CN105929694A - Adaptive neural network nonsingular terminal sliding mode control method for micro gyroscope - Google Patents

Abstract

The invention discloses an adaptive neural network nonsingular terminal sliding mode control method for a micro gyroscope. The method includes the steps of the establishing a mathematical model of the micro gyroscope, approximating the sum of the dynamic characteristics and external disturbance of the micro gyroscope by using a neural network control method, designing an adaptive neural network nonsingular terminal sliding mode device based on a dynamic surface; and controlling the micro gyroscope by using the adaptive neural network nonsingular terminal sliding mode device based on the dynamic surface. Through the method, a micro gyroscope system can rapidly reach a stable state, and manufacturing error and environment interference can be compensated. The algorithm designed based on dynamic surface method reduces parameters introduced, simplifies calculation and minimizes buffeting. Meanwhile, a nonsingular terminal sliding mode is introduced in the method to ensure that the system state converges in the sliding phase for a finite time and the control rules have no negative exponential terms, so that the effectiveness of the system can be improved.

Description

A kind of microthrust test adaptive neural network non-singular terminal sliding-mode control

Technical field

The present invention relates to gyroscope dynamic control technology field, a kind of microthrust test self adaptation based on dynamic surface Neutral net non-singular terminal synovial membrane control method.

Background technology

Gyroscope is that the navigation being widely used in Aeronautics and Astronautics, navigation and land vehicle is opened with location and oil field prospecting Send out and wait military, the measurement inertial navigation of civil area and the sensor of inertial guidance system angular velocity.Compared with conventional gyro, Gyroscope has big advantage on volume and cost.But, due to the existence of error and the external world during manufacturing The impact of ambient temperature, causes the difference between original paper characteristic and design, causes stiffness coefficient and the damped coefficient that there is coupling, Reduce sensitivity and the precision of gyroscope.It addition, gyroscope self belongs to multi-input multi-output system, there is parameter not Definitiveness and under external interference systematic parameter easily fluctuate, therefore, reduce system chatter become gyroscope control main One of problem.

Summary of the invention

It is an object of the invention to provide a kind of microthrust test adaptive neural network non-singular terminal sliding-mode control, its tool Have buffeting low, reliability is high, the feature high to Parameters variation robustness.

The technical scheme that the present invention takes is particularly as follows: a kind of microthrust test adaptive neural network non-singular terminal sliding formwork controls Method, comprises the following steps:

Step one, sets up the mathematical model of gyroscope:

Step 2, utilizes neural network control method to approach dynamic characteristic and the external interference sum of gyroscope；

Step 3, based on Dynamic Surface Design adaptive neural network non-singular terminal sliding mode controller；

Step 4, the adaptive neural network non-singular terminal sliding mode controller utilizing step 3 to design controls microthrust test Instrument.

The principle of the present invention is: adaptive neural network non-singular terminal sliding-mode control based on dynamic surface applied In the middle of gyroscope, the gyroscope dynamic model of the approximate ideal of one band noise of design, as system reference track, whole Individual microthrust test adaptive neural network non-singular terminal sliding formwork based on dynamic surface controls to ensure actual gyroscope trajectory track Upper reference locus, reaches a kind of preferably dynamic characteristic, compensate for foozle and environmental disturbances, reduce the buffeting of system.Root According to the parameter of gyroscope own and input angle speed, the dynamic surface control device of one Parameter adjustable of design and adaptive neural network net Network controller, using the tracking error signal of system as the input signal of controller, the initial value of any setting controller parameter, protect Card tracking error converges on zero, and the most all estimates of parameters converge on true value.

In step one, the mathematical model of gyroscope is:

$\left\{\begin{array}{c}m\stackrel{\·\·}{x}+d_{xx}\stackrel{\·}{x}+d_{xy}\stackrel{\·}{y}+k_{xx}x+k_{xy}y=u_x+2{\mathrm{m\Ω}}_z\stackrel{\·}{y}\\ m\stackrel{\·\·}{y}+d_{xy}\stackrel{\·}{x}+d_{yy}\stackrel{\·}{y}+k_{xy}x+k_{yy}y=u_y-2{\mathrm{m\Ω}}_z\stackrel{\·}{x}\end{array}\right.$

Wherein, x, y represent gyroscope displacement in X, Y direction, d respectively_xx、d_yyIt is respectively X, Y of gyroscope The coefficient of elasticity of direction of principal axis spring, k_xx、k_yyIt is respectively gyroscope at X, the damped coefficient of Y direction, d_xy、k_xyFor processing by mistake The coupling parameter that difference etc. causes, m is the quality of gyroscope mass, Ω_zFor the angular velocity of mass rotation, u_x、u_yIt is respectively X, the input of Y-axis control power, and shape is such asParameter represent the first derivative of Γ, shape is such asParameter represent the second dervative of Γ；

Preferably, the present invention carries out nondimensionalization and processes and obtain nondimensionalization model model:

Both members is simultaneously divided by m, and makes Then nondimensionalization model is:

Model is rewritten into vector form:

$\stackrel{\·\·}{q}+D\stackrel{\·}{q}+Kq=u-2\mathrm{\Ω}\stackrel{\·}{q}$

Wherein, u is dynamic surface control rule,

Considering that systematic parameter is uncertain and external interference, model is write as:

$\stackrel{\·\·}{q}+(D+\mathrm{\Δ}D)\stackrel{\·}{q}+(K+\mathrm{\Δ}K)q=u-2\mathrm{\Ω}\stackrel{\·}{q}+d$

Wherein Δ D, Δ K are parameter perturbations, and d is external interference；

Model is write as state equation form is:

$\left\{\begin{array}{c}{\stackrel{\·}{q}}_1=q_2\\ {\stackrel{\·}{q}}_2=-(D+\mathrm{\Δ}D+2\mathrm{\Ω})\stackrel{\·}{q}-(K+\mathrm{\Δ}K)q+u+d\end{array}\right.$

Wherein, q₁=q,

Q=x will be defined for the ease of calculating₁,x₁、x₂For input variable；

Then the state equation of gyroscope model becomes following formula:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f+u\end{array}\right.$

Wherein f is dynamic characteristic and the external interference sum of gyroscope, and:

F=-(D+ Δ D+2 Ω) x₂-(K+ΔK)x₁+d。

RBF (RBF) neutral net has a kind of forward direction three-layer network topological structure.Wherein, input layer simply letter Number receiving layer does not do any signal processing.The dimension of input layer is relevant to the dimension of concrete signal, such as neutral net in this example Input signal is x, and it is four dimensional vectors, therefore RBF network input layer has four input nodes.Intermediate layer is hidden layer, implements The nonlinear mapping effect of signal, is mapped to more higher-dimension by signal from the input space, the hidden layer space of signal characteristic linear separability. Output layer does sum operation with coefficient, produces the output of RBF network.

Preferably, in step 2 of the present invention, utilize RBF neural principle, useApproach f, including step:

With the x (t) input vector as RBF neural, x (t) refers to and includes x₁、x₂Input variable；If RBF nerve net The radial direction base vector h=[h of network₁,h₂,h₃... h_m]^T, wherein h_iFor Gaussian bases, it may be assumed that

$h_i=\exp (-\frac{\left|\right|x\left(t\right)-c_i|{|}^2}{2b_i^2}),i=1,2,...,m$

In formula, c=[c₁,c₂,c₃,…c_m]^TIt is the center vector of network hidden layer node, with the dimension phase of input vector With；

B=[b₁,b₂,b₃,…b_m]^TBeing the sound stage width vector of network hidden layer node, m is hidden layer neuron number, RBF net Network input layer is 1 to the weights of hidden layer, and network hidden layer to output layer weight vector is W=[w₁,w₂,w₃,…w_m]^T；

RBF network is output as:

Y=h^T*W

h^TTransposition for RBF；

By the c of RBF neural_iAnd b_iKeep fixing, and only regulating networks weights W, then the output of RBF neural with Hidden layer output is linear；

RBF neural is output as:

$\hat{f}=h^T\hat{W}$

With the output of neutral netApproach dynamic characteristic f of gyroscope；

Definition best approximation constant, W^*

$W^{*}=\arg \underset{W\∈\mathrm{\Ω}}{min}\[sup|\hat{f}-f|\]$

Ω is the set of W.

Order

$\tilde{W}=\hat{W}-W^{*}$

Then:

F=h^TW^*+ε

$f-\hat{f}=h^T{W}^{*}+\mathrm{\ϵ}-h^T\hat{W}=-h^T\tilde{W}+\mathrm{\ϵ}$

Wherein ε is the approximate error of neutral net, sets up for given arbitrarily small constant ε (ε ＞ 0), such as lower inequality: |f-h^TW^*|≤ε。

Preferably, step 3 of the present invention comprises the following steps:

Definition site error

z₁=x₁-x_1d

Wherein x_1dFor instruction references signal, then

${\stackrel{\·}{z}}_1={\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d}$

Definition Lyapunov function isWhereinFor z₁Transposition, then

${\stackrel{\·}{V}}_1={z_1}^T{\stackrel{\·}{z}}_1={z_1}^T({\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d})={z_1}^T(x_2-{\stackrel{\·}{x}}_{1d})$

For ensureingIntroduceFor x₂Virtual controlling amount, definition

${\stackrel{\‾}{x}}_2=-c_1{z}_1+{\stackrel{\·}{x}}_{1d}$

c₁For the constant more than 0；

For the phenomenon overcoming differential to explode, introduce low pass filter: take α₁For low pass filterAbout input it isTime output, and meet:

$\left\{\begin{array}{c}\mathrm{\τ}{\stackrel{\·}{\mathrm{\α}}}_1+{\mathrm{\α}}_1={\stackrel{\‾}{x}}_2\\ {\mathrm{\α}}_1\left(0\right)={\stackrel{\‾}{x}}_2\left(0\right)\end{array}\right.$

Wherein τ is filter time constant, for the constant more than 0, α₁For the output of low pass filter, α₁(0)、 It is respectively α₁WithInitial value:

${\stackrel{\·}{\mathrm{\α}}}_1=\frac{{\stackrel{\‾}{x}}_2-{\mathrm{\α}}_1}{\mathrm{\τ}}$

Produced filtering error is:

$y_2={\mathrm{\α}}_1-{\stackrel{\‾}{x}}_2$

Definition virtual controlling error: z₂=x₂-α₁, then

Second Lyapunov function is defined as:

$V_2=\frac{1}{2}{z_2}^T{z_2}^2$

In order to ensure

It is defined as microthrust test design dynamic surface non-singular terminal sliding-mode surface:

$s={\[s_1,s_2\]}^T=z_1+\frac{1}{\mathrm{\β}}{z_2}^{p_1/p_2}$

In formula, β=diag (β₁,β₂) it is sliding-mode surface constant, β₁,β₂It is normal number, p₁,p₂For positive odd number, and 1 ＜ p₁/p₂＜ 2；

For makingFor microthrust test system, using dynamic surface non-singular terminal sliding-mode surface, design dynamic surface is nonsingular TSM control rule is:

U=u₀+u₁+u₂+u₃

Wherein,

$u_0=-f+{\stackrel{\·}{\mathrm{\α}}}_1$

$u_1=-\frac{p_2}{p_1}\mathrm{\β}diag\left({z_2}^{1-p_1/p_2}\right){\stackrel{\·}{z}}_1$

$u_2=-\frac{p_2}{p_1}\mathrm{\β}diag\left({z_2}^{1-p_1/p_2}\right)\frac{s}{\left|\right|s|{|}^2}({z_1}^T{z}_2+\frac{1}{2})$

$u_3=-\mathrm{\ρ}\frac{{\[s^T\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)\]}^T}{\left|\right|s^T\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)|{|}^2}\left|\right|s\left|\right|\left|\right|\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)\left|\right|$

Now export by neutral netGo to approach dynamic characteristic f of gyroscope, then the control law after updating is:

U=u₀'+u₁+u₂+u₃

Wherein:

The invention has the beneficial effects as follows:

Gyroscope is dynamically controlled by the neural network control device utilizing the present invention to relate to based on dynamic surface, Gyroscope system can be made to reach stable state with speed quickly, and the dynamic characteristic of gyroscope is that one tends to preferable mould Formula, it is possible to compensate foozle and environmental disturbances.The present invention based on the algorithm that dynamic surface method designs decrease the parameter of introducing, Simplify calculating degree, reduce buffeting, improve the effectiveness of system.

Accompanying drawing explanation

Fig. 1 is the simplified model schematic diagram of gyroscope of the present invention；

Fig. 2 is principle of the invention schematic diagram；

Fig. 3 is the time-domain response curve schematic diagram of error in the specific embodiment of the invention；

Fig. 4 be the present invention specific embodiment in x-axis control power and y-axis and control the time-domain response curve schematic diagram of power.

Detailed description of the invention

Below in conjunction with accompanying drawing and specific embodiment, technical solution of the present invention is described in further detail, so that ability The technical staff in territory can be better understood from the present invention and can be practiced, but illustrated embodiment is not as the limit to the present invention Fixed.

With reference to shown in Fig. 2, present invention microthrust test based on Dynamic Surface Design method of adaptive fuzzy sliding mode control, including such as Lower step:

Step one, sets up the mathematical model of gyroscope:

Step 2, utilizes neural network control method to approach dynamic characteristic and the external interference sum of gyroscope；

Step 3, based on Dynamic Surface Design adaptive neural network non-singular terminal sliding mode controller；

Step 4, the adaptive neural network non-singular terminal sliding mode controller utilizing step 3 to design controls microthrust test Instrument.

Embodiment

Carry out step one:

With reference to shown in Fig. 1, general gyroscope consists of the following components: a mass, along X, propping up of Y direction Support spring, electrostatic drive and induction installation, wherein electrostatic drive drives mass to vibrate along drive shaft direction, sensing Device can detect displacement and the speed of mass on detection direction of principal axis.

Then, the mathematical model of the gyroscope set up in step one is:

$\left\{\begin{array}{c}m\stackrel{\·\·}{x}+d_{xx}\stackrel{\·}{x}+d_{xy}\stackrel{\·}{y}+k_{xx}x+k_{xy}y=u_x+2{\mathrm{m\Ω}}_z\stackrel{\·}{y}\\ m\stackrel{\·\·}{y}+d_{xy}\stackrel{\·}{x}+d_{yy}\stackrel{\·}{y}+k_{xy}x+k_{yy}y=u_y-2{\mathrm{m\Ω}}_z\stackrel{\·}{x}\end{array}\right.---\left(1\right)$

Wherein, x, y represent gyroscope displacement in X, Y direction, d respectively_xx、d_yyIt is respectively X, Y direction spring Coefficient of elasticity, k_xx、k_yyIt is respectively X, the damped coefficient of Y direction, d_xy、k_xyIt it is the coupling ginseng caused due to mismachining tolerance etc. Number, m is the quality of gyroscope mass, Ω_zFor the angular velocity of mass rotation, u_x、u_yIt is the input control power of X, Y-axis respectively, Shape is such asParameter represent the first derivative of Γ, shape is such asParameter represent the second dervative of Γ.

Owing to equation also having unit quantity except numerical quantities, add the complexity of the design of controller.Gyroscope model The frequency of vibration of middle mass reaches the KHz order of magnitude, and the angular velocity of mass rotation simultaneously only has one hour several years quantity Level, very big this of order of magnitude difference can be made troubles to emulation.In order to solve different unit quantity and the big problem of order of magnitude difference, can Dimensionless process is carried out with peer-to-peer.

Both members is simultaneously divided by m, and makes Then nondimensionalization model is:

Model is rewritten into vector form:

$\stackrel{\·\·}{q}+D\stackrel{\·}{q}+Kq=u-2\mathrm{\Ω}\stackrel{\·}{q}---\left(3\right)$

Wherein, u is dynamic surface control rule,

Considering that systematic parameter is uncertain and external interference, model can be write as:

$\stackrel{\·\·}{q}+(D+\mathrm{\Δ}D)\stackrel{\·}{q}+(K+\mathrm{\Δ}K)q=u-2\mathrm{\Ω}\stackrel{\·}{q}+d---\left(4\right)$

Wherein Δ D, Δ K are parameter perturbations, and d is external interference；

Being write as state equation form is:

$\left\{\begin{array}{c}{\stackrel{\·}{q}}_1=q_2\\ {\stackrel{\·}{q}}_2=-(D+\mathrm{\Δ}D+2\mathrm{\Ω})\stackrel{\·}{q}-(K+\mathrm{\Δ}K)q+u+d\end{array}\right.---\left(5\right)$

Wherein, q₁=q,

Q=x will be defined for the ease of calculating₁,x₁、x₂For input variable；

Then state equation becomes following formula:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f+u\end{array}\right.---\left(6\right)$

Wherein f is dynamic characteristic and the external interference sum of gyroscope, and:

F=-(D+ Δ D+2 Ω) x₂-(K+ΔK)x₁+d (7)

Preferably, step 2 introduces neural networks principles, usesApproach f, specifically include following steps:

RBF (RBF) neutral net has a kind of forward direction three-layer network topological structure.Wherein, input layer simply letter Number receiving layer does not do any signal processing.The dimension of input layer is relevant to the dimension of concrete signal, such as neutral net in this example Input signal is x, and it is four dimensional vectors, therefore RBF network input layer has four input nodes.Intermediate layer is hidden layer, implements The nonlinear mapping effect of signal, is mapped to more higher-dimension by signal from the input space, the hidden layer space of signal characteristic linear separability. Output layer does sum operation with coefficient, produces the output of RBF network.

In RBF network structure, x (t) is the input vector of network.If the radial direction base vector h=[h of RBF network₁,h₂, h₃,…h_m]^T, wherein h_iFor Gaussian bases, i.e.

$h_i=\exp (-\frac{\left|\right|x\left(t\right)-c_i|{|}^2}{2b_i^2}),i=1,2,...,m---\left(8\right)$

In formula, c=[c₁,c₂,c₃,…c_m]^TIt is the center vector of network hidden layer node, identical with input dimension.

B=[b₁,b₂,b₃,…b_m]^TBeing the sound stage width vector of network hidden layer node, which determine the size in region, m is hidden Containing layer neuron number, the weights of RBF network input layer to hidden layer are 1, and network hidden layer to output layer weight vector is W= [w₁,w₂,w₃,…w_m]^T。

RBF network is output as

Y=h^T*W (9)

h^TTransposition for RBF.

In practice, how by the c of RBF network_iAnd b_iKeep fixing, and only regulating networks weights W, then RBF network is defeated Go out linear with hidden layer output.

Utilize the approximation properties that neutral net is powerful, with the output of neutral netApproach dynamic characteristic f of gyroscope:

RBF neural is output as:

$\hat{f}=h^T\hat{W}---\left(10\right)$

Definition best approximation constant, W^*

$W^{*}=\arg \underset{W\∈\mathrm{\Ω}}{min}\[sup|\hat{f}-f|\]---\left(11\right)$

Ω is the set of W.

Order

$\tilde{W}=\hat{W}-W^{*}---\left(12\right)$

Then:

F=h^TW^*+ε (13)

$f-\hat{f}=h^T{W}^{*}+\mathrm{\ϵ}-h^T\hat{W}=-h^T\tilde{W}+\mathrm{\ϵ}---\left(14\right)$

Wherein ε is the approximate error of neutral net.Given arbitrarily small constant ε (ε ＞ 0), such as lower inequality are set up: |f-h^TW^*|≤ε。

Preferably, step 3 specifically includes following steps:

Definition site error

z₁=x₁-x_1d (15)

Wherein x_1dFor command signal, then

${\stackrel{\·}{z}}_1={\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d}---\left(16\right)$

Definition Lyapunov function isWhereinFor z₁Transposition, then

${\stackrel{\·}{V}}_1={z_1}^T{\stackrel{\·}{z}}_1={z_1}^T({\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d})={z_1}^T(x_2-{\stackrel{\·}{x}}_{1d})---\left(17\right)$

For ensureingIntroduceFor x₂Virtual controlling amount, definition

${\stackrel{\‾}{x}}_2=-c_1{z}_1+{\stackrel{\·}{x}}_{1d}---\left(18\right)$

c₁For the constant more than 0；

For the phenomenon overcoming differential to explode, introduce low pass filter:

Take α₁For low pass filterAbout input it isTime output,

And meet:

Wherein τ is filter time constant, for the constant more than 0, α₁For the output of low pass filter, α₁(0)、 It is respectively α₁WithInitial value:

Can be obtained by (16):

${\stackrel{\·}{\mathrm{\α}}}_1=\frac{{\stackrel{\‾}{x}}_2-{\mathrm{\α}}_1}{\mathrm{\τ}}---\left(20\right)$

Produced filtering error is

$y_2={\mathrm{\α}}_1-{\stackrel{\‾}{x}}_2---\left(21\right)$

Virtual controlling error:

z₂=x₂-α₁ (22)

Then:

${\stackrel{\·}{z}}_2=f+u-{\stackrel{\·}{\mathrm{\α}}}_1---\left(23\right)$

Above formula occurs in that real control input.

Second Lyapunov function is defined as:

$V_2=\frac{1}{2}{z_2}^T{z_2}^2---\left(24\right)$

In order to ensure

It is defined as microthrust test design dynamic surface non-singular terminal sliding-mode surface:

$s={\[s_1,s_2\]}^T=z_1+\frac{1}{\mathrm{\β}}{z_2}^{p_1/p_2}---\left(25\right)$

In formula, β=diag (β₁,β₂) it is sliding-mode surface constant, β₁,β₂It is normal number,p₁, p₂For positive odd number, and 1 ＜ p₁/p₂＜ 2

For makingFor microthrust test system, using dynamic surface non-singular terminal sliding-mode surface, design dynamic surface is nonsingular TSM control rule is:

U=u₀+u₁+u₂+u₃ (26)

Wherein,

$u_0=-f+{\stackrel{\·}{\mathrm{\α}}}_1---\left(27\right)$

$u_1=-\frac{p_2}{p_1}\mathrm{\β}diag\left({z_2}^{1-p_1/p_2}\right){\stackrel{\·}{z}}_1---\left(28\right)$

$u_2=-\frac{p_2}{p_1}\mathrm{\β}diag\left({z_2}^{1-p_1/p_2}\right)\frac{s}{\left|\right|s|{|}^2}({z_1}^T{z}_2+\frac{1}{2})---\left(29\right)$

$u_3=-\mathrm{\ρ}\frac{{\[s^T\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)\]}^T}{\left|\right|s^T\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)|{|}^2}\left|\right|s\left|\right|\left|\right|\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)\left|\right|---\left(30\right)$

Now export by neutral netGo to approach dynamic characteristic f of gyroscope, then the overall control law after updating is:

U=u₀'+u₁+u₂+u₃ (31)

Wherein:

${u^{\′}}_0=-\hat{f}+{\stackrel{\·}{\mathrm{\α}}}_1---\left(32\right)$

Concrete principle is as shown in Figure 2.

The stability of system proves as follows:

In view of position tracking error, virtual controlling error and worry wave error and the approximate error of RBF neural.Fixed Justice Lyapunov function is

$V=\frac{1}{2}{z_1}^T{z}_1+\frac{1}{2}{s}^{T}s+\frac{1}{2}{y_2}^T{y}_2+\frac{1}{2\mathrm{\γ}}{\tilde{W}}^T\tilde{W}---\left(33\right)$

Z in formula₁For tracking error and correlation function thereof, s is sliding-mode surface, y₂It is filtering error,It is that RBF is neural Network parameter error.γ is the number more than 0.

Theorem: take V (0)≤p, p ＞ 0, the then all convergence signals of closed loop system, bounded.

Lyapunov function derivative is:

$\stackrel{\·}{V}={z_1}^T{\stackrel{\·}{z}}_1+s^T\stackrel{\·}{s}+{y_2}^T{\stackrel{\·}{y}}_2+\frac{1}{\mathrm{\γ}}{\tilde{W}}^T\stackrel{\·}{\hat{W}}---\left(34\right)$

Wherein

${\stackrel{\·}{z}}_1={\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d}=x_2-{\stackrel{\·}{x}}_{1d}=z_2+{\mathrm{\α}}_1-{\stackrel{\·}{x}}_{1d}=z_2+y_2+{\stackrel{\‾}{x}}_2-{\stackrel{\·}{x}}_{1d}---\left(35\right)$

$\stackrel{\·}{s}={\stackrel{\·}{z}}_1+\frac{p_1}{p_2}\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right){\stackrel{\·}{z}}_2---\left(36\right)$

${\stackrel{\·}{y}}_2={\stackrel{\·}{\mathrm{\α}}}_1-{\stackrel{\·}{\stackrel{\‾}{x}}}_2=\frac{{\stackrel{\‾}{x}}_2-{\mathrm{\α}}_1}{\mathrm{\τ}}-{\stackrel{\·}{\stackrel{\‾}{x}}}_2=\frac{-y_2}{\mathrm{\τ}}-{\stackrel{\·}{\stackrel{\‾}{x}}}_2=\frac{-y_2}{\mathrm{\τ}}+c_1{\stackrel{\·}{z}}_1-{\stackrel{\·\·}{x}}_{1d}---\left(37\right)$

The adaptive law that can obtain neutral net according to Liapunov stability is:

$\stackrel{\·}{\hat{W}}=\mathrm{\γ}\frac{p_1}{p_2}\left|\right|s\left|\right|\left|\right|\frac{1}{\mathrm{\β}}diag\left({z_2}^{p_1/p_2-1}\right)\left|\right|h\left(x\right)---\left(38\right)$

By obtaining above:

$\stackrel{\·}{V}=-{{\mathrm{rz}}_1}^T{z}_1\≤0---\left(39\right)$

Illustrate that pursuit path reaches sliding-mode surface in finite time, and rest on sliding-mode surface.Negative semidefinite Property ensure that V, s are all bounded.According to formula (36), it is known thatAlso it is bounded.Due to V (0) bounded, 0≤V (t)≤V (0), can be inferred thatIt is bounded.Further according to Barbalat theorem and inference thereof, s (t) will go to zero, i.e.And then also have

Hereinafter carry out Matlab emulation experiment.

Dynamic model and adaptive neural network non-singular terminal sliding formwork based on dynamic surface in conjunction with microthrust test sensor The method for designing controlled, goes out mastery routine by Matlab/Simulink software design, as in figure 2 it is shown, by self adaptation Dynamic sliding mode The dimension of controller, controlled device micro-mechanical gyroscope and parameter is asked for utilizing the characteristic of S function to be write as subprogram and is put respectively In several S-Function.

From existing document, the parameter selecting one group of gyroscope is as follows:

The parameter selecting one group of gyroscope is as follows:

M=1.8 × 10^-7kg,k_xx=63.955N/m, k_yy=95.92N/m, k_xy=12.779N/m

d_xx=1.8 × 10^-6Ns/m,d_yy=1.8 × 10^-6Ns/m,d_xy=3.6 × 10^-7Ns/m

Assume that input angular velocity is Ω_z=100rad/s, reference frequency is ω₀=1000Hz.Obtain the non-dimension of gyroscope Changing parameter is:

ω_x ²=355.3, ω_y ²=532.9, ω_xy=70.99, d_xx=0.01, d_yy=0.01, d_xy=0.02, Ω_Z= 0.01。

Reference model is chosen for: r₁=sin (4.17t), r₂=1.2sin (5.11t).

Initial condition is set to: x₁₁(0)=0.01, x₁₂(0)=0, x₁₂(0)=0.01, x₂₂(0)=0.

According to control law Selecting All Parameters it is:

c₁₁=2500, c₁₂=2500；r₁=1, r₂=1；

γ₁=500, γ₂=500；tol₁=0.01, tol₂=0.01.

Take distracter: [sin (5t)；sin(2t)].

c₁=[-1 ,-0.8 ,-0.6 ,-0.4 ,-0.2,0,0.2,0.4,0.6,0.8,1]

C=[c₁；c₁；c₁；c₁]

B=0.03

c_jCoordinate vector for hidden layer jth neuron Gaussian bases central point.

b_jWidth for hidden layer jth neuron Gaussian bases.

In sliding formwork control law, sliding-mode surface parameter takes p₁=99, p₂=51, β=diag (1,1), then non-singular terminal sliding-mode surface It is respectively as follows: s=e₁+e₂ ^99/51。

Experiment result as shown in Figure 3, Figure 4:

Error change between actual output and expectation is as it is shown on figure 3, result shows that actual output is permissible within a very short time The upper desired output of perfect tracking, error is close to zero and relatively stable.

As shown in Figure 4, result shows that dynamic surface sliding mode controller successfully reduces drawing of parameter to control power input value curve Enter, make system chatter significantly be reduced.

The present invention is applied to the adaptive neural network non-singular terminal sliding formwork based on dynamic surface of gyroscope and controls, and adopts By adaptive neural network non-singular terminal sliding-mode method based on Dynamic Surface Design, gyroscope is controlled, effectively drops Low buffet, improve tracking velocity.In the case of to systematic parameter the unknown, can effectively estimate every ginseng of system Number, and ensure the stability of system.In traditional self adaptation backstepping, introduce dynamic surface technology, both maintain former pusher The advantage of technology, decrease the quantity of parameter, it is to avoid parameters inflation problem, hence it is evident that reduces the complexity of calculating.Simultaneously Introduce neutral net adaptive approach in the controller to have carried out well approaching to the dynamic property of gyroscope.

A kind of non-singular terminal sliding formwork the most introduced herein, it is ensured that system mode at sliding phase finite time convergence control and Control law is without negative exponent item.And on the basis of Lyapunov stability theory, demonstrate the stability of whole system.Use This system can effectively reduce the buffeting of system, compensates foozle and environmental disturbances, improves sensitivity and the robustness of system.

These are only the preferred embodiments of the present invention, not thereby limit the scope of the claims of the present invention, every utilize this Equivalent structure or equivalence flow process that bright description and accompanying drawing content are made convert, or it is relevant to be directly or indirectly used in other Technical field, be the most in like manner included in the scope of patent protection of the present invention.

Claims (4)

1. a microthrust test adaptive neural network non-singular terminal sliding-mode control, comprises the following steps:

Step one, sets up the mathematical model of gyroscope:

Step 2, utilizes neural network control method to approach dynamic characteristic and the external interference sum of gyroscope；

Step 3, based on Dynamic Surface Design adaptive neural network non-singular terminal sliding mode controller；

Step 4, the adaptive neural network non-singular terminal sliding mode controller utilizing step 3 to design controls gyroscope.

Method the most according to claim 1, is characterized in that, in step one, the mathematical model of gyroscope is:

$\left\{\begin{array}{c}m\stackrel{\·\·}{x}+d_{xx}\stackrel{\·}{x}+d_{xy}\stackrel{\·}{y}+k_{xx}x+k_{xy}y=u_x+2{\mathrm{m\Ω}}_z\stackrel{\·}{y}\\ m\stackrel{\·\·}{y}+d_{xy}\stackrel{\·}{x}+d_{yy}\stackrel{\·}{y}+k_{xy}x+k_{yy}y=u_y-2{\mathrm{m\Ω}}_z\stackrel{\·}{x}\end{array}\right.$

Wherein, x, y represent gyroscope displacement in X, Y direction, d respectively_xx、d_yyIt is respectively the X of gyroscope, Y-axis side To the coefficient of elasticity of spring, k_xx、k_yyIt is respectively gyroscope at X, the damped coefficient of Y direction, d_xy、k_xyFor coupling parameter, m For the quality of gyroscope mass, Ω_zFor the angular velocity of mass rotation, u_x、u_yIt is the input control power of X, Y-axis respectively, shape AsParameter represent the first derivative of Γ, shape is such asParameter represent the second dervative of Γ；

Model carries out nondimensionalization process and obtain nondimensionalization model:

Both members is simultaneously divided by m, and makes Then nondimensionalization model is:

Model is rewritten into vector form:

$\stackrel{\·\·}{q}+D\stackrel{\·}{q}+Kq=u-2\mathrm{\Ω}\stackrel{\·}{q}$

Wherein, u is dynamic surface control rule,

Considering that systematic parameter is uncertain and external interference, model is write as:

$\stackrel{\·\·}{q}+(D+\mathrm{\Δ}D)\stackrel{\·}{q}+(K+\mathrm{\Δ}K)q=u-2\mathrm{\Ω}\stackrel{\·}{q}+d$

Wherein Δ D, Δ K are parameter perturbations, and d is external interference；

Model is write as state equation form is:

$\left\{\begin{array}{c}{\stackrel{\·}{q}}_1=q_2\\ {\stackrel{\·}{q}}_2=-(D+\mathrm{\Δ}D+2\mathrm{\Ω})\stackrel{\·}{q}-(K+\mathrm{\Δ}K)q+u+d\end{array}\right.$

Wherein, q₁=q,

Q=x will be defined for the ease of calculating₁,x₁、x₂For input variable；

Then the state equation of gyroscope model becomes following formula:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f+u\end{array}\right.$

Wherein f is dynamic characteristic and the external interference sum of gyroscope, and:

F=-(D+ Δ D+2 Ω) x₂-(K+ΔK)x₁+d。

Method the most according to claim 2, is characterized in that, in step 2, utilizes RBF neural principle, usesApproach F, including step:

With the x (t) input vector as RBF neural, if the radial direction base vector h=[h of RBF neural₁,h₂,h₃,…h_m]^T, Wherein h_iFor Gaussian bases, it may be assumed that

$h_i=\exp (-\frac{\left|\right|x\left(t\right)-c_i|{|}^2}{2b_i^2}),i=1,2,...,m$

In formula, c=[c₁,c₂,c₃,…c_m]^TIt is the center vector of network hidden layer node, identical with the dimension of input vector；B= [b₁,b₂,b₃,…b_m]^TBeing the sound stage width vector of network hidden layer node, which determine the size in region, m is hidden layer neuron Number, the weights of RBF network input layer to hidden layer are 1, and network hidden layer to output layer weight vector is W=[w₁, w₂, w₃... w_m ]^T；

RBF network is output as:

Y=h^T*W

h^TTransposition for RBF；

By the c of RBF neural_iAnd b_iKeep fixing, and only regulating networks weights W, then the output of RBF neural and hidden layer Export linear；

RBF neural is output as:

$\hat{f}=h^T\hat{W}$

With the output of neutral netApproach dynamic characteristic f of gyroscope；

Definition best approximation constant, W^*

$W^{*}=\arg \underset{W\∈\mathrm{\Ω}}{min}\[sup|\hat{f}-f|\]$

Ω is the set of W；

Order

$\tilde{W}=\hat{W}-W^{*}$

Then:

F=h^TW^*+ε

$f-\hat{f}=h^T{W}^{*}+\mathrm{\ϵ}-h^T\hat{W}=-h^T\tilde{W}+\mathrm{\ϵ}$

Wherein ε is the approximate error of neutral net, sets up for given arbitrarily small constant ε (ε ＞ 0), such as lower inequality: | f- h^TW^*|≤ε。

Method the most according to claim 3, is characterized in that, step 3 comprises the following steps:

Definition site error

z₁=x₁-x_1d

Wherein x_1dFor instruction references signal, then

${\stackrel{\·}{z}}_1={\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d}$

Definition Lyapunov function isWhereinFor z₁Transposition, then

${\stackrel{\·}{V}}_1={z_1}^T{\stackrel{\·}{z}}_1={z_1}^T({\stackrel{\·}{x}}_1-{\stackrel{\·}{x}}_{1d})={z_1}^T(x_2-{\stackrel{\·}{x}}_{1d})$

For ensureingIntroduceFor x₂Virtual controlling amount, definition

${\stackrel{\‾}{x}}_2=-c_1{z}_1+{\stackrel{\·}{x}}_{1d}$

c₁For the constant more than 0；

For the phenomenon overcoming differential to explode, introduce low pass filter: take α₁For low pass filterAbout input it isTime Output, and meet:

$\left\{\begin{array}{c}\mathrm{\τ}{\stackrel{\·}{\mathrm{\α}}}_1+{\mathrm{\α}}_1={\stackrel{\‾}{x}}_2\\ {\mathrm{\α}}_1\left(0\right)={\stackrel{\‾}{x}}_2\left(0\right)\end{array}\right.$

Wherein τ is filter time constant, for the constant more than 0, α₁For the output of low pass filter, α₁(0)、Respectively For α₁WithInitial value:

${\stackrel{\·}{\mathrm{\α}}}_1=\frac{{\stackrel{\‾}{x}}_2-{\mathrm{\α}}_1}{\mathrm{\τ}}$

Produced filtering error is:

$y_2={\mathrm{\α}}_1-{\stackrel{\‾}{x}}_2$

Definition virtual controlling error: z₂=x₂-α₁, then

Second Lyapunov function is defined as:

$V_2=\frac{1}{2}{z_2}^T{z_2}^2$

In order to ensure

It is defined as microthrust test design dynamic surface non-singular terminal sliding-mode surface:

$s={\[s_1,s_2\]}^T=z_1+\frac{1}{\mathrm{\β}}{z_2}^{p_1/p_2}$

In formula, β=diag (β₁,β₂) it is sliding-mode surface constant, β₁,β₂It is normal number,p₁,p₂For Positive odd number, and 1 < p₁/p₂<2；

For makingFor microthrust test system, using dynamic surface non-singular terminal sliding-mode surface, design dynamic surface non-singular terminal is sliding Mould control law is:

U=u₀+u₁+u₂+u₃

Wherein,

$u_0=-f+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1$

$u_1=-\frac{p_2}{p_1}\mathrm{\&beta;}diag\left({z_2}^{1-p_1/p_2}\right){\stackrel{\&CenterDot;}{z}}_1$

$u_2=-\frac{p_2}{p_1}\mathrm{\&beta;}diag\left({z_2}^{1-p_1/p_2}\right)\frac{s}{\left|\right|s|{|}^2}({z_1}^T{z}_2+\frac{1}{2})$

$u_3=-\mathrm{\&rho;}\frac{{\&lsqb;s^T\frac{1}{\mathrm{\&beta;}}diag\left({z_2}^{p_1/p_2-1}\right)\&rsqb;}^T}{\left|\right|s^T\frac{1}{\mathrm{\&beta;}}diag\left({z_2}^{p_1/p_2-1}\right)|{|}^2}\left|\right|s\left|\right|\left|\right|\frac{1}{\mathrm{\&beta;}}diag\left({z_2}^{p_1/p_2-1}\right)\left|\right|$

Now export by neutral netGo to approach dynamic characteristic f of gyroscope, then the overall control law after updating is:

U=u₀'+u₁+u₂+u₃

Wherein: