CN103324087A - Micro gyroscope self-adaptation inversion control system and method based on neural network - Google Patents

Abstract

The invention discloses a micro gyroscope self-adaptation inversion control system and method based on a neural network. The control system comprises a reference track module, a middle signal generating module, an inversion controller, a neural network self-adaptation system, a micro gyroscope self-adaptation controller, a first adding device and a micro gyroscope system. According to the micro gyroscope self-adaptation inversion control system and method based on the neural network, the advantages of the inversion design technology are utilized, the design processes of the micro gyroscope control system are simplified, a new path of the design of the micro gyroscope control system is opened up, meanwhile, the characteristics of the control technology of the neural network are combined, the weight parameters of the neural network are adjusted in an on-line and real-time mode, an updating algorithm of network weights is designed based on the Lyapunov stability theory, and the stability of a closed-loop system is ensured. According to the micro gyroscope self-adaptation inversion control system and method based on the neural network, unknown dynamic characteristics and influences of noise interference of the micro gyroscope can be compensated in an on-line mode, two-shaft vibration tracks of the micro gyroscope are made to track the reference track, and meanwhile the reliability and the anti-interference robustness of the system are improved.

Description

Self-adaptation inverting control system and method based on the gyroscope of neural network

Technical field

The present invention relates to adaptive control system and the method for gyroscope, particularly relate to gyroscope self-adaptation inverting control system and method based on neural network.

Background technology

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 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, 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 traditional adaptive control design process is comparatively complicated, and calculated amount is large, and the robustness of to external world 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 have that model is uncertain, under the various disturbed conditions such as Parameter Perturbation and outside noise, be to improve the gyroscope system to tracking performance and the robustness of whole system and the design process of simplified control system of reference locus, and a kind of self-adaptation inverting control system and method for the gyroscope based on neural network are provided.

The object of the invention to solve the technical problems realizes by the following technical solutions,

Self-adaptation inverting control system based on the gyroscope of neural network comprises:

Reference locus module 101 is used for exporting the reference locus of gyroscope two shaft vibrations, comprises position, speed and acceleration signal;

M signal generation module 102 is used for receiving the output of reference locus and gyroscope system, and produces the M signal in the inverting controller design process;

Inverting controller 103 is used for receiving M signal, and the output that produces the inverting controller;

Neural network adaptive system 104 is used for receiving the output of M signal and gyroscope system, and the online neural network weight of adjusting in real time, produces the output of ANN (Artificial Neural Network) Control signal;

Gyroscope adaptive controller 105 is inverting controller 103 and neural network adaptive system 104 sums, is the master controller of system;

First adder 106 is with the reverse output addition of 103 outputs of inverting controller and neural network adaptive system 104;

Gyroscope system 107, controlled gyroscope object has been considered the impact of mechanical noise, produces the vibration signal output of gyroscope vibrating mass;

Control method based on the self-adaptation inverting control system of the gyroscope of neural network may further comprise the steps,

1) based on Based Inverse Design Method, sets up the nondimensionalization kinetic model of gyroscope;

2) design inverting controller;

3) design neural network adaptive system;

4) utilize first adder to obtain the output of gyroscope adaptive controller, as the control inputs of gyroscope.

Aforesaid step 1) is set up the nondimensionalization kinetic model of gyroscope, is specially:

1-1) the existence of consideration mechanical noise, the nondimensionalization vector form of diaxon gyroscope kinetics equation is:

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

In the formula, $q=\left[\begin{array}{c}x\\ y\end{array}\right],\mathrm{\&tau;}=\left[\begin{array}{c}{\mathrm{\&tau;}}_x\\ {\mathrm{\&tau;}}_y\end{array}\right],d=\left[\begin{array}{c}{d}_x\\ d_y\end{array}\right],D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],K=\left[\begin{array}{cc}{k}_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{xy}}& k_{\mathrm{yy}}\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right]$

Q is the oscillation trajectory of gyroscope, and x, y represent that respectively the vibrating mass of gyroscope is in the position of vibration diaxon; d _Xx, d _Xy, d _YyInternally-damped coefficient for gyroscope; k _Xx, k _Xy, k _YyInside spring ratio for gyroscope; Ω _zThe input angle speed of gyroscope; τ _x, τ _yIt is the control inputs of gyroscope; d _x, d _yThe internal mechanical noise of expression gyroscope system;

1-2) defining variable X ₁, X ₂, based on the inverting designing technique, the kinetics equation (2) of gyroscope is transformed to following form,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=-(D+2\mathrm{\&Omega;})X_2-{\mathrm{<figure-callout\; id="1"\; label="KX"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">KX</figure-callout>}}_1+\mathrm{\&tau;}+d\end{array}\right.---\left(4\right)$

In the formula, ${\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1=q,X_2=\stackrel{\&CenterDot;}{q};$

1-3) the unknown dynamic perfromance f of definition (z) is,

f(z)＝-(D+2Ω)X ₂-KX ₁ （6）

The kinetic model of gyroscope is further write as,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=f\left(z\right)+\mathrm{\&tau;}+d\end{array}\right.---\left(7\right)$

Variable z is z=[X ₁, X ₂] ^T, be measurable signal in the system, X ₁Be the oscillation trajectory of gyroscope, take kinetic model equation (7) as basic engineering inverting controller.

Aforesaid step 2), design inverting controller is specially:

2-1) by the reference locus of reference locus module 101 output gyroscope vibrations, comprise position signalling q _d, rate signal Acceleration signal

Export position signalling q and the rate signal of the vibration of vibrating mass by gyroscope system 107

Generate signaling module 102 2-2) and receive the reference locus signal With gyroscope vibration signal q and

Generate the M signal in the inverting controller design process, the M signal design is as follows

Tracking error e ₁: e ₁=X ₁-q _d

Virtual controlling amount α ₁And derivative ${\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1:{\mathrm{\&alpha;}}_1={-c}_1{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{q}}_d$

Deviation e ₂: e ₂=X ₂-α ₁

2-3) inverting controller 103 receives M signal

Lyapunov function V according to design ₂Produce control signal u, consist of the part of overhead control signal, control signal u design is as follows

$u=-c_2{e}_2-{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)$

Wherein, v=-ρ sgn (e ₂) be the robust item, the upper bound of the internal mechanical noise of ρ gyroscope system; c ₁, c ₂Be any symmetric positive definite matrix; Sgn () represents sign function.

Aforesaid Lyapunov function V ₂For:

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{1}{2}{e_1}^T{e}_{1.}$

Design neural network adaptive system is specially in the aforesaid step 3)

3-1) design neural network adaptive system 104 is in order to approach the unknown dynamic perfromance f (z) of gyroscope, described neural network structure is selected the RBF neural network, comprise three-decker: input layer, hidden layer and output layer, but input layer is accepted the measuring-signal in the system, hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping, and output layer obtains the output of whole RBF neural network by the output of each hidden node of weighting

3-2) with the output z of gyroscope system 107 input as the RBF neural network, hidden layer is selected fixing center vector c and sound stage width b, and output layer produces the output of RBF neural network

$\hat{f}\left(z\right)={\hat{W}}^T\mathrm{\&phi;}\left(z\right)---\left(22\right)$

In the formula,

The instantaneous value of expression RBF neural network weight, φ (z) is the output vector of hidden layer,

$\mathrm{\&phi;}\left(z\right)=\exp (-\frac{{\left|\right|z-c\left|\right|}^2}{b^2})---\left(23\right)$

3-3) based on the Lyapunov stability theory, the design neural network weight

Adaptive algorithm, obtain adaptive law

For:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{F\&phi;}\left(z\right){e_2}^T---\left(28\right)$

Matrix F is any symmetric positive definite matrix in the formula.

Aforesaid Lyapunov function is V

$V=\frac{1}{2}{e_1}^T{e}_1+\frac{1}{2}{e_2}^T{e}_2+\frac{1}{2}\mathrm{tr}\left\{{\tilde{W}}^T{F}^{-1}\tilde{W}\right\}---\left(26\right)$

Wherein,

Expression weights evaluated error.

The control inputs τ of aforesaid step 4) gyroscope is

$\mathrm{\&tau;}=u-\hat{f}\left(z\right)={-c}_2{e}_2-{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)-{\hat{W}}^T\mathrm{\&phi;}.$

The present invention compared with prior art, advantage is:

(1) control method that has adopted self_adaptive RBF network and inverting designing technique to combine, can effectively overcome the dynamic perfromance of gyroscope the unknown and the impact of mechanical noise, improve systematic tracking accuracy and robustness, simplified again the design process of micro-gyroscope control system.

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

(3) 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 the principle assumption diagram of control system of the present invention;

Fig. 2 is the structural drawing of the RBF neural network that adopts of the present invention;

Fig. 3 is the tracking curves based on gyroscope driving shaft of the present invention;

Fig. 4 is the tracking curves based on gyroscope sensitive axis of 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, self-adaptation inverting control system and method based on the gyroscope of neural network that foundation the present invention is proposed are elaborated as rear.

As shown in Figure 1, the self-adaptation inverting control system based on the gyroscope of neural network comprises:

Reference locus module 101 is used for exporting the reference locus of gyroscope two shaft vibrations, comprises position, speed and acceleration signal;

M signal generation module 102 is used for receiving the output of reference locus and gyroscope, and produces the M signal output in the inverting controller design process;

Inverting controller 103 is used for receiving M signal, and the output that produces the inverting controller;

Neural network adaptive system 104 is used for receiving the output of M signal and gyroscope system, and the online neural network weight of adjusting in real time, produces the output of ANN (Artificial Neural Network) Control signal;

Gyroscope adaptive controller 105 is inverting controller 103 and neural network adaptive system 104 sums, is the master controller of system;

First adder 106 is with the reverse output addition of 103 outputs of inverting controller and neural network adaptive system 104;

Gyroscope system 107, controlled gyroscope object has been considered the impact of mechanical noise, produces the vibration signal output of gyroscope vibrating mass;

Control method based on the self-adaptation inverting control system of the gyroscope of neural network may further comprise the steps,

(1) based on Based Inverse Design Method, sets up the nondimensionalization kinetic model of gyroscope

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

$\begin{array}{c}m\stackrel{\&CenterDot;\&CenterDot;}{x}+d_{\mathrm{xx}}\stackrel{\&CenterDot;}{x}+d_{\mathrm{xy}}\stackrel{\&CenterDot;}{y}+k_{\mathrm{xx}}x+k_{\mathrm{xy}}y={\mathrm{\&tau;}}_x+{2\mathrm{m\&Omega;}}_z\stackrel{\&CenterDot;}{y}+d_x\\ m\stackrel{\&CenterDot;\&CenterDot;}{y}+d_{\mathrm{xy}}\stackrel{\&CenterDot;}{x}+d_{\mathrm{yy}}\stackrel{\&CenterDot;}{y}+k_{\mathrm{xy}}x+k_{\mathrm{yy}}y={\mathrm{\&tau;}}_y-2m{\mathrm{\&Omega;}}_z\stackrel{\&CenterDot;}{x}+d_y\end{array}---\left(1\right)$

In the formula, m is the quality of vibrating machine parts; X, y are respectively vibrating mass along the position of driving shaft and sensitive axis; d _Xx, d _Xy, d _YyBe the ratio of damping of gyroscope, k _Xx, k _Xy, k _YySpring ratio for gyroscope; Ω _zThe angular velocity in the gyroscope working environment; τ _x, τ _yIt is control inputs; d _x, d _yIt is mechanical noise.Process through nondimensionalization, the non-dimension form of the kinetic model of gyroscope is write as following vector form,

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

In the formula, $q=\left[\begin{array}{c}x\\ y\end{array}\right],\mathrm{\&tau;}=\left[\begin{array}{c}{\mathrm{\&tau;}}_x\\ {\mathrm{\&tau;}}_y\end{array}\right],d=\left[\begin{array}{c}{d}_x\\ d_y\end{array}\right],D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],K=\left[\begin{array}{cc}{k}_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{xy}}& k_{\mathrm{yy}}\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right],$ Can reasonably suppose mechanical noise d (t) bounded, the upper bound is ρ, namely || d (t) ||≤ρ.

Based on the inverting designing technique, at first the model of gyroscope carried out equivalent transformation, defining variable X ₁, X ₂,

${\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1=q,X_2=\stackrel{\&CenterDot;}{q}---\left(3\right)$

X ₁Be the oscillation trajectory of gyroscope,

Based on variable X ₁, X ₂, kinetic model formula (2) is rewritten as

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=-(D+2\mathrm{\&Omega;})X_2-{\mathrm{<figure-callout\; id="1"\; label="KX"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">KX</figure-callout>}}_1+\mathrm{\&tau;}+d\end{array}\right.---\left(4\right)$

The parameter D of gyroscope, K, Ω are unknown ,-(D+2 Ω) X ₂-KX ₁Consisted of the unknown dynamic perfromance of system, defining variable z

z＝[X ₁,X ₂] ^T （5）

Defining unknown dynamic perfromance is f (z),

f(z)＝-(D+2Ω)X ₂-KX ₁ （6）

Then the kinetic model of gyroscope is further write as,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=f\left(z\right)+\mathrm{\&tau;}+d\end{array}\right.---\left(7\right)$

The model that formula (7) is described is the basis of inverting controller design of the present invention.

(2) design inverting controller

The target of control system is so that the oscillation trajectory X of gyroscope system ₁Given reference locus in the tracking, definition tracking error e ₁For:

e ₁＝X ₁-q _d （8）

q _dBe reference locus.

Based on Based Inverse Design Method, the inverting controller of design gyroscope,

(2-a) combined mathematical module formula (7), design virtual controlling amount α ₁, so that X ₁→ q _d, i.e. e ₁→ 0, tracking error trends towards zero.To tracking error e ₁Differentiate:

${\stackrel{\&CenterDot;}{e}}_1={\stackrel{\&CenterDot;}{X}}_1-{\stackrel{\&CenterDot;}{q}}_d=X_2-{\stackrel{\&CenterDot;}{q}}_d---\left(9\right)$

Can be with variable X ₂Be designed to the virtual controlling amount, α ₁Goal expression be:

$X_2={\mathrm{\&alpha;}}_1\&equiv;{-c}_1{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{q}}_d---\left(10\right)$

In the formula, c ₁=c ₁ ^T＞0.

Tracking error systematic (9) is chosen a Lyapunov function V ₁For:

V ₁To the time differentiate, ${\stackrel{\&CenterDot;}{V}}_1={e_1}^T{\stackrel{\&CenterDot;}{e}}_1={e_1}^T(X_2-{\stackrel{\&CenterDot;}{q}}_d)={{-e}_1}^T{c}_1{e}_1---\left(12\right)$

Yi Zhi Satisfy negative definiteness, thus tracking error systematic (9) asymptotically stable in the large, e ₁Asymptotic convergence is to zero.

Yet (2-b), X ₂Be not and α ₁Constantly equate definition deviation e between the two ₂For:

e ₂＝X ₂-α ₁ （13）

To e ₂Carry out differentiate:

$\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_2={\stackrel{\&CenterDot;}{X}}_2-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1\\ =f\left(z\right)-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1+\mathrm{\&tau;}+d\end{array}---\left(14\right)$

Formula real control inputs occurred in (14).Design new Lyapunov function V ₂For:

$V_2={\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">V</figure-callout>}}_1+\frac{1}{2}{e_2}^T{e}_2---\left(15\right)$

Right

The differentiate of the time of carrying out,

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2={e_1}^T(X_2-{\stackrel{\&CenterDot;}{q}}_d)+{e_2}^T{\stackrel{\&CenterDot;}{e}}_2\\ ={e_1}^T({-c}_1{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+e_2)+{e_2}^T[f\left(z\right)-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1+\mathrm{\&tau;}+d]\\ =-{e_1}^T{c}_1{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{e_1}^T{e}_2+{e_2}^T[f\left(z\right)-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1+\mathrm{\&tau;}+d]\end{array}---\left(16\right)$

For guaranteeing Design control law τ is:

$\mathrm{\&tau;}={-c}_2{e}_2-e_1-f\left(z\right)+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1+v---\left(17\right)$

In the formula, c ₂=c ₂ ^T＞0, v is the robust item, is used for compensating the impact of mechanical noise d,

v＝-ρsgn(e ₂) （18）

Bring formula (17), (18) into formula (16) and obtain,

${\stackrel{\&CenterDot;}{V}}_2={{-e}_1}^T{c}_1{e}_1-{e_2}^T{c}_2{e}_2+{e_2}^{T}d-{{\mathrm{\&rho;e}}_2}^T\mathrm{sgn}\left(e_2\right)\&le;0---\left(19\right)$

Formula (19) has shown

Negative definiteness, i.e. control system.

(2-c) still, f (z) is unknown, and the control law shown in the formula (17) can't directly be implemented, and needs improvement, then utilizes the estimated value of f (z)

Replace f (z), control law formula (17) becomes like this:

$\mathrm{\&tau;}={-c}_2{e}_2-e_1-\hat{f}\left(z\right)+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1+v---\left(20\right)$

In the formula,

Be the estimated value of unknown dynamic perfromance f (z), its online constantly correction is to approach f (z), the validity of Guarantee control system.

In the above-mentioned steps, the position signalling q of reference locus _d, rate signal

Acceleration signal

By 101 outputs of reference locus module; Position signalling q and the rate signal of the output vibration of gyroscope system

Generate signaling module 102 in the middle of the design, make it receive the reference locus signal

Position q and speed with the gyroscope vibration Signal generates the M signal in the inverting controller design process

Design inverting controller 103 receives M signal Produce control signal u, consist of the part of overhead control signal, control signal u is designed to

$u={-c}_2{e}_2-{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)---\left(21\right);$

Because neural network has powerful non-linear mapping capability, the present invention adopts Neural Network Online to approach the unknown dynamic perfromance f (z) of unknown gyroscope, the estimated value of unknown dynamic perfromance f (z)

By 104 outputs of neural network adaptive system.

The reverse output of inverting controller 103 control output u and neural network adaptive system 104

By first adder 106 additions, obtain the output τ of gyroscope adaptive controller 105, be the control inputs τ of gyroscope.

Control law formula (20) is the control inputs of gyroscope, and the closed-loop system equation can be written as following form:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_1=e_2+{\mathrm{\&alpha;}}_1-{\stackrel{\&CenterDot;}{q}}_d\\ {\stackrel{\&CenterDot;}{e}}_2={-c}_2{e}_2-e_1-\tilde{f}\left(z\right)+d-\mathrm{\&rho;sgn}\left(e_2\right)\end{array}\right.$

In the formula

The evaluated error that represents unknown dynamic perfromance.

(3) design neural network adaptive system

Design neural network adaptive system 104 is used for approaching the unknown dynamic perfromance f (z) of gyroscope, output signal

The neural network structure that the present invention selects is the RBF neural network, as shown in Figure 2, comprise three-decker: input layer, hidden layer and output layer, but input layer is accepted the measuring-signal in the system, hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping, and output layer obtains the output of whole RBF neural network by the output of each hidden node of weighting.The RBF neural network be input as z, hidden layer is selected fixing center vector c and sound stage width b, output layer produces neural network output Another part as the overhead control signal

$\hat{f}\left(z\right)={\hat{W}}^T\mathrm{\&phi;}\left(z\right)---\left(22\right)$

In the formula, The instantaneous value of expression RBF neural network weight, φ (z) is the output vector of hidden layer,

$\mathrm{\&phi;}\left(z\right)=\exp (-\frac{{\left|\right|z-c\left|\right|}^2}{b^2})---\left(23\right)$

Like this, the control inputs of gyroscope just becomes

$\mathrm{\&tau;}=u-\hat{f}\left(z\right)={-c}_2{e}_2-{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)-{\hat{W}}^T\mathrm{\&phi;}\left(z\right).$

Can make the following assumptions for f (z),

f(z)＝W ^Tφ(z)+ε(z) （24）

In the formula, W represents desirable neural network weight, the modeling error of the desirable neural network of ε (z) expression, and ε (z) bounded, || ε (z) ||≤ε _b

With formula (22) and formula (24), bring closed-loop system into, obtain

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_1=e_2+{\mathrm{\&alpha;}}_1-{\stackrel{\&CenterDot;}{q}}_d\\ {\stackrel{\&CenterDot;}{e}}_2={-c}_2{e}_2-e_1-{\tilde{W}}^T\mathrm{\&phi;}\left(z\right)+\mathrm{\&epsiv;}\left(z\right)+d-\mathrm{\&rho;sgn}\left(e_2\right)\end{array}\right.---\left(25\right)$

In the formula, Expression weights evaluated error.

For the closed-loop system of formula (25), choose a Lyapunov function V,

$V=\frac{1}{2}{e_1}^{\mathrm{<figure-callout\; id="1"\; label="T\; e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">T</figure-callout>}}{e}_{}{}_1+\frac{1}{2}{e_2}^T{e}_2+\frac{1}{2}\mathrm{tr}\left\{{\tilde{W}}^T{F}^{-1}\tilde{W}\right\}---\left(26\right)$

F in the formula ^-1Representing matrix F's is contrary, and F is any symmetric positive definite matrix, to formula (26) both sides differentiate,

$\stackrel{\&CenterDot;}{V}=-{e_1}^T{c}_1{e}_1-{e_2}^T{c}_2{e}_2+{e_2}^{T}d-{{\mathrm{\&rho;e}}_2}^T\mathrm{sgn}\left(e_2\right)-{e_2}^T{\tilde{W}}^T\mathrm{\&phi;}\left(z\right)+\mathrm{tr}\left\{{\tilde{W}}^T{F}^{-1}\stackrel{\&CenterDot;}{\tilde{W}}\right\}+{e_2}^T\mathrm{\&epsiv;}\left(z\right)---\left(27\right)$

Design

Adaptive law be:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{F\&phi;}\left(z\right){e_2}^T---\left(28\right)$

Because

Therefore

Bring this adaptive law (28) into formula (27) and get,

$\begin{array}{c}\stackrel{\&CenterDot;}{V}={{-e}_1}^T{c}_1{e}_1-{e_2}^T{c}_2{e}_2+{e_2}^{T}d-{{\mathrm{\&rho;e}}_2}^T\mathrm{sgn}\left(e_2\right)+{e_2}^T\mathrm{\&epsiv;}\left(z\right)\\ \&le;-{e_1}^T{c}_1{e}_1-{e_2}^T{c}_2{e}_2+\left|\right|e_2\left|\right|{\mathrm{\&epsiv;}}_b\\ \&le;-{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1\left|\right|}^2-{\mathrm{\&lambda;}}_2{\left|\right|e_2\left|\right|}^2+\left|\right|e_2\left|\right|{\mathrm{\&epsiv;}}_b\end{array}---\left(29\right)$

In the formula, λ ₁, λ ₂Be respectively positive definite symmetric matrices c ₁, c ₂The minimal characteristic root.Formula (29) further has,

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1\left|\right|}^2-{\mathrm{\&lambda;}}_2{\left|\right|e_2\left|\right|}^2+\left|\right|e_2\left|\right|{\mathrm{\&epsiv;}}_b\\ =-{\mathrm{\&lambda;}}_1{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00003367095200021.png,HDA00003367095200022.png"\; state="\{\{state\}\}">e</figure-callout>}}_1\left|\right|}^2-\left|\right|e_2\left|\right|\left({\mathrm{\&lambda;}}_2\right|\left|e_2\right||-{\mathrm{\&epsiv;}}_b)\end{array}---\left(30\right)$

So work as

The time,

It is the final Uniform boundedness that inequality (30) has been guaranteed closed-loop system.

In sum, the adaptive algorithm (28) based on the self-adaptation inverting controller (21) of the gyroscope of neural network and neural network of the present invention design has guaranteed the stability of closed-loop system, and system can resist the dynamic perfromance of gyroscope the unknown and the impact of mechanical noise.

Carry out at last Computer Simulation

In the present embodiment, utilize mathematical software MatLab/Simulink to carry out computer simulation experiment, 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 ^-6Ns/m，d _yy＝1.8×10 ^-6Ns/m,d _xy＝3.6×10 ^-7Ns/m

Suppose that extraneous angular velocity is Ω _z=100rad/s, three parameter matrixs of the gyroscope behind the nondimensionalization are:

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

Reference locus is designed to: x _d=cos (ω ₁T), y _d=cos (ω ₂T), ω wherein ₁=6.17, ω ₂=5.11,

In the emulation experiment, inverting controller parameter c ₁=c ₂=20*I, I represent the second order unit matrix,

The node number of RBF neural network hidden layer elects 81 as through repeatedly attempting, and the average c of center vector is distributed in the vector space of position and speed reference track, sound stage width b=10,

The gain matrix F=500 of Weight number adaptively algorithm,

Gyroscope is zero original state, and mechanical noise d is thought of as white noise, and expression formula is

d＝30.0randn(1,1)。Under above simulation parameter, working procedure obtains the as a result figure of the specific embodiment of the invention.

With reference to Fig. 3 and Fig. 4, wherein Fig. 3 is the drive axle position aircraft pursuit course, and Fig. 4 is sensitive axis position aircraft pursuit course.Among two figure, solid line is the output of gyroscope, dotted line is the output of reference locus, control system can be so that the two shaft positions output of gyroscope, in the situation that has unknown dynamic perfromance and mechanical noise, can promptly follow the tracks of given reference locus, reach desirable tracking effect.

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 content that is not described in detail in the instructions of the present invention belongs to the known technical know-how of this area professional and technical personnel.

The above; it only is preferred embodiment of the present invention; 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; making a little change or be modified to the equivalent embodiment of equivalent variations when the technology contents that can utilize above-mentioned announcement, is the content that does not break away from technical solution of the present invention in every case, all still belongs to the protection domain of our bright technical scheme.

Claims (8)

1. based on the self-adaptation inverting control system of the gyroscope of neural network, it is characterized in that, comprising:

Reference locus module (101) is used for exporting the reference locus of gyroscope two shaft vibrations, comprises position, speed and acceleration signal;

M signal generation module (102) is used for receiving the output of reference locus and gyroscope system, and produces the M signal in the inverting controller design process;

Inverting controller (103) is used for receiving M signal, and the output that produces the inverting controller;

Neural network adaptive system (104) is used for receiving the output of M signal and gyroscope system, and the online neural network weight of adjusting in real time, produces the output of ANN (Artificial Neural Network) Control signal;

Gyroscope adaptive controller (105) is inverting controller (103) and neural network adaptive system (104) sum, is the master controller of system;

First adder (106) is with the reverse output addition of inverting controller (103) output and neural network adaptive system (104);

Gyroscope system (107), controlled gyroscope object has been considered the impact of mechanical noise, produces the vibration signal output of gyroscope vibrating mass.

2. based on the control method of the self-adaptation inverting control system of the gyroscope based on neural network claimed in claim 1, it is characterized in that: may further comprise the steps,

1) based on Based Inverse Design Method, sets up the nondimensionalization kinetic model of gyroscope;

2) design inverting controller;

3) design neural network adaptive system;

4) utilize first adder to obtain the output of gyroscope adaptive controller, as the control inputs of gyroscope.

3. control method according to claim 2 is characterized in that: described step 1), set up the nondimensionalization kinetic model of gyroscope, and be specially:

1-1) the existence of consideration mechanical noise, the nondimensionalization vector model of diaxon gyroscope is:

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

In the formula, $q=\left[\begin{array}{c}x\\ y\end{array}\right],\mathrm{\&tau;}=\left[\begin{array}{c}{\mathrm{\&tau;}}_x\\ {\mathrm{\&tau;}}_y\end{array}\right],d=\left[\begin{array}{c}{d}_x\\ d_y\end{array}\right],D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],K=\left[\begin{array}{cc}{k}_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{xy}}& k_{\mathrm{yy}}\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_z& 0\end{array}\right]$

Q is the oscillation trajectory of gyroscope, and x, y represent that respectively the vibrating mass of gyroscope is in the position of vibration diaxon; d _Xx, d _Xy, d _YyInternally-damped coefficient for gyroscope; k _Xx, k _Xy, k _YyInside spring ratio for gyroscope; Ω _zThe input angle speed of gyroscope; τ _x, τ _yIt is the control inputs of gyroscope; d _x, d _yThe internal mechanical noise of expression gyroscope system;

1-2) defining variable X ₁, X ₂, based on the inverting designing technique, the kinetics equation (2) of gyroscope is transformed to following form,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=-(D+2\mathrm{\&Omega;})X_2-{\mathrm{KX}}_1+\mathrm{\&tau;}+d\end{array}\right.---\left(4\right)$

In the formula, $X_1=q,X_2=\stackrel{\&CenterDot;}{q};$

1-3) the unknown dynamic perfromance f of definition (z) is,

f(z)＝-(D+2Ω)X ₂-KX ₁ （6）

The kinetic model of gyroscope is further write as,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_1=X_2\\ {\stackrel{\&CenterDot;}{X}}_2=f\left(z\right)+\mathrm{\&tau;}+d\end{array}\right.---\left(7\right)$

Variable z is z=[X ₁, X ₂] ^T, be measurable signal in the system;

X ₁Be the oscillation trajectory of gyroscope, take kinetic model equation (7) as basic engineering inverting controller.

4. control method according to claim 2 is characterized in that: described step 2), design inverting controller is specially:

2-1) by the reference locus of reference locus module (101) output gyroscope vibration, comprise position signalling q _d, rate signal

Acceleration signal

Position signalling q and rate signal by gyroscope system (107) output vibrating mass vibration

Generate signaling module (102) 2-2) and receive the reference locus signal

With gyroscope vibration signal q and

Generate the M signal in the inverting controller design process, the M signal design is as follows,

Tracking error e ₁: e ₁=X ₁-q _d

Virtual controlling amount α ₁And derivative ${\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1:{\mathrm{\&alpha;}}_1={-c}_1{e}_1+{\stackrel{\&CenterDot;}{q}}_d$

Deviation e ₂: e ₂=X ₂-α ₁

2-3) inverting controller (103) receives M signal

Lyapunov function V according to design ₂Produce control signal u, consist of the part of overhead control signal, control signal u design is as follows

$u=-c_2{e}_2-e_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)$

Wherein, v=-ρ sgn (e ₂) be the robust item, ρ is the upper bound of the internal mechanical noise of gyroscope system; c ₁, c ₂Be any symmetric positive definite matrix; Sgn () represents sign function.

5. control method according to claim 4 is characterized in that: described Lyapunov function V ₂For:

$V_2=V_1+\frac{1}{2}{e_2}^T{e}_2$

Wherein, $V_1=\frac{1}{2}{e_1}^T{e}_1.$

6. control method according to claim 2 is characterized in that: design the neural network adaptive system in the described step 3), be specially

3-1) design neural network adaptive system (104) is in order to approach the unknown dynamic perfromance f (z) of gyroscope, output signal

Described neural network structure is selected the RBF neural network, comprise three-decker: input layer, hidden layer and output layer, but input layer is accepted the measuring-signal in the system, hidden layer adopts the output after the gaussian basis function calculation Nonlinear Mapping, and output layer obtains the output of whole RBF neural network by the output of each hidden node of weighting;

3-2) with the output z of gyroscope system (107) input as the RBF neural network, hidden layer is selected fixing center vector c and sound stage width b, and output layer produces the output of RBF neural network

$\hat{f}\left(z\right)={\hat{W}}^T\mathrm{\&phi;}\left(z\right)---\left(22\right)$

In the formula, The instantaneous value of expression RBF neural network weight, φ (z) is the output vector of hidden layer,

$\mathrm{\&phi;}\left(z\right)=\exp (-\frac{{\left|\right|z-c\left|\right|}^2}{b^2})---\left(23\right)$

3-3) based on the Lyapunov stability theory, the design neural network weight

Adaptive algorithm, obtain adaptive law

For:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{F\&phi;}\left(z\right){e_2}^T---\left(28\right)$

Matrix F is any symmetric positive definite matrix in the formula,

The output of neural network adaptive system (104)

Adaptive law according to design

Real-time online upgrades.

7. control method according to claim 6, it is characterized in that: described Lyapunov function is V

$V=\frac{1}{2}{e_1}^T{e}_1+\frac{1}{2}{e_2}^T{e}_2+\frac{1}{2}\mathrm{tr}\left\{{\tilde{W}}^T{F}^{-1}\tilde{W}\right\}---\left(26\right)$

Wherein,

Expression weights evaluated error.

8. control method according to claim 2 is characterized in that, the control inputs τ of described step 4) gyroscope is

$\mathrm{\&tau;}=u-\hat{f}\left(z\right)={-c}_2{e}_2-e_1+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\mathrm{\&rho;sgn}\left(e_2\right)-{\hat{W}}^T\mathrm{\&phi;}\left(z\right).$

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