CN103616818A - Self-adaptive fuzzy neural global rapid terminal sliding-mode control method for micro gyroscope - Google Patents

Abstract

The invention discloses an adaptive fuzzy neural global fast terminal sliding mode control method for a micro gyroscope. The invention is to combine the global fast terminal sliding mode control with adaptive control, and design the global fast terminal according to the Lyapunov stability method The sliding mode control law enables the system state to converge to the equilibrium point in a short finite time, and at the same time uses adaptive control to identify the angular velocity of the micro gyroscope and other system parameters, and further considers when the upper bound of the model error and external disturbance is unknown In this situation, the fuzzy neural network learning function is used to adaptively learn the uncertain items of the micro-gyroscope system and the upper bound of external disturbances, and the automatic tracking of modeling errors and uncertain disturbances is realized. While ensuring the convergence speed and tracking performance, the invention has strong robustness and self-adaptive ability to external disturbances.

Description

The neural overall fast terminal sliding-mode control of adaptive fuzzy of gyroscope

Technical field

The present invention relates to the control system of gyroscope, specifically the neural overall fast terminal sliding-mode control of a kind of adaptive fuzzy of gyroscope.

Background technology

Gyroscope is the fundamental measurement element of inertial navigation and inertial guidance system, and because it is in the huge advantage aspect volume and cost, gyroscope is widely used in Aeronautics and Astronautics, automobile, biomedicine, military affairs and consumer electronics field.But, because design and the error in manufacturing exist and thermal perturbation, can cause the difference between original paper characteristic and design, reduced the performance of gyroscope system.In addition, gyroscope itself belongs to multi-input multi-output system and systematic parameter and has impact uncertain and that be subject to external environment.Compensation foozle and measured angular speed become the subject matter that gyroscope is controlled, and are necessary gyroscope system to carry out dynamic compensation and adjustment.And traditional control method concentrates in the stable control and diaxon frequency matching of driving shaft oscillation amplitude and frequency, can not solve well the defect of gyroscope dynamic equation.

International article has various advanced control methods is applied in the middle of the control of gyroscope, typically has adaptive control and sliding-mode control.Adaptive control is in the situation that entirely even not knowing little about it of knowing of the model knowledge of controlled device or environmental knowledge makes system can automatically work in optimum or close to optimum running status, provide high-quality control performance.But the adaptive control to external world robustness of disturbance is very low, easily makes system become unstable.Sliding mode variable structure control be the special nonlinear Control of a class in essence, the uncontinuity of its non-linear behavior for controlling, the difference of this control strategy and other control is that the structure of system is unfixing, but can on purpose constantly change according to system current state according to system in dynamic process, force system according to the state trajectory motion of predetermined sliding mode.The shortcoming of the method is to arrive after sliding-mode surface when state trajectory, is difficult to strictly along sliding-mode surface, towards equilibrium point, slide, but passes through back and forth in sliding-mode surface both sides, thereby produce vibration.

Summary of the invention

The present invention is directed to the micro-gyrotron trajectory track that contains modeling error and uncertain noises controls, a kind of neural overall fast terminal sliding-mode control of adaptive fuzzy of gyroscope has been proposed, estimated value based on Liapunov stability method design gyroscope parameter matrix and the adaptive algorithm of fuzzy neural network weights, guarantee the global stability of whole control system, improved the reliability of system and the robustness that parameter is changed.

The technical solution used in the present invention is:

The neural overall fast terminal sliding-mode control of adaptive fuzzy of gyroscope, comprises the following steps;

1) mathematical model of structure gyroscope system is:

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

Wherein, the mass that q is gyroscope, in the position vector of driving shaft and sensitive axis diaxon, is the output of gyroscope system; U is the control inputs of gyroscope; D is damping matrix; The natural frequency that K has comprised diaxon and the stiffness coefficient of coupling; Ω is angular speed matrix; F is parameter uncertainty and the external disturbance of system;

2) building overall fast terminal sliding-mode surface s is:

$s=\stackrel{\&CenterDot;}{e}+\mathrm{\&alpha;e}+{\mathrm{\&beta;<figure-callout\; id="2"\; label="e\; p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^{p_{}}---\left(6\right)$

Wherein, α=diag (α ₁, α ₂), β=diag (β ₁, β ₂) be sliding-mode surface constant; E=q-q _rfor tracking error; q _rfor the ideal position output vector of mass along diaxon; Q is two shaft position output vectors of gyroscope; p ₁, p ₂(p ₁> p ₂) be positive odd number;

3) build the neural overall fast terminal sliding mode controller of adaptive fuzzy:

3-1) for described gyroscope system, the sliding-mode surface of employing formula (6), overall fast terminal sliding formwork control law U is comprised of three control laws:

U＝u ₀+u ₁+u ₂ (7)

Wherein,

u ₀＝a+(D+2Ω)v+Kq，

D, K, three parameter matrixs that Ω is gyroscope,

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=-W\frac{s}{\left|\right|s\left|\right|},W=\mathrm{diag}(w_1,w_2);$

W is sliding mode controller parameter;

the upper bound for parameter uncertainty and the external disturbance f of system;

3-2) due to three parameter matrix D of gyroscope, K, Ω is unknown, according to Adaptive Control Theory, uses estimated value

alternate parameter matrix D, K, Ω, and design the adaptive algorithm of three estimated values, online real-time update estimated value, control law u ₀be adjusted into u' ₀:

$u_0^{\&prime;}=a+(\hat{D}+2\widehat{\mathrm{\&Omega;}})v+\hat{K}q;$

3-3) according to Fuzzy Neural Network Theory, adopt fuzzy neural network to approach the parameter uncertainty of system and the upper bound ρ (t) of external disturbance f, and design the adaptive algorithm of fuzzy neural network weights, the output of online real-time update fuzzy neural network, the output of fuzzy neural network

for:

Wherein,

the weights of fuzzy neural network, the normalization confidence level that φ (X) is fuzzy neural network, $X={\left[\begin{array}{cc}q& \stackrel{\&CenterDot;}{q}\end{array}\right]}^T$ For the input of fuzzy neural network,

Control law u ₂be adjusted into u' ₂:

$u_2^{\&prime;}=-\widehat{\mathrm{\&rho;}}\left(t\right)\frac{s}{\left|\right|s\left|\right|};$

3-4) with described step 3-2) and step 3-3) control law u' after adjusting ₀and u' ₂, replace step 3-1) in control law u ₀and u ₂, obtain the control law U'' of the neural overall fast terminal sliding mode controller of adaptive fuzzy

U''＝u' ₀+u ₁+u' ₂；

3-5) control inputs using the control law U'' of the neural overall fast terminal sliding mode controller of adaptive fuzzy as gyroscope system, brings in the mathematical model of gyroscope system, realizes the tracking of gyroscope system is controlled.

Aforesaid gyroscope parameter matrix D, K, the adaptive algorithm of the adaptive algorithm of the estimated value of Ω and fuzzy neural network weights designs based on Lyapunov stability theory:

Lyapunov function is:

$V=\frac{1}{2}{s}^{T}s+\frac{1}{2}\mathrm{tr}\left\{\tilde{D}{M}^{-1}{\tilde{D}}^T\right\}+\frac{1}{2}\mathrm{tr}\left\{\tilde{K}{N}^{-1}{\tilde{K}}^T\right\}+\frac{1}{2}\mathrm{tr}\left\{\widetilde{\mathrm{\&Omega;}}{P}^{-1}{\widetilde{\mathrm{\&Omega;}}}^T\right\}+\frac{1}{2}{\mathrm{\&eta;}}^{-1}{\tilde{w}}^T\tilde{w}$

Wherein, the mark of tr () representing matrix; M, N, P is adaptive gain, M=M ^t> 0, N=N ^t> 0, P=P ^t> 0 is symmetric positive definite matrix, and η is fuzzy neural network learning rate,

the evaluated error of neural network weight, be respectively parameter matrix D, K, the parameter estimating error of Ω,

In order to guarantee the derivative of Lyapunov function

choose gyroscope parameter matrix D, K, the adaptive algorithm of the estimated value of Ω is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{D}}}^T=-\frac{1}{2}M(\stackrel{\&CenterDot;}{q}{s}^T+s{\stackrel{\&CenterDot;}{q}}^T)\\ {\stackrel{\&CenterDot;}{\hat{K}}}^T=-\frac{1}{2}N({\mathrm{qs}}^T+{\mathrm{sq}}^T)\\ {\stackrel{\&CenterDot;}{\widehat{\mathrm{\&Omega;}}}}^T=-\frac{1}{2}P(2\stackrel{\&CenterDot;}{q}{s}^T-2s{\stackrel{\&CenterDot;}{q}}^T)\end{array}\right.$

The adaptive algorithm of fuzzy neural network weights is:

Compared with prior art, beneficial effect of the present invention is embodied in: first, the proposition that overall situation fast terminal sliding formwork is controlled has solved the optimal problem of convergence time, it combines traditional sliding formwork and controls the advantage of controlling with terminal sliding mode in the process of sliding mode design, in the arrival stage, also use the concept of quick arrival, guarantee that tracking error converges to zero in shorter finite time simultaneously; Secondly, when all parameters of gyroscope and angular speed are all regarded unknown variable as, for control and the parameter measurement problem of gyroscope, designed a kind of novel Adaptive Identification method, the online angular velocity of real-time update gyroscope and the estimated value of other systematic parameter; Finally, by fuzzy neural network, can carry out online adaptive study to the upper bound of uncertain system and external interference, and can reduce buffeting, realized to modeling error and uncertain noises from motion tracking.

Accompanying drawing explanation

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

Fig. 2 is the theory diagram of the neural overall fast terminal sliding-mode control of adaptive fuzzy of gyroscope in the present invention;

Fig. 3 is structure of fuzzy neural network figure in the present invention;

Fig. 4 is X in specific embodiments of the invention, Y-axis location tracking curve;

Fig. 5 is X in specific embodiments of the invention, Y-axis location tracking graph of errors;

Fig. 6 is overall fast terminal sliding-mode surface convergence curve in specific embodiments of the invention;

Fig. 7 is X in specific embodiments of the invention, Y-axis control inputs response curve;

Fig. 8 is gyroscope systematic parameter d in specific embodiments of the invention _xx, d _xy, d _yyand ω _x ², ω _xy, ω _y ²adaptive Identification curve;

Fig. 9 is gyroscope angular velocity Ω in specific embodiments of the invention _zadaptive Identification curve;

Figure 10 is X in specific embodiments of the invention, Y-axis upper bound change curve.

Embodiment

Above-mentioned explanation is only general introduction of the present invention, in order to better understand technological means of the present invention, and can be implemented according to the content of instructions, below in conjunction with accompanying drawing and preferred embodiment, the neural overall fast terminal sliding-mode control of the adaptive fuzzy of the gyroscope proposing according to the present invention is elaborated.

The present invention is achieved in the following ways:

One, build the mathematical model of gyroscope system

As shown in Figure 1, the Newton's law according in rotation system, takes into account manufacturing defect and mismachining tolerance, then processes by the nondimensionalization of model, and the lumped parameter mathematical model that obtains actual gyroscope is:

$\stackrel{\&CenterDot;\&CenterDot;}{q}+D\stackrel{\&CenterDot;}{q}+\mathrm{Kq}=u-2\mathrm{\&Omega;}\stackrel{\&CenterDot;}{q}+d---\left(1\right)$

Wherein, $q=\left[\begin{array}{c}x\\ y\end{array}\right]$ For the mass of the gyroscope position vector at driving shaft and sensitive axis diaxon, be the output of gyroscope system; $u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right]$ Control inputs for gyroscope diaxon; $d=\left[\begin{array}{c}{d}_x\\ d_y\end{array}\right]$ For external disturbance effect; $D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right]$ For damping matrix, wherein, d _xx, d _yyfor the ratio of damping of diaxon, d _xyfor Coupling Damping coefficient; $K=\left[\begin{array}{cc}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">x</figure-callout>}}^2& {\mathrm{\&omega;}}_{\mathrm{xy}}\\ {\mathrm{\&omega;}}_{\mathrm{xy}}& {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">y</figure-callout>}}^2\end{array}\right],$ Wherein, $\sqrt{\frac{k_{\mathrm{xx}}}{{{\mathrm{m\&omega;}}_0}^2}}\&RightArrow;{\mathrm{\&omega;}}_x,\sqrt{\frac{k_{\mathrm{yy}}}{{{\mathrm{m\&omega;}}_0}^2}}\&RightArrow;{\mathrm{\&omega;}}_y,\frac{k_{\mathrm{xy}}}{{{\mathrm{m\&omega;}}_0}^2}\&RightArrow;{\mathrm{\&omega;}}_{\mathrm{xy}},$ ω ₀for the natural frequency of diaxon, k _xx, k _yyfor the stiffness coefficient of diaxon, k _xystiffness coefficient for coupling; $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right]$ For angular speed matrix, Ω _zfor the angular speed in gyroscope working environment, it is a unknown quantity.

The parameter uncertainty of taking into account system and external disturbance, can be shown as gyroscope system table following form according to the mathematical model of gyroscope:

$\stackrel{\&CenterDot;\&CenterDot;}{q}+(D+2\mathrm{\&Omega;}+\mathrm{\&Delta;D})\stackrel{\&CenterDot;}{q}+(K+\mathrm{\&Delta;K})q=u+d---\left(2\right)$

In formula, Δ D is the uncertainty of the unknown parameter of inertial matrix D+2 Ω, and Δ K is the uncertainty of the unknown parameter of inertial matrix K, and d represents external interference.

Further, formula (2) can be write as:

$\stackrel{\&CenterDot;\&CenterDot;}{q}+(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+\mathrm{Kq}=u+f---\left(3\right)$

In formula, f represents parameter uncertainty and the external disturbance of system, meets:

$f=d-\mathrm{\&Delta;D}\stackrel{\&CenterDot;}{q}-\mathrm{\&Delta;Kq}---\left(4\right)$

Generally, to the uncertainty of system unknown parameter and external disturbance, can do following hypothesis:

||f(t)||＜ρ(t) (5)

ρ (t) is the upper bound of parameter uncertainty and external disturbance f.

Two, build overall fast terminal sliding-mode surface

The control problem that the present invention considers is the tracking problem of gyroscope, and the target of control is exactly that suitable control law of design reaches to ideal trajectory q system output q in finite time _rtracking completely.

As shown in Figure 2, for the track following of gyroscope system, overall fast terminal sliding-mode surface s is designed to:

$s={[{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">s</figure-callout>}}_1,s_2]}^T=\stackrel{\&CenterDot;}{e}+\mathrm{\&alpha;e}+{\mathrm{\&beta;<figure-callout\; id="2"\; label="e\; p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^{p_{}}---\left(6\right)$

In formula, α=diag (α ₁, α ₂), β=diag (β ₁, β ₂) be sliding-mode surface constant, e=q-q _r=[x-x _r, y-y _r] ^ttracking error,

the derivative of tracking error, q _rfor the ideal position output vector of mass along diaxon, the position output vector that q is gyroscope;

p ₁, p ₂(p ₁> p ₂) be positive odd number.

Three, build the neural overall fast terminal sliding mode controller of adaptive fuzzy

For gyroscope system, the sliding-mode surface that employing formula (6) is described, overall fast terminal sliding formwork control law U is designed to be comprised of three control laws:

U＝u ₀+u ₁+u ₂ (7)

Wherein,

u ₀＝a+(D+2Ω)v+Kq (8)

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=-W\frac{s}{\left|\right|s\left|\right|}---\left(9\right)$

${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=-\mathrm{\&rho;}\left(t\right)\frac{s}{\left|\right|s\left|\right|}---\left(10\right)$

In formula, W is sliding mode controller parameter; W=diag (w ₁, w ₂), w _i> 0, i=1, and 2, and have:

$v={\stackrel{\&CenterDot;}{q}}_r-\mathrm{\&alpha;e}-{\mathrm{\&beta;<figure-callout\; id="2"\; label="e\; p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^{p_{}}---\left(11\right)$

$a=\stackrel{\&CenterDot;}{v}={\stackrel{\&CenterDot;\&CenterDot;}{q}}_r-\mathrm{\&alpha;}\stackrel{\&CenterDot;}{e}-\frac{p_2}{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}\mathrm{\&beta;diag}({e_1}^{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2/p_1-1},{e_2}^{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">p</figure-callout>}}_2/p_1-1})\stackrel{\&CenterDot;}{e}---\left(12\right)$

Due to three parameter matrix D of gyroscope, K, Ω is unknown, so the control law shown in formula (7) cannot be implemented.According to Adaptive Control Theory, three gyroscope parameter matrixs in formula (7) are used respectively to their estimated value

substitute, and design the adaptive algorithm of three estimated values, online real-time update estimated value, so the control law u shown in formula (8) ₀can be adjusted into u' ₀:

${\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_0^{\&prime;}=a+(\hat{D}+2\widehat{\mathrm{\&Omega;}})v+\hat{K}q---\left(13\right)$

Control law U becomes U', U'=u' ₀+ u ₁+ u ₂.

Definition D, K, the parameter estimating error of Ω is respectively:

$\tilde{D}=\hat{D}-D$

$\tilde{K}=\hat{K}-K---\left(14\right)$

$\widehat{\mathrm{\&Omega;}}=\widehat{\mathrm{\&Omega;}}-\mathrm{\&Omega;}$

After adjusting control law U' as the control inputs of gyroscope system, be updated in the mathematical model of the gyroscope system that formula (3) represents:

$\stackrel{\&CenterDot;\&CenterDot;}{q}+(D+2\mathrm{\&Omega;}+\mathrm{\&Delta;D})\stackrel{\&CenterDot;}{q}+(K+\mathrm{\&Delta;K})q=a+(\hat{D}+2\widehat{\mathrm{\&Omega;}})v+\hat{K}q+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+d---\left(15\right)$

$\&DoubleRightArrow;(\stackrel{\&CenterDot;\&CenterDot;}{q}-a)+(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}-(\hat{D}+2\widehat{\mathrm{\&Omega;}})v+\mathrm{Kq}-\hat{K}q=-\mathrm{\&Delta;D}\stackrel{\&CenterDot;}{q}-\mathrm{\&Delta;Kq}+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+d$

$\&DoubleRightArrow;\stackrel{\&CenterDot;}{s}=(\hat{D}+2\widehat{\mathrm{\&Omega;}})v-(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+\hat{K}q+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+f$

$\&DoubleRightArrow;\stackrel{\&CenterDot;}{s}=(\hat{D}+2\widehat{\mathrm{\&Omega;}})v-[(\hat{D}+2\widehat{\mathrm{\&Omega;}})-(\tilde{D}+2\widetilde{\mathrm{\&Omega;}})]\stackrel{\&CenterDot;}{q}+\tilde{K}q+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1\text{+}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+f$

$\&DoubleRightArrow;\stackrel{\&CenterDot;}{s}=(\hat{D}+2\widehat{\mathrm{\&Omega;}})v-(\hat{D}+2\widehat{\mathrm{\&Omega;}})\stackrel{.}{q}+(\tilde{D}+2\widetilde{\mathrm{\&Omega;}})\stackrel{\&CenterDot;}{q}+\tilde{K}q+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+f$

$\&DoubleRightArrow;\stackrel{\&CenterDot;}{s}=-(\hat{D}+2\widehat{\mathrm{\&Omega;}})s+\tilde{D}\stackrel{\&CenterDot;}{q}+2\widetilde{\mathrm{\&Omega;}}\stackrel{\&CenterDot;}{q}+\tilde{K}q+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+f---\left(16\right)$

Generally, the upper dividing value of uncertain factor and external interference is difficult to or cannot predicts at all, according to the feature of fuzzy neural network, can adopt fuzzy neural network to carry out the upper bound ρ (t) of approximating parameter uncertainty and external disturbance f, guarantee system stability and tracking characteristics.As shown in Figure 3, fuzzy neural network is fuzzy system and neural network to be combined and the network that forms, it is to give fuzzy input signal and fuzzy weights by conventional neural network in itself, and its learning algorithm is Learning Algorithm or its popularization normally.Fuzzy neural network consists of input layer, obfuscation layer, fuzzy reasoning layer and output layer, utilizes the upper bound of fuzzy neural network approximating parameter uncertainty and external disturbance, is described as:

$\widehat{\mathrm{\&rho;}}\left(t\right)={\hat{w}}^T\mathrm{\&phi;}\left(X\right)---\left(17\right)$

Wherein, $X={\left[\begin{array}{cc}q& \stackrel{\&CenterDot;}{q}\end{array}\right]}^T$ For the input of fuzzy neural network, it is measurable signal in system;

the weights of fuzzy neural network, online real-time update; φ (X) is called the normalization confidence level of fuzzy neural network;

being the output of fuzzy neural network, is the estimation to the f upper bound.

Suppose the weight w that has one group of optimum fuzzy neural network, make to set up with lower inequality:

|ε(X)|＝|w ^Tφ(X)-ρ(t)|ε ^* (18)

Wherein, ε (X) is the best approximation error of parameter uncertainty and external disturbance upper bound ρ (t).

Parameter uncertainty and external disturbance f are also the function of time t,

The upper bound ρ (t) that supposes parameter uncertainty and external disturbance f (t) meets following condition:

ρ(t)-||f(t)||＞ε ₀＞ε ^* (19)

Wherein for very little positive number.

Based on this, the control law u shown in formula (10) ₂can be adjusted into u' ₂:

${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000413504470000022.png,HDA0000413504470000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{\&prime;}=-\widehat{\mathrm{\&rho;}}\left(t\right)\frac{s}{\left|\right|s\left|\right|}---\left(20\right)$

Like this, the control law U' after adjustment is adjusted again, becomes U'', U''=u' ₀+ u ₁+ u' ₂, U'' is the control law of the neural overall fast terminal sliding mode controller of adaptive fuzzy.

Getting Lyapunov function is:

$V=\frac{1}{2}{s}^{T}s+\frac{1}{2}\mathrm{tr}\left\{\tilde{D}{M}^{-1}{\tilde{D}}^T\right\}+\frac{1}{2}\mathrm{tr}\left\{\tilde{K}{N}^{-1}{\tilde{K}}^T\right\}\frac{1}{2}\mathrm{tr}\left\{\widetilde{\mathrm{\&Omega;}}{P}^{-1}{\widetilde{\mathrm{\&Omega;}}}^T\right\}+\frac{1}{2}{\mathrm{\&eta;}}^{-1}{\tilde{w}}^T\tilde{w}---\left(21\right)$

In formula, the mark of tr (A) representing matrix A;

be the evaluated error of neural network weight, because w is definite value, have

m, N, P is adaptive gain, M=M ^t> 0, N=N ^t> 0, P=P ^t> 0 is symmetric positive definite matrix, and η is fuzzy neural network learning rate.

In order to guarantee the derivative of Lyapunov function design

adaptive algorithm be respectively:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{D}}}^T=-\frac{1}{2}M(\stackrel{\&CenterDot;}{q}{s}^T+s{\stackrel{\&CenterDot;}{q}}^T)\\ {\stackrel{\&CenterDot;}{\hat{K}}}^T=-\frac{1}{2}N({\mathrm{qs}}^T+{\mathrm{sq}}^T)\\ {\stackrel{\&CenterDot;}{\widehat{\mathrm{\&Omega;}}}}^T=-\frac{1}{2}P(2\stackrel{\&CenterDot;}{q}{s}^T-2s{\stackrel{\&CenterDot;}{q}}^T)\end{array}\right.---\left(22\right)$

The Weight number adaptively algorithm of design fuzzy neural network is:

$\stackrel{\&CenterDot;}{\hat{w}}=\mathrm{\&eta;}\left|\right|s\left|\right|\mathrm{\&phi;}\left(X\right)=---\left(23\right)$

Control inputs using the control law U'' of the neural overall fast terminal sliding mode controller of adaptive fuzzy as gyroscope system, brings in the mathematical model of gyroscope system,

Lyapunov function V, along time t differentiate, and is brought into the Weight number adaptively algorithm of the parameters adaption algorithm of formula (22) and formula (23), obtains:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=s^T\stackrel{\&CenterDot;}{s}+\mathrm{tr}\left\{\tilde{D}{M}^{-1}{\stackrel{\&CenterDot;}{\tilde{D}}}^T\right\}+\mathrm{tr}\left\{\tilde{K}{N}^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}^T\right\}+\mathrm{tr}\left\{\widetilde{\mathrm{\&Omega;}}{P}^{-1}{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}}^T\right\}-{\mathrm{\&eta;}}^{-1}{\tilde{w}}^T\stackrel{\&CenterDot;}{\hat{w}}\\ =s^T(u_1+u_2^{\&prime;}+f)+s^T[-(\hat{D}+2\widehat{\mathrm{\&Omega;}})]s+s^T\tilde{D}\stackrel{\&CenterDot;}{q}+\mathrm{tr}\left\{\tilde{D}{M}^{-1}{\stackrel{\&CenterDot;}{\tilde{D}}}^T\right\}+s^T\tilde{K}q\\ +\mathrm{tr}\left\{\tilde{K}{N}^{-1}{\stackrel{\&CenterDot;}{\tilde{K}}}^T\right\}+2s^T\widetilde{\mathrm{\&Omega;}}\stackrel{\&CenterDot;}{q}+\mathrm{tr}\left\{\widetilde{\mathrm{\&Omega;}}{P}^{-1}{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}}^T\right\}-{\mathrm{\&eta;}}^{-1}{\tilde{w}}^T\stackrel{\&CenterDot;}{\hat{w}}\\ =s^T(u_1+u_2^{\&prime;}+f)+s^T[-(\hat{D}+2\widehat{\mathrm{\&Omega;}})]s-{\tilde{w}}^T\left|\right|s\left|\right|\mathrm{\&phi;}\left(X\right)\\ =s^T{u}_1+s^T[-(\hat{D}+2\widehat{\mathrm{\&Omega;}})]s+s^{T}f-\left|\right|s\left|\right|[{\hat{w}}^T\mathrm{\&phi;}\left(X\right)-\mathrm{\&rho;}\left(t\right)+\mathrm{\&rho;}\left(t\right)]-{\tilde{w}}^T\left|\right|s\left|\right|\mathrm{\&phi;}\left(X\right)\\ \&le;-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|-\left|\right|s\left|\right|[\mathrm{\&rho;}\left(t\right)-|\left|f\right|\left|\right]-\left|\right|s\left|\right|[{\hat{w}}^T\mathrm{\&phi;}\left(X\right)-\mathrm{\&rho;}\left(t\right)]-{\tilde{w}}^T\left|\right|s\left|\right|\mathrm{\&phi;}\left(X\right)\\ =-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|-\left|\right|s\left|\right|[\mathrm{\&rho;}\left(t\right)-|\left|f\right||=-|\left|s\right|\left|\right[{\hat{w}}^T\mathrm{\&phi;}\left(X\right)-w^T\mathrm{\&phi;}\left(X\right)+\mathrm{\&epsiv;}\left(X\right)]-(w^T-{\hat{w}}^T)|\left|s\right||\mathrm{\&phi;}\left(X\right)\\ =-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|-\left|\right|s\left|\right|[\mathrm{\&rho;}\left(t\right)-|\left|f\right|\left|\right]-\left|\right|s\left|\right|\mathrm{\&epsiv;}\left(X\right)\\ \&le;-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|-\left|\right|s\left|\right|[\mathrm{\&rho;}\left(t\right)-|\left|f\right|\left|\right]+\left|\right|s\left|\right|\left|\mathrm{\&epsiv;}\left(X\right)\right|\\ =\left|\right|s\left|\right|\left\{\right|\mathrm{\&epsiv;}\left(X\right)|-[\mathrm{\&rho;}\left(t\right)-\left|\right|f\left|\right|\left]\right\}-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|\\ \&le;\left|\right|s\left|\right|({\mathrm{\&epsiv;}}^{*}-{\mathrm{\&epsiv;}}_0)-{\mathrm{\&lambda;}}_{\min }\left(W\right)\left|\right|s\left|\right|\&le;-\mathrm{\&xi;}\left|\right|s\left|\right|<0\end{array}---\left(24\right)$

In formula, ξ=λ _min(W)-(ε ^*-ε ₀) > 0 and || s|| ≠ 0, λ _min(W) be the minimal characteristic root of W.

Thus, based on Liapunov stability the second method, can judge that designed controller has guaranteed the global stability of system, and make the output tracking error of system in finite time, converge to zero.

Four, Computer Simulation

In order to show more intuitively the validity of the neural overall fast terminal sliding-mode control of gyroscope adaptive fuzzy that the present invention proposes, now utilize mathematical software MATLAB/SIMULINK to carry out computer simulation experiment to the present invention.

With reference to existing document, the parameter of choosing gyroscope is:

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

Suppose that unknown input angular velocity is Ω _z=100rad/s, reference length is chosen for q ₀=1 μ m, natural frequency ω ₀=1000Hz, after nondimensionalization, three parameter matrixs of gyroscope are:

$D=\left[\begin{array}{cc}0.01& 0.002\\ 0.002& 0.01\end{array}\right],K=\left[\begin{array}{cc}355.3& 70.99\\ 70.99& 532.9\end{array}\right],\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -0.1\\ 0.1& 0\end{array}\right]---\left(25\right)$

Wherein, nondimensionalization process is, $\frac{d_{\mathrm{xx}}}{{\mathrm{m\&omega;}}_0}\&RightArrow;d_{\mathrm{xx}},\frac{d_{\mathrm{xy}}}{{\mathrm{m\&omega;}}_0}\&RightArrow;d_{\mathrm{xy}},\frac{d_{\mathrm{yy}}}{{\mathrm{m\&omega;}}_0}\&RightArrow;d_{\mathrm{yy}},\sqrt{\frac{k_{\mathrm{xx}}}{{{\mathrm{m\&omega;}}_0}^2}}\&RightArrow;{\mathrm{\&omega;}}_x,$ $\frac{k_{\mathrm{xy}}}{{{\mathrm{m\&omega;}}_0}^2}\&RightArrow;{\mathrm{\&omega;}}_{\mathrm{xy}},\sqrt{\frac{k_{\mathrm{yy}}}{{{\mathrm{m\&omega;}}_0}^2}}\&RightArrow;{\mathrm{\&omega;}}_y,\frac{{\mathrm{\&Omega;}}_z}{{\mathrm{\&omega;}}_0}\&RightArrow;{\mathrm{\&Omega;}}_z.$

In emulation experiment, the estimation initial value of three parameter matrixs of gyroscope is taken as respectively:

adaptive gain M, N, P is taken as: M=N=P=diag (150,150); The ideal trajectory of diaxon is taken as respectively: x _r=sin (π t), y _r=cos (0.5 π t); The starting condition of system is taken as:

parameter uncertainty and the external disturbance of system are taken as:

f＝[0.5*randn(1,1);0.5*randn(1,1)]。

Sliding-mode surface parameter is chosen for: p ₁=5, p ₂=3, α ₁=α ₂=0.25, β ₁=β ₂=0.5; Sliding mode controller parameter W=diag (w ₁, w ₂) be taken as: W=diag (2,4) (w ₁=2, w ₂=4).

Structure of fuzzy neural network is selected 2-10-25-1, and the initial value of neural network weight w is got the random value between [1,1], and the initial value of center vector and gaussian basis fat vector is got $C=\left(c_{\mathrm{ij}}\right)=\left[\begin{array}{ccc}0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5\end{array}\right]$ And B=(b _ij)=[0.20.20.2] ^t, fuzzy neural network learning rate is got η=0.001.

Fig. 4 is position curve of pursuit in the gyroscope X that adopts the neural overall fast terminal sliding-mode control of adaptive fuzzy and obtain, Y direction, and as seen from the figure, tracking effect is better, and through after a while, system can be followed the tracks of desired movement locus.Fig. 5 is the tracking error curve in X, Y direction, as can be seen from the figure, substantially converges to zero, and keep this motion through very short time error curve.

Fig. 6 is terminal sliding mode face convergence curve in gyroscope X, Y direction, through terminal sliding mode face after a while, can constantly level off to zero, shows that system can arrive sliding mode stabilized zone, i.e. s=0.System is not subject to the impact of external disturbance and uncertain factor, and the time very short is arrived to sliding-mode surface, and control system will enter sliding formwork track, keeps this motion.Control and compare with traditional fast terminal sliding formwork, overall fast terminal sliding formwork is controlled and has been solved the optimal problem of convergence time, thereby realize system state, converges to quickly and accurately equilibrium state.

Fig. 7 is control inputs response curve in X, Y direction, as can be seen from the figure, adopts the control inputs of fuzzy neural network upper bound adaptive learning substantially not produce and buffet.

Fig. 8 is the Adaptive Identification curve of gyroscope systematic parameter, and result shows d _xx, d _xy, d _yyand ω _x ², ω _xy, ω _y ²these parameters not only can converge to true value separately soon, and overshoot is also less.Fig. 9 is gyroscope angular velocity Ω _zidentification curve, result shows that angular velocity estimates finally to converge to its true value.

Figure 10 is X, Y direction upper bound change curve, and it is the result of learning by fuzzy neural network that the upper bound changes.According to the external environment condition that system is different, adaptive learning is carried out in the upper bound, make it can adapt to well adaptive terminal System with Sliding Mode Controller, reduce the generation that control system is buffeted simultaneously.

The above, it is only preferred embodiment of the present invention, not the present invention is done to any large restriction in form, although the present invention discloses as above with preferred embodiment, yet not in order to limit the present invention, any those skilled in the art, do not departing within the scope of technical solution of the present invention, when can utilizing the technology contents of above-mentioned announcement to make a little change or being modified to the equivalent embodiment of equivalent variations, in every case be the content that does not depart from technical solution of the present invention, any simple modification of above embodiment being done according to technical spirit of the present invention, equivalent variations and modification, all still belong in the scope of our bright technical scheme.

Claims (2)

1. the neural overall fast terminal sliding-mode control of the adaptive fuzzy of gyroscope, is characterized in that, comprises the following steps;

1) mathematical model of structure gyroscope system is:

$\stackrel{\&CenterDot;\&CenterDot;}{q}+(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+\mathrm{Kq}=u+f---\left(3\right)$

Wherein, the mass that q is gyroscope, in the position vector of driving shaft and sensitive axis diaxon, is the output of gyroscope system; U is the control inputs of gyroscope; D is damping matrix; The natural frequency that K has comprised diaxon and the stiffness coefficient of coupling; Ω is angular speed matrix; F is parameter uncertainty and the external disturbance of system;

2) building overall fast terminal sliding-mode surface s is:

$s=\stackrel{\&CenterDot;}{e}+\mathrm{\&alpha;e}+{\mathrm{\&beta;e}}^{p_2/p_1}---\left(6\right)$

Wherein, α=diag (α ₁, α ₂), β=diag (β ₁, β ₂) be sliding-mode surface constant; E=q-q _rfor tracking error; q _rfor the ideal position output vector of mass along diaxon; Q is two shaft position output vectors of gyroscope; p ₁, p ₂(p ₁> p ₂) be positive odd number;

3) build the neural overall fast terminal sliding mode controller of adaptive fuzzy:

3-1) for described gyroscope system, the sliding-mode surface of employing formula (6), overall fast terminal sliding formwork control law U is comprised of three control laws:

U＝u ₀+u ₁+u ₂ (7)

Wherein,

u ₀＝a+(D+2Ω)v+Kq，

D, K, three parameter matrixs that Ω is gyroscope,

$u_1=-W\frac{s}{\left|\right|s\left|\right|},W=\mathrm{diag}(w_1,w_2);$

W is sliding mode controller parameter;

the upper bound for parameter uncertainty and the external disturbance f of system;

3-2) due to three parameter matrix D of gyroscope, K, Ω is unknown, according to Adaptive Control Theory, uses estimated value

alternate parameter matrix D, K, Ω, and design the adaptive algorithm of three estimated values, online real-time update estimated value, control law u ₀be adjusted into u' ₀:

$u_0^{\&prime;}=a+(\hat{D}+2\widehat{\mathrm{\&Omega;}})v+\hat{K}q;$

3-3) according to Fuzzy Neural Network Theory, adopt fuzzy neural network to approach the parameter uncertainty of system and the upper bound ρ (t) of external disturbance f, and design the adaptive algorithm of fuzzy neural network weights, the output of online real-time update fuzzy neural network, the output of fuzzy neural network

Wherein,

the weights of fuzzy neural network, the normalization confidence level that φ (X) is fuzzy neural network, $X={\left[\begin{array}{cc}q& \stackrel{\&CenterDot;}{q}\end{array}\right]}^T$ For the input of fuzzy neural network,

Control law u ₂be adjusted into u' ₂:

$u_2^{\&prime;}=-\widehat{\mathrm{\&rho;}}\left(t\right)\frac{s}{\left|\right|s\left|\right|};$

3-4) with described step 3-2) and step 3-3) control law u' after adjusting ₀and u' ₂, replace step 3-1) in control law u ₀and u ₂, obtain the control law U'' of the neural overall fast terminal sliding mode controller of adaptive fuzzy

U''＝u' ₀+u ₁+u' ₂；

3-5) control inputs using the control law U'' of the neural overall fast terminal sliding mode controller of adaptive fuzzy as gyroscope system, brings in the mathematical model of gyroscope system, realizes the tracking of gyroscope system is controlled.

2. the neural overall fast terminal sliding-mode control of the adaptive fuzzy of gyroscope according to claim 1, it is characterized in that, described gyroscope parameter matrix D, K, the adaptive algorithm of the adaptive algorithm of the estimated value of Ω and fuzzy neural network weights designs based on Lyapunov stability theory:

Lyapunov function is:

$V=\frac{1}{2}{s}^{T}s+\frac{1}{2}\mathrm{tr}\left\{\tilde{D}{M}^{-1}{\tilde{D}}^T\right\}+\frac{1}{2}\mathrm{tr}\left\{\tilde{K}{N}^{-1}{\tilde{K}}^T\right\}+\frac{1}{2}\mathrm{tr}\left\{\widetilde{\mathrm{\&Omega;}}{P}^{-1}{\widetilde{\mathrm{\&Omega;}}}^T\right\}+\frac{1}{2}{\mathrm{\&eta;}}^{-1}{\tilde{w}}^T\tilde{w}$

Wherein, the mark of tr () representing matrix; M, N, P is adaptive gain, M=M ^t> 0, N=N ^t> 0, P=P ^t> 0 is symmetric positive definite matrix, and η is fuzzy neural network learning rate,

the evaluated error of neural network weight,

be respectively parameter matrix D, K, the parameter estimating error of Ω,

In order to guarantee the derivative of Lyapunov function

choose gyroscope parameter matrix D, K, the adaptive algorithm of the estimated value of Ω is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{D}}}^T=-\frac{1}{2}M(\stackrel{\&CenterDot;}{q}{s}^T+s{\stackrel{\&CenterDot;}{q}}^T)\\ {\stackrel{\&CenterDot;}{\hat{K}}}^T=-\frac{1}{2}N({\mathrm{qs}}^T+{\mathrm{sq}}^T)\\ {\stackrel{\&CenterDot;}{\widehat{\mathrm{\&Omega;}}}}^T=-\frac{1}{2}P(2\stackrel{\&CenterDot;}{q}{s}^T-2s{\stackrel{\&CenterDot;}{q}}^T)\end{array}\right.$

The adaptive algorithm of fuzzy neural network weights is:

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