up micro-gyroscope dynamics model, output micro-gyroscope motion track according to said model; The model is shown in the following formula:

in,

Among them, q is the trajectory of the gyroscope, u is the control input of the gyroscope, D is the damping parameter matrix, K is the spring parameter matrix, Ω is the time-varying angular velocity parameter matrix, and d is the external disturbance; 2) calculate the tracking error according to the micro-gyroscope motion track that step 1) obtains, set up the sliding mode surface according to the tracking error; The tracking error is shown in the following formula: e=q _d -q; Among them, e is the tracking error, and q _d is the reference trajectory of the micro-gyroscope movement; The sliding mode surface is established according to the following formula:

Among them, S is the sliding mode surface, and λ is the parameter of the sliding mode surface; 3) using the RBF neural network to take the tracking error as an input vector, and output an estimated time-varying angular velocity parameter matrix; The estimated time-varying angular velocity parameter matrix is:

in,

To estimate the time-varying angular velocity parameter matrix,

are the corresponding RBF neural network weights, φ ₁ and φ ₂ are Gaussian functions; 4) According to the micro-gyroscope trajectory obtained in step 1), the estimated time-varying angular velocity parameter matrix obtained in step 3) and the control law design disturbance observer of the micro-gyroscope; The disturbance observer is:

in,

is an estimate of the disturbance d,

for

The first derivative of ,

is the first derivative of q,

for right

The estimation of , k ₁ and k ₂ are constants, and k ₁ >0, k ₂ >0; 5) according to described sliding mode surface, step 3) the estimated time-varying angular velocity parameter matrix that obtains and step 4) obtain the disturbance observer design the control law of micro-gyroscope; The control law of the micro gyroscope is:

Among them, u is the control law of the micro gyroscope,

is the first derivative of q,

is the first derivative of _qd , ρ is the switching gain, and sgn() is the sign function; 6) Based on the Lyapunov stability theory, design the Lyapunov function, design the update algorithm of the RBF neural network weight according to the Lyapunov function, and apply the update algorithm to the RBF neural network to ensure that the tracking error converges to zero and guarantees system stability; The Lyapunov function is:

Wherein, η ₁ and η ₂ are the corresponding RBF neural network weight adaptive law gain parameters respectively, which are taken as positive numbers,

is the estimation error of the external disturbance,

is the estimation error of the micro-gyroscope velocity,

is the weight estimation error,

is the ideal weight of the neural network; The update algorithm is:

in,

is the speed of the micro gyroscope on the X and Y axes, S ₁ and S ₂ are the components of the sliding surface S on the X and Y axes,

is the estimation error of the micro-gyroscope velocity

Components on the X, Y axes.

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