CN102914972A - Micro-gyroscope RBF (Radial Basis Function) network self-adapting control method based on model global approximation - Google Patents

Abstract

The invention discloses a micro-gyroscope RBF (Radial Basis Function) network self-adapting control method based on model global approximation. According to the control method, based on a tracking error deign after filtering, a controller comprises a proportion differential item and an RBF neural network item. The RBF neural network item is approximated to an unknown function of a micro-gyroscope system and an updating algorithm based on a weight guarantees the global stability of the system based on a Lyapunov stability theory design. A robust item is added into the updating algorithm to guarantee the boundedness of control input; and the proportion differential item finally maintains a tracking error in any small range. The control method disclosed by the invention can realize high-precision tracking control on the micro-gyroscope system under the condition of no need of knowing about the structure or non-structure parameters of a micro-gyroscope, and in the presence of external interferences; and meanwhile, the robustness and the reliability of the system are improved.

Description

The gyroscope RBF network self-adapting control method of approaching based on model integral body

Technical field

The present invention relates to the control method of gyroscope, particularly relate to the gyroscope RBF network self-adapting control method of approaching based on model integral body.

Background technology

Micro-mechanical gyroscope (MEMS Gyroscope) is the inertial sensor that utilizes the sense angular speed that is used for that microelectric technique and micro-processing technology process.It detects angular velocity by the micromechanical component of a vibration of being made by silicon, so micro-mechanical gyroscope is very easy to miniaturization and batch production, has the characteristics such as the low and volume of cost is little.In recent years, micro-mechanical gyroscope is paid close attention in a lot of the application nearly, and for example, gyroscope cooperates micro-machine acceleration transducer to be used for inertial navigation, to be used for stabilized image at digital camera, to be used for wireless inertial mouse of computer etc.But the impact owing to inevitable mismachining tolerance and environment temperature in the manufacturing process can cause the difference between original paper characteristic and the design, causes gyroscope to have parameter uncertainty, is difficult to set up accurate mathematical model.The external disturbance effect of adding in the working environment be can not ignore, so that the control of the trajectory track of gyroscope is difficult to realization, and robustness is lower.Traditional control method is fully based on the nominal value parameter designing of gyroscope, and ignore the effect of quadrature error and external disturbance, although system is still stable in most of situation, but it is far undesirable to follow the trail of effect, and this controller for the single environment design has very large use limitation.

Domestic research for gyroscope mainly concentrates on structural design and manufacturing technology aspect at present, and above-mentioned mechanical compensation technology and driving circuit research, oscillation trajectory with advanced control method compensation foozle and control mass seldom appears, to reach the fully control of gyroscope and the measurement of angular velocity.The typical mechanism of domestic research gyroscope is Southeast China University's instrumental science and engineering college and Southeast China University's micro inertial instrument and advanced navigation techniques key lab.

International article has various advanced control methods is applied in the middle of the control of gyroscope, and adaptive control and sliding-mode control are typically arranged.These advanced methods have compensated on the one hand and have made the quadrature error that error causes, have realized on the other hand the TRAJECTORY CONTROL to gyroscope.But the adaptive control to external world robustness of disturbance is very low, easily makes system become unstable.

This shows, above-mentioned existing gyroscope obviously still has inconvenience and defective, and demands urgently further being improved in the use.The problem that exists in the use in order to solve existing gyroscope, relevant manufacturer there's no one who doesn't or isn't seeks solution painstakingly, is finished by development but have no for a long time applicable design always.

Summary of the invention

The object of the invention is to, overcome the defective that existing gyroscope control method exists, particularly improve the gyroscope system have that model is uncertain, under the various disturbed conditions such as Parameter Perturbation and external disturbance power, to the tracking performance of ideal trajectory and the robustness of whole system, and provide a kind of gyroscope RBF network self-adapting control system and method for approaching based on model integral body.Technical matters to be solved is a kind of self_adaptive RBF network control scheme of design, the structure and parameter function of online compensation gyroscope system the unknown, simultaneously additional proportion differential control, guarantee the global stability of whole gyroscope system, and given ideal trajectory on the gyroscope two track shafts energy high precision tracking, the robustness of raising gyroscope system.The adaptive algorithm of the RBF network weight among the present invention designs based on the Lyapunov stability theory, add the robust item that guarantees weights bounded, guaranteed that whole control system still can stablize and control inputs bounded admitting to exist under the condition of neural net model establishing error, thereby more be suitable for practicality, and have the value on the industry.

To achieve these goals, address the above problem, the technical solution used in the present invention is: the gyroscope RBF network self-adapting control method of approaching based on model integral body,

It is characterized in that may further comprise the steps:

(1), sets up the filtering error model of gyroscope

The target of micro-gyroscope control system is the oscillation trajectory q=[x that makes gyroscope, y] ^TGiven ideal trajectory q in the tracking _d=[x _d, y _d] ^T, tracking error is defined as e (t)=q thus _d(t)-and q (t), filtered tracking error is

The kinetic model of rewriting gyroscope based on r is:

$M\stackrel{\·}{r}=-\mathrm{Dr}-\mathrm{\τ}+f\left(x\right)-{\mathrm{\τ}}_d$

In the formula, M, D, f (x) is the unknown term of gyroscope system, and x is the signal that can measure in the system,

τ represents control inputs; τ _dBe the external interference effect.The control method of invention guarantees the final bounded of error r namely based on the filtering error modelling of this gyroscope, and converge on one more among a small circle in.

(2), the structure of CONTROLLER DESIGN

The control inputs of control method design of the present invention is:

$\mathrm{\τ}=\hat{f}\left(x\right)+K_{v}r$

In the formula,

Estimated value for the gyroscope function f (x) of the unknown is the output of RBF network, utilizes that the powerful Nonlinear Mapping of neural network and approximation capability are online estimates its true value in real time.

Be the proportion differential control item.

For the RBF network among the present invention, select three-decker: input layer, hidden layer and output layer.But input layer is accepted the measuring-signal input x in the system; Hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping; Output layer obtains the output of whole RBF network by the output of each hidden node of weighting.The center vector of the RBF network among the present invention and sound stage width are determined according to priori, are designed to fixed value, do not change in system's operational process, and the online real-time update of weights.Based on this, the RBF network model is described as

y＝W ^Tφ(x)

In the formula, W is the adjustable weights of RBF network, and φ (x) is RBF network hidden node output vector, because center vector and sound stage width are fixed, φ (x) is known signal.

Based on the approximation capability of RBF network, can do to suppose as this: have one group of optimum weights W ^*, so that belong to one when compacting S as the input x of RBF network, the RBF network can Nonlinear Function Approximation f (x), the network approximate error ε bounded under the optimum weights

f(x)＝W ^*Tφ(x)+ε(x)

In the formula, || ε (x) ||≤ε _N,

Optimum weights bounded || W ^*|| _F≤ W _B, || || _FThe F norm of representing matrix.

Therefore utilize the RBF network to approach in real time online f (x), reality is exactly to design the adaptive algorithm of adjustable network weight W, so that W can approach optimum weights W ^*, suppose W ^*Estimated value be

The RBF network is output as:

$\hat{f}\left(x\right)={\hat{W}}^T\mathrm{\φ}\left(x\right)$

Control inputs becomes:

$\mathrm{\τ}={\hat{W}}^T\mathrm{\φ}\left(x\right)+K_{v}r$

Bringing this control inputs into closed-loop system equation that the gyroscope model gets newly is:

In the formula,

Be the weights evaluated error.

So far, structure and the closed loop error equation of described controller have been obtained inventing.

(3), design adaptive algorithm gyroscope RBF network self-adapting control system and the method for approaching based on model integral body of the present invention of RBF network weight based on the Lyapunov stability theory, the adaptive algorithm of its RBF network weight designs based on the Lyapunov stability theory, the global stability of assurance system, form is as follows:

$\stackrel{\·}{\hat{W}}=\mathrm{F\φ}\left(x\right)r^T-\mathrm{\γF}\left|\right|r\left|\right|\hat{W}$

In the formula, F=F ^T＞0 gain matrix for the weights adjustment, the arbitrary value of γ＞0, similar forgetting factor.

Right value update algorithm in the following formula can guarantee tracking error r (t) and weights estimated value

Final bounded.Simultaneously, by enlarging state feedback factor matrix K _v, can be so that tracking error r (t) be maintained to arbitrarily small scope.First in the right value update algorithm in the formula is based on the error back propagation algorithm that the lyapunov stability theory is derived, and second be the robust item that adds, be used for guaranteeing the boundedness of weights, thereby guarantee the boundedness of control inputs, this point is very important to engineering reality.This right value update algorithm based on the design of Lyapunov stability theory sees the analytical proof process in the specific embodiment for details.

The present invention compared with prior art, advantage is:

(1) control method that has adopted the control of self_adaptive RBF network and proportion differential to combine can overcome unknown term and the external interference effect of gyroscope model effectively, can greatly improve the trajectory track precision again.

(2) the present invention adopts neural network adaptive algorithm, but the on-line control parameter control system, and adaptive algorithm has guaranteed the global stability of closed-loop system based on the design of Lyapunov stability theory.

(3) also added the robust item of assurance weights boundeds in the adaptive algorithm of network weight, thereby guaranteed the boundedness of control inputs, so that the present invention is easy to implement in engineering.

(4) the present invention does not need to be based upon on the basis of object Accurate Model to the control of gyroscope, has saved the expense of modeling.

Description of drawings

Fig. 1 is principle assumption diagram of the present invention.

Fig. 2 is the tracking curves of gyroscope driving shaft behind employing the present invention.

Fig. 3 is the tracking curves of gyroscope sensitive axis behind employing the present invention.

Fig. 4 is the control inputs curve among the present invention.

Embodiment

Reach technological means and the effect that predetermined goal of the invention is taked for further setting forth the present invention, below in conjunction with accompanying drawing and preferred embodiment, a kind of gyroscope RBF network self-adapting control system and its embodiment of method, structure, feature and effect thereof of approaching based on model integral body to foundation the present invention proposes is described in detail as follows.

Foundation is based on gyroscope filtering error model

Take into account foozle and external interference effect, the kinetics equation of diaxon micro-mechanical gyroscope is:

$m\stackrel{\·\·}{x}+d_{\mathrm{xx}}\stackrel{\·}{x}+d_{\mathrm{xy}}\stackrel{\·}{y}+k_{\mathrm{xx}}x+k_{\mathrm{xy}}y=u_x+d_x+2m{\mathrm{\Ω}}_z\stackrel{\·}{y}$

$m\stackrel{\·\·}{y}+d_{\mathrm{xy}}\stackrel{\·}{x}+d_{\mathrm{yy}}\stackrel{\·}{y}+k_{\mathrm{xy}}x+k_{\mathrm{yy}}y=u_y+d_y-2m{\mathrm{\Ω}}_z\stackrel{\·}{x}---\left(1\right)$

In the formula, m is the quality of mass; X, y are respectively mass along the position of driving shaft and sensitive axis; d _Xx, d _Xy, d _Yy, k _Xx, k _Xy, k _YyBe the parameter of gyroscope, become when unknown and slow; Ω _zBeing the angular velocity in the gyroscope working environment, also is unknown quantity; u _x, u _yIt is control inputs; d _x, d _yIt is the external interference effect.

Rewrite gyroscope kinetic model (1) with vector form:

$M\stackrel{\·\·}{q}+D\stackrel{\·}{q}+\mathrm{Kq}=\mathrm{\τ}-2\mathrm{\Ω}\stackrel{\·}{q}+{\mathrm{\τ}}_d---\left(2\right)$

In the formula, $q=\left[\begin{array}{c}x\\ y\end{array}\right],$ $\mathrm{\&tau;}=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],$ ${\mathrm{\&tau;}}_d=\left[\begin{array}{c}{d}_x\\ d_y\end{array}\right],$ $M=\left[\begin{array}{cc}m& 0\\ 0& m\end{array}\right],$ $D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],$ $K=\left[\begin{array}{cc}{k}_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{xy}}& k_{\mathrm{yy}}\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -m{\mathrm{\&Omega;}}_z\\ m{\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00002343279800021.png,HDA00002343279800022.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right]$

We can make following standard hypothesis for gyroscope:

I. the quality m of mass remains unchanged in the whole course of work and working environment, namely

Also be $\stackrel{.}{M}=0$

II. the ratio of damping d of gyroscope _Xx, d _Xy, d _YySatisfy relation: d _Xxd _Xy, d _Yyd _XySo the D matrix is positive definite symmetric matrices

The control target of gyroscope is that the oscillation trajectory of mass diaxon is followed the trail of upper given ideal trajectory q _d=[x _d, y _d] ^T, the definition tracking error is:

e(t)＝q _d(t)-q(t) (3)

Designing filtered tracking error is:

$r\left(t\right)=\stackrel{\&CenterDot;}{e}\left(t\right)+\mathrm{\&Lambda;e}\left(t\right)---\left(4\right)$

In the formula, Λ=Λ ^T＞0, be a controller design parameter, generally namely be taken as element and entirely be positive diagonal matrix.R (t) is carried out differentiate, bring formula (2) into, the mathematical model of gyroscope is written as with filtered errors of form:

$M\stackrel{\&CenterDot;}{r}=-\mathrm{Dr}-\mathrm{\&tau;}+f\left(x\right)-{\mathrm{\&tau;}}_d---\left(5\right)$

In the formula,

$f\left(x\right)=M({\stackrel{\&CenterDot;\&CenterDot;}{q}}_d+\mathrm{\&Lambda;}\stackrel{\&CenterDot;}{e})+D({\stackrel{\&CenterDot;}{q}}_d+\mathrm{\&Lambda;e})+\mathrm{Kq}+2\mathrm{\&Omega;}\stackrel{\&CenterDot;}{q}---\left(6\right)$

Gyroscope parameter and structure function that expression is unknown.In the formula,

Be the signal that can measure, as the input of neural network

$x={\left[\begin{array}{ccccc}{e}^T& {\stackrel{\&CenterDot;}{e}}^T& q_d^T& {\stackrel{\&CenterDot;}{q}}_d^T& {\stackrel{\&CenterDot;\&CenterDot;}{q}}_d^T\end{array}\right]}^T---\left(7\right)$

The CONTROLLER DESIGN structure

Controller's design is based on the gyroscope mathematical model (5) that obtains in the step (1), and the control inputs of design is:

$\mathrm{\&tau;}=\hat{f}\left(x\right)+K_{v}r---\left(8\right)$

In the formula,

Estimated value for the gyroscope function f (x) of the unknown is the output of RBF network, utilizes that the powerful Nonlinear Mapping of neural network and approximation capability are online estimates its true value in real time.

Be the proportion differential control item, wherein The principle assumption diagram of whole control system as shown in Figure 1.

Bringing control law (8) into model (5) must the closed-loop system equation be:

In the formula, the network-evaluated error of RBF is:

$\tilde{f}=f-\tilde{f}---\left(10\right)$

Formula (9) is the kinetics equation of filtered tracking error system, and the purpose of control system makes error r bounded, and converges on a less scope.As seen from formula (4), be a stable wave filter from e to r, if the final bounded of r, then tracking error e bounded.

For the RBF network among the present invention, select three-decker: input layer, hidden layer and output layer.But input layer is accepted the measuring-signal input x in the system; Hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping; Output layer obtains the output of whole RBF network by the output of each hidden node of weighting, as follows with mathematical description RBF network model:

$y_i=\underset{j=1}{\overset{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{ij}}{\mathrm{\&phi;}}_j,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{<figure-callout\; id="3"\; label="n"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_3$

${\mathrm{\&phi;}}_j\left(x\right)=\exp \left(\right||x-c_j||/{\mathrm{\&sigma;}}_j),j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;n_2---\left(11\right)$

In the formula, n ₂, n ₃Represent respectively hidden node number and output layer node number, and the dimension of input signal x is designated as n ₁ω _IjThe expression network weight; y _iThe output of expression RBF network; φ _j(x) be hidden node output; c _j, σ _jThe center vector and the sound stage width that represent respectively each hidden node.Existing document is verified, and the RBF network can approach with arbitrary accuracy the nonlinear function of arbitrary smooth.The center vector of the RBF network among the present invention and sound stage width are determined according to priori, are designed to fixed value, do not change in system's operational process, and the online real-time update of weights.Based on this, the RBF network model is rewritten as:

y＝W ^Tφ(x) (12)

In the formula, W ^T=[ω _Ij], φ (x)=[φ _j(x)], because c _j, σ _jFixing, φ (x) is known signal.Based on the approximation capability of RBF network, can do to suppose as this: have one group of optimum weights W ^*, so that belong to one when compacting S as the input x of RBF network, the RBF network can Nonlinear Function Approximation f (x), the network approximate error ε bounded under the optimum weights

f(x)＝W ^*Tφ(x)+ε(x) (13)

In the formula, || ε (x) ||≤ε _N,

Optimum weights bounded || W ^*|| _F≤ W _B, || || _FThe F norm of representing matrix.

Utilize the RBF network to approach f (x), the RBF network is output as:

$\hat{f}\left(x\right)={\hat{W}}^T\mathrm{\&phi;}\left(x\right)---\left(14\right)$

Convolution (8), control inputs becomes:

$\mathrm{\&tau;}={\hat{W}}^T\mathrm{\&phi;}\left(x\right)+K_{v}r---\left(15\right)$

Bringing control inputs (15) into model (5) must closed-loop system equation newly be:

In the formula,

Be the weights evaluated error.

So far, structure and the closed loop error equation of described controller have been obtained inventing.

The update algorithm of design RBF neural network weight

Gyroscope RBF network self-adapting control system and method for approaching based on model integral body of the present invention, the update algorithm of its RBF network weight is:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{F\&phi;}\left(x\right)r^T-\mathrm{\&gamma;F}\left|\right|r\left|\right|\hat{W}---\left(17\right)$

In the formula, F is gain matrix, and r is filtered error, F=F ^T＞0 gain matrix for the weights adjustment, the arbitrary value of γ＞0, similar forgetting factor.

Below right value update algorithm in the proof formula (17) can guarantee tracking error r (t) and weights estimated value

Final bounded, and boundary separately is shown in lower inequality (24), (25) right side.Simultaneously, by enlarging state feedback factor matrix K _v, can be so that tracking error r (t) be maintained to arbitrarily small scope.

The closed-loop system of (16) is chosen a Lyapunov candidate functions:

$L=\frac{1}{2}{r}^T\mathrm{Mr}+\frac{1}{2}\mathrm{tr}\left({\tilde{w}}^T{F}^{-1}\tilde{W}\right)---\left(18\right)$

To formula (18) both sides differentiate:

$\stackrel{\&CenterDot;}{L}=r^{T}M\stackrel{\&CenterDot;}{r}+\mathrm{tr}\left({\tilde{w}}^T{F}^{-1}\stackrel{\&CenterDot;}{\tilde{W}}\right)$

$=-r^T(K_v+D)r+\mathrm{tr}\left({\tilde{w}}^T(F^{-1}\stackrel{\&CenterDot;}{\tilde{w}}+\mathrm{\&phi;}\left(x\right)r^T)\right)+r^T(\mathrm{\&epsiv;}-{\mathrm{\&tau;}}_d)---\left(19\right)$

Bringing the right value update algorithm in the formula (17) into formula (19) gets:

$\stackrel{\&CenterDot;}{L}=-r^T(K_v+D)r+\mathrm{\&gamma;}\left|\right|r\left|\right|\mathrm{tr}\left\{{\tilde{W}}^T(W-\tilde{W})\right\}+r^T(\mathrm{\&epsiv;}-{\mathrm{\&tau;}}_d)---\left(20\right)$

The character of associate(d) matrix mark and matrix F norm has:

$\mathrm{tr}\left\{{\tilde{W}}^T(W-\tilde{W})\right\}={<\widetilde{W,}W>}_F-{\left|\right|\tilde{W}\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">F</figure-callout>}}^2\&le;{\left|\right|\tilde{W}\left|\right|}_F{\left|\right|W\left|\right|}_F-{\left|\right|\tilde{W}\left|\right|}_F^2---\left(21\right)$

So,

$\stackrel{\&CenterDot;}{L}\&le;-r^T{K}_{v}r+\mathrm{\&gamma;}\left|\right|r\left|\right|\&CenterDot;{\left|\right|\tilde{W}\left|\right|}_F({\left|\right|W\left|\right|}_F-{\left|\right|\tilde{W}\left|\right|}_F)+({\mathrm{\&epsiv;}}_N+b_d)\left|\right|r\left|\right|$

$\&le;-K_{v\min }{\left|\right|r\left|\right|}^2+\mathrm{\&gamma;}\left|\right|r\left|\right|\&CenterDot;{\left|\right|\tilde{W}\left|\right|}_F(W_B-{\left|\right|\tilde{W}\left|\right|}_F)+({\mathrm{\&epsiv;}}_N+b_d)\left|\right|r\left|\right|$

$=-\left|\right|r\left|\right|\left[K_{v\min }\right|\left|r\right||+\mathrm{\&gamma;}{\left|\right|\tilde{W}\left|\right|}_F({\left|\right|\tilde{W}\left|\right|}_F-W_B)-({\mathrm{\&epsiv;}}_N+d_d)]---\left(22\right)$

Can find out from formula (22), suc as formula transition formula evaluation in the middle bracket for just, then For negative, i.e. system stability.

Because:

$K_{v\min }\left|\right|r\left|\right|+\mathrm{\&gamma;}{\left|\right|\tilde{W}\left|\right|}_F({\left|\right|\tilde{W}\left|\right|}_F-W_B)-({\mathrm{\&epsiv;}}_N+b_d)$

$=\mathrm{\&gamma;}{({\left|\right|\tilde{W}\left|\right|}_F-W_B/2)}^2-\mathrm{\&gamma;}{\mathrm{<figure-callout\; id="2"\; label="W\; B"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">W</figure-callout>}}_B^{}/4+K_{v\min }\left|\right|r\left|\right|-({\mathrm{\&epsiv;}}_N+b_d)$

Formula (23) can guarantee to need only into just

$\left|\right|r\left|\right|>\frac{\mathrm{\&gamma;}{\mathrm{<figure-callout\; id="2"\; label="W\; B"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">W</figure-callout>}}_B^{}/4({\mathrm{\&epsiv;}}_N+b_d)}{K_{v\min }}\&equiv;b_r---\left(24\right)$

Perhaps

${\left|\right|\tilde{W}\left|\right|}_F>W_B/2+\sqrt{\mathrm{\&gamma;}{\mathrm{<figure-callout\; id="2"\; label="W\; B"\; filenames="HDA00002343279800012.png,HDA00002343279800021.png"\; state="\{\{state\}\}">W</figure-callout>}}_B^{}/4+({\mathrm{\&epsiv;}}_N+b_d)/\mathrm{\&gamma;}}\&equiv;b_W---\left(25\right)$

Comprehensive above analytic process, can reach a conclusion:

Outside the zone of formula (24) or (25) description, it is negative definite.According to the standard of Lyapunov stability theory expansion theorem, as can be known || r|| and Ultimate boundedness be guaranteed.Because, in case r or

Exceeded formula (24) and (25) regulation regional extent, will cause the decline of Lyapunov function L, this again can so that r and

Get back in the two formula restricted portions.So formula (24) (25) is separate provision in fact just || r|| and

The upper bound.And, can notice larger feedback gain matrix K from formula (24) _vWill obtain less || the upper bound of r||, so tracking error r finally can maintain in the arbitrarily small scope.Can find out from formula (15), the boundedness of RBF network weight has guaranteed the boundedness of control inputs, and this point is very important for Practical Project.

Can find out from top analytical proof process, first in the right value update algorithm in the formula (17) is based on the error back propagation algorithm that the lyapunov stability theory is derived, and second be the robust item that adds, and is used for guaranteeing the boundedness of weights.

Computer simulation experiment

For the gyroscope RBF network self-adapting control system of approaching based on model integral body that shows more intuitively that the present invention proposes and the validity of method, now utilize mathematical software MATLAB/SIMULINK that this control program is carried out computer simulation experiment.With reference to existing document, the parameter of choosing gyroscope is:

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

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

Unknown angular speed is assumed to Ω _z=100rad/s.Ideal trajectory is described as: q _Dx=0.1*cos (6.17t), q _Dy=0.1*cos (5.11t).Gyroscope is zero original state.Consider that external disturbance act as the noise that resonates with ideal trajectory, is embodied as: τ in MATLAB _d=[(sin (6.17*t)) ²+ cos (6.17*t), (sin (5.11*t)) ²+ cos (5.11*t)] ^TIn the emulation experiment, get feedback of status gain K _v=diag{50,50}, the coefficient Λ=diag{5 of wave filter, 5}; The hidden node number of RBF network is set as 45; The initial weight of RBF network all is made as 1.Under the situation of above each controller parameter, move simulated program, obtain simulation result curve such as the accompanying drawing 2,3 of invention specific embodiment, shown in 4.

Accompanying drawing 2, accompanying drawing 3 have been showed the track following effect curve of the gyroscope under the control method that the present invention proposes.Can find out from these two accompanying drawings, control system can be so that the output of gyroscope in the situation that do not know gyroscope parameter and structure and have the external interference effect, can promptly be followed the tracks of given ideal trajectory, and tracking error is very little, has reached satisfied effect.

Accompanying drawing 4 has been showed the curve of control inputs in the emulation experiment, and smooth curve in the time of can finding out the control inputs of the control method that the present invention proposes is easy to Project Realization.

Can find out from above analogous diagram, the control method that the present invention proposes has good control effect to the track following of gyroscope, greatly improved tracking performance and the robustness of gyroscope system, the high precision of gyroscope diaxon oscillation trajectory is controlled provides theoretical foundation and From Math.

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

Claims (8)

1. the gyroscope RBF network self-adapting control method of approaching based on model integral body is characterized in that: may further comprise the steps:

(1), sets up the filtering error model of gyroscope;

(2), CONTROLLER DESIGN structure;

(3), design the adaptive algorithm of RBF network weight based on the Lyapunov stability theory.

2. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 1 is characterized in that: the filtering error model of setting up gyroscope; The target of micro-gyroscope control system is the oscillation trajectory q=[x that makes gyroscope, y] ^TGiven ideal trajectory q in the tracking _d=[x _d, y _d] ^T, tracking error is defined as e (t)=q thus _d(t)-and q (t), filtered tracking error is

The kinetic model of rewriting gyroscope based on r is:

$M\stackrel{\&CenterDot;}{r}=-\mathrm{Dr}-\mathrm{\&tau;}+f\left(x\right)-{\mathrm{\&tau;}}_d$

In the formula, M, D, f (x) is the unknown term of gyroscope system, and x is the signal that can measure in the system; τ represents control inputs; τ _dBe the external interference effect, the control method of invention guarantees the final bounded of error r namely based on the filtering error modelling of this gyroscope, and converge on one more among a small circle in.

3. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 2 is characterized in that: described RBF network be input as measurable signal in the system

E wherein,

Be respectively tracking error and derivative thereof, q _d,

Be respectively reference locus and all-order derivative thereof.

4. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 3 is characterized in that: the CONTROLLER DESIGN structure, and the control inputs of control method design of the present invention is:

$\mathrm{\&tau;}=\hat{f}\left(x\right)+K_{v}r$

In the formula,

Estimated value for the gyroscope function f (x) of the unknown is the output of RBF network, utilizes that the powerful Nonlinear Mapping of neural network and approximation capability are online estimates its true value in real time,

Be the proportion differential control item.

5. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 4, it is characterized in that: described RBF network is three-decker: input layer, hidden layer and output layer, but input layer is accepted the measuring-signal input x in the system; Hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping; Output layer obtains the output of whole RBF network by the output of each hidden node of weighting, the center vector of RBF network and sound stage width are determined according to priori, be designed to fixed value, do not change in system's operational process, and the online real-time update of weights, based on this, the RBF network model is described as

y＝W ^Tφ(x)

In the formula, W is the adjustable weights of RBF network, and φ (x) is RBF network hidden node output vector, because center vector and sound stage width are fixed, φ (x) is known signal.

6. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 5 is characterized in that: based on the approximation capability of RBF network, can do to suppose as this: have one group of optimum weights W ^*, so that belong to one when compacting S as the input x of RBF network, the RBF network can Nonlinear Function Approximation f (x), the network approximate error ε bounded under the optimum weights

f(x)＝W ^*Tφ(x)+ε(x)

In the formula, || ε (x) ||≤ε _N,

Optimum weights bounded || W ^*|| _F≤ W _B, || || _FThe F norm of representing matrix,

Therefore utilize the RBF network to approach in real time online f (x), reality is exactly to design the adaptive algorithm of adjustable network weight W, so that W can approach optimum weights W ^*, suppose W ^*Estimated value be

The RBF network is output as:

$\hat{f}\left(x\right)={\hat{W}}^T\mathrm{\&phi;}\left(x\right)$

Control inputs becomes:

$\mathrm{\&tau;}={\hat{W}}^T\mathrm{\&phi;}\left(x\right)+K_{v}r$

Bringing this control inputs into closed-loop system equation that the gyroscope model gets newly is:

In the formula, Be the weights evaluated error, so far, obtained inventing structure and the closed loop error equation of described controller.

7. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 6 is characterized in that: based on the adaptive algorithm of Lyapunov stability theory design RBF network weight,

Form is as follows:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{F\&phi;}\left(x\right)r^T-\mathrm{\&gamma;F}\left|\right|r\left|\right|\hat{W}$

In the formula, F is gain matrix, and r is filtered error, F=F ^T＞0 gain matrix for the weights adjustment, the arbitrary value of γ＞0, similar forgetting factor,

Right value update algorithm in the following formula can guarantee tracking error r (t) and weights estimated value

Final bounded, the right value update algorithm designs based on Leah Pu Nuofu stability theory, the global stability of Guarantee control system,

Simultaneously, by enlarging state feedback factor matrix K _vCan be so that tracking error r (t) be maintained to arbitrarily small scope, first in the right value update algorithm in the formula is based on the error back propagation algorithm that the lyapunov stability theory is derived, and second be the robust item that adds, be used for guaranteeing the boundedness of weights, thereby guarantee the boundedness of control inputs.

8. gyroscope RBF network self-adapting control method of approaching based on model integral body according to claim 7, it is characterized in that: control inputs τ has also comprised a proportion differential item K _vR, wherein K _vBe the feedback gain of deviser's designed, designed, improve K _vSize can reduce tracking error to arbitrarily small scope.

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