CN105371872A - Extended high-gain observer based disturbance estimation method for gyrowheel system - Google Patents

Abstract

The invention provides an extended high-gain observer based disturbance estimation method for a gyrowheel system, belongs to the field of inertial navigation and aims to solve the problem about dynamic disturbance estimation of a gyrowheel rotor in a large heeling angle working state. The method comprises the following steps: step 1, a gyrowheel system state equation containing unknown disturbance is established according to a kinetic equation of the gyrowheel system; step 2, an extended high-gain observer is designed according to the gyrowheel system state equation containing unknown disturbance; step 3, observation error convergence is verified and an observer design parameter epsilon is adjusted; step 4, disturbance estimation of the gyrowheel system is performed. The extended high-gain observer based disturbance estimation method is applicable to disturbance estimation of the gyrowheel system.

Description

Based on the gyroscope flywheel system disturbance method of estimation of expansion High-gain observer

Technical field

The present invention is the gyroscope flywheel system disturbance method of estimation based on expansion High-gain observer, is specifically related to inertial navigation field.

Background technology

Gyroscope flywheel is a kind of electromechanical servo device having actuator and sensor function concurrently being applied to spacecraft, and its physical arrangement based on traditional inertial instruments-dynamically tuned gyro, DTG develops.But gyroscope flywheel and dynamically tuned gyro, DTG functionally obviously different are, gyroscope flywheel not only realizes the two-dimensional carrier angular rate measurement function the same with dynamically tuned gyro, DTG, can also realize Three dimensions control moment output function.And gyroscope flywheel is for realizing three-dimensional moment output function, gyroscope flywheel rotor need produce the rolling motion of wide-angle in bidimensional radial direction, axially need produce speed governing campaign, the remarkable difference of these motion states, result in gyroscope flywheel and exports at three-dimensional moment and basis realizes two-dimentional spacecraft angular rate measurement function comparatively dynamically tuned gyro, DTG is more complicated.

All need to realize drift error compensation in dynamically tuned gyro, DTG development, to overcome the impact of undesirable factor, thus ensure measuring accuracy.And the static drift error compensating method that dynamically tuned gyro, DTG the most often adopts is servo turntable method and torque-feedback method, these two kinds of static drift error compensating methods can to such as different elasticity, and the systematic error that the factors such as mass unbalance cause carries out calibration compensation; But, due to the scaling method that the method is a kind of static state, cannot work long hours to the rotor as gyroscope flywheel in the system of large rolling motion state and carry out complete calibration compensation, therefore need the disturbance method of estimation of further research trends to estimate the drift error produced due to the large rolling motion of gyroscope flywheel rotor, the test data sequence obtained carries out modeling compensation to disturbance to utilize experiment to estimate.

Kalman Filter Technology is a kind of optimal State Estimation method, and it is by recursive algorithm, by the discrete experimental data that there is noise pollution obtained in real time, carries out the optimal estimation without inclined and minimum variance to system state.But, Kalman filtering depends on accurately complete system mathematic model, and to gyroscope flywheel system, the disturbance caused due to undesirable factor is unknown, and be difficult to carry out modeling to it, so the disturbance utilizing Kalman filtering to carry out gyroscope flywheel system estimates to there is larger difficulty.Developing extended mode observer based on active disturbance rejection thought is a kind of Nonlinear Observer, disturbance expansion in gyroscope flywheel system can be single order state by this kind of Nonlinear Observer method, utilize specific nonsmooth nonlinearities Error Feedback, in conjunction with suitable design parameter, realize the observation to all states.Although numerous scholar conducts in-depth research this kind of Nonlinear Observer method, but, Nonlinear Observer method due to design parameter numerous, cause parameter tuning difficulty, and Nonlinear Observer method adopts continuous nonsmooth nonlinearities structure, be difficult to carry out convergence and observational error analysis by traditional Design of Observer theory, especially the error convergence problem of high-order (more than second order) system be well solved not yet.To gyroscope flywheel system, if utilize Nonlinear Observer method to carry out disturbance estimation, comparatively reasonably design parameter selection and error convergence prove then to seem and realize difficulty larger by comparatively very complicated.

Summary of the invention

The present invention in order to solve the dynamic disturbances estimation problem of gyroscope flywheel in large angle of heel duty, and then proposes, based on the gyroscope flywheel system disturbance method of estimation of expansion High-gain observer, to comprise the following steps:

Step one, kinetics equation according to gyroscope flywheel system, build the gyroscope flywheel system state equation containing unknown disturbance impact;

Rotor radially motion bidimensional angle of heel φ directly measured by the canting sensor of gyroscope flywheel system _x, φ _y, the gyroscope flywheel system dynamics equation utilizing Equations of The Second Kind Lagrangian method to set up, by corresponding coordinate transform, not considering system that the ideal kinetics equation of disturbance is converted to and directly measure by sensor the φ obtained _x, φ _yunder the housing coordinate system at place, thus the gyroscope flywheel system state equation considering non-modeling disturbance can be obtained;

Select gyroscope flywheel rotor at the angle of heel (φ of two-dimensional direction _x, φ _y) and angle of heel speed as state variable: $x={\left[\begin{array}{cccc}{x}_1& x_2& x_3& x_4\end{array}\right]}^T={\left[\begin{array}{cccc}{\mathrm{\φ}}_x& {\stackrel{\·}{\mathrm{\φ}}}_x& {\mathrm{\φ}}_y& {\stackrel{\·}{\mathrm{\φ}}}_y\end{array}\right]}^T,$ Gyroscope flywheel system state equation then containing non-modeling disturbance is as shown in formula (1):

$\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f_1(x,t)+g_{x1}(x,t)u_x+g_{y1}(x,t)u_y+{\mathrm{\σ}}_x(x,t)\\ {\stackrel{\·}{x}}_3=x_4\\ {\stackrel{\·}{x}}_4=f_2(x,t)+g_{x2}(x,t)u_x+g_{y2}(x,t)u_y+{\mathrm{\σ}}_y(x,t)\end{array}---\left(1\right)$

Measurement equation is as shown in formula (2):

$y={\left[\begin{array}{cc}{y}_1& y_2\end{array}\right]}^T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]---\left(2\right)$

Wherein, f ₁(x, t), f ₂(x, t) represents ideally, the Nonlinear Mechanism item of gyroscope flywheel; u _x, u _yrepresent the control moment of bidimensional torquer, g _x1(x, t), g _x2(x, t), g _y1(x, t), g _y2(x, t) represents that the nonlinear system of bidimensional torquer is several;

σ _x(x, t), σ _y(x, t) represents the non-modeling disturbance term of system; y ₁, y ₂represent measurable gyroscope flywheel rotor bidimensional angle of heel (φ respectively _x, φ _y);

After being arranged by formula (1) (2), formula (3) can be obtained:

$\left\{\begin{array}{c}\stackrel{\·}{x}=Ax+B\[f(x,t)+{\mathrm{\σ}}_d(x,t)+g(x,t)u\]\\ y=Cx\end{array}\right.---\left(3\right)$

Wherein, σ _dthe non-modeling nonlinear disturbance item that (x, t) is the continuous bounded of gyroscope flywheel system; U is the continuous bounded control input of bidimensional, and namely bidimensional torquer exports; F (x, t), g (x, t) are nominal model, and are the nonlinear function of twice continuously differentiable bounded;

Wherein, $\begin{array}{cccc}A=\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right];& B=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 0\\ 0& 1\end{array}\right];& C=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right];& u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right]=\left[\begin{array}{c}{T}_{cx}\\ T_{cy}\end{array}\right];\end{array}$

$\begin{array}{ccc}f(x,t)=\left[\begin{array}{c}{f}_1(x,t)\\ f_2(x,t)\end{array}\right];& {\mathrm{\σ}}_d(x,t)=\left[\begin{array}{c}{\mathrm{\σ}}_x(x,t)\\ {\mathrm{\σ}}_y(x,t)\end{array}\right];& g(x,t)=\left[\begin{array}{cc}{g}_{x1}(x,t)& g_{y1}(x,t)\\ g_{x2}(x,t)& g_{y2}(x,t)\end{array}\right];\end{array}$

$\begin{array}{c}{f}_1(x,y)=\frac{{\mathrm{\φ}}_y{S}_{{\mathrm{\φ}}_y}}{C_{{\mathrm{\φ}}_y}^2}\[C_{{\mathrm{\φ}}_z}{C}_{{\mathrm{\θ}}_y}{\stackrel{\·}{\mathrm{\θ}}}_x-S_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\θ}}}_y-\left(C_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{C}_{{\mathrm{\φ}}_z}+S_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}\right){\stackrel{\·}{\mathrm{\θ}}}_z\]\\ +\frac{1}{C_{{\mathrm{\φ}}_y}}\left[\begin{array}{c}\left(-{\stackrel{\·}{\mathrm{\φ}}}_z{S}_{{\mathrm{\φ}}_z}{C}_{{\mathrm{\θ}}_y}-{\stackrel{\·}{\mathrm{\θ}}}_y{C}_{{\mathrm{\φ}}_z}{S}_{{\mathrm{\θ}}_y}\right){\stackrel{\·}{\mathrm{\θ}}}_x-{\stackrel{\·}{\mathrm{\φ}}}_z{C}_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\θ}}}_y-\left(C_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{C}_{{\mathrm{\φ}}_z}+S_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}\right){\stackrel{\·\·}{\mathrm{\θ}}}_z\\ +\left({\stackrel{\·}{\mathrm{\φ}}}_z{C}_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{S}_{{\mathrm{\φ}}_z}-C_{{\mathrm{\φ}}_z}\left({\stackrel{\·}{\mathrm{\θ}}}_y{C}_{{\mathrm{\θ}}_x}{C}_{{\mathrm{\θ}}_y}-{\stackrel{\·}{\mathrm{\θ}}}_x{S}_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}\right)-{\stackrel{\·}{\mathrm{\φ}}}_z{S}_{{\mathrm{\θ}}_x}{C}_{{\mathrm{\φ}}_z}-C_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\θ}}}_x\right){\stackrel{\·}{\mathrm{\θ}}}_z\end{array}\right]\\ +\frac{{\mathrm{\β}}_1}{I_1}\left(-c_{gx}{\stackrel{\·}{\mathrm{\θ}}}_x-k_x{\mathrm{\θ}}_x+-\frac{1}{2}{I}_2{S}_{2{\mathrm{\θ}}_x}\·{\stackrel{\·}{\mathrm{\θ}}}_z^2-\[\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_x{\stackrel{\·}{\mathrm{\θ}}}_y-\[\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\θ}}_y}-I_{ry}\]S_{{\mathrm{\θ}}_x}{\stackrel{\·}{\mathrm{\θ}}}_y{\stackrel{\·}{\mathrm{\θ}}}_z\right)\\ -\frac{\mathrm{\η}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\·}{\mathrm{\θ}}}_y-k_y{\mathrm{\θ}}_y-\[\frac{1}{2}\left(I_{rz}-I_{rx}\right)C_{{\mathrm{\θ}}_x}^2{S}_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_z^2\\ +\[\frac{1}{2}\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_x^2+\[\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\θ}}_y}-I_{ry}\]{\stackrel{\·}{\mathrm{\θ}}}_x{\stackrel{\·}{\mathrm{\θ}}}_z{S}_{{\mathrm{\θ}}_x}\end{array}\right)\end{array};$

$\begin{array}{c}{f}_2(x,t)=\left({\stackrel{\·}{\mathrm{\φ}}}_z{C}_{{\mathrm{\θ}}_y}{C}_{{\mathrm{\φ}}_z}-{\stackrel{\·}{\mathrm{\θ}}}_y{S}_{{\mathrm{\θ}}_y}{S}_{{\mathrm{\φ}}_z}\right){\stackrel{\·}{\mathrm{\θ}}}_x-S_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\φ}}}_z{\stackrel{\·}{\mathrm{\θ}}}_y-\left(C_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{S}_{{\mathrm{\φ}}_z}-S_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}\right){\stackrel{\·\·}{\mathrm{\θ}}}_z\\ -\[{\stackrel{\·}{\mathrm{\φ}}}_z{C}_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{C}_{{\mathrm{\φ}}_z}+S_{{\mathrm{\φ}}_z}\left({\stackrel{\·}{\mathrm{\θ}}}_y{C}_{{\mathrm{\θ}}_x}{C}_{{\mathrm{\θ}}_y}-{\stackrel{\·}{\mathrm{\θ}}}_x{S}_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}\right)-\left({\stackrel{\·}{\mathrm{\θ}}}_x{C}_{{\mathrm{\θ}}_x}{C}_{{\mathrm{\φ}}_z}-{\stackrel{\·}{\mathrm{\φ}}}_z{S}_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\φ}}_z}\right)\]{\stackrel{\·}{\mathrm{\θ}}}_z\\ +\frac{{\mathrm{\β}}_2}{I_1}\left(-c_{gx}{\stackrel{\·}{\mathrm{\θ}}}_x-k_x{\mathrm{\θ}}_x-\frac{1}{2}{I}_2{S}_{2{\mathrm{\θ}}_x}\·{\stackrel{\·}{\mathrm{\θ}}}_z^2-\[\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_x{\stackrel{\·}{\mathrm{\θ}}}_y-\[\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\θ}}_y}-I_{ry}\]C_{{\mathrm{\θ}}_x}{\stackrel{\·}{\mathrm{\θ}}}_y{\stackrel{\·}{\mathrm{\θ}}}_z\right)\\ +\frac{C_{{\mathrm{\φ}}_z}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\·}{\mathrm{\θ}}}_y-k_y{\mathrm{\θ}}_y-\[\frac{1}{2}\left(I_{rz}-I_{rx}\right)C_{{\mathrm{\θ}}_x}^2{S}_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_z^2+\\ \[\frac{1}{2}\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\θ}}_y}\]{\stackrel{\·}{\mathrm{\θ}}}_x^2+\[\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\θ}}_y}-I_{ry}\]{\stackrel{\·}{\mathrm{\θ}}}_x{\stackrel{\·}{\mathrm{\θ}}}_z{C}_{{\mathrm{\θ}}_x}\end{array}\right)\end{array};$

$\begin{array}{cc}{g}_{x1}(x,t)=\frac{{\mathrm{\β}}_1}{I_1}{C}_{{\mathrm{\θ}}_z}+\frac{\mathrm{\η}}{I_{ry}}{S}_{{\mathrm{\θ}}_z}{C}_{{\mathrm{\θ}}_x}& g_{y1}(x,t)=\frac{{\mathrm{\β}}_1}{I_1}{S}_{{\mathrm{\θ}}_z}-\frac{\mathrm{\η}}{I_{ry}}{C}_{{\mathrm{\θ}}_z}{C}_{{\mathrm{\θ}}_x}\end{array};$

$\begin{array}{cc}{g}_{x2}(x,t)=\frac{{\mathrm{\β}}_2}{I_1}{C}_{{\mathrm{\θ}}_z}-\frac{C_{{\mathrm{\φ}}_z}}{I_{ry}}{S}_{{\mathrm{\θ}}_z}{C}_{{\mathrm{\θ}}_x}& g_{y2}(x,t)=\frac{{\mathrm{\β}}_2}{I_1}{S}_{{\mathrm{\θ}}_z}+\frac{C_{{\mathrm{\φ}}_z}}{I_{ry}}{C}_{{\mathrm{\θ}}_z}{C}_{{\mathrm{\θ}}_x}\end{array};$

Wherein, C _θwith S _θexpression formula be respectively cosine value cos θ and the sine value sin θ of rotational angle theta;

I _rx, I _ry, I _rzbeing respectively rotor at rotor block coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

I _gx, I _gy, I _gzbeing respectively gimbal at balance ring body coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

K _x, k _ybe respectively known flexible support torsion bar torsional rigidity; c _gx, c _gybe respectively known flexible support ratio of damping;

T _cx=k _tyi _y, T _cy=k _txi _xbe respectively the control moment that bidimensional torquer exports rotor to, the u namely in equation (1) _x, u _y;

K _tx, k _tybe respectively the scaling factor of known sensor, i _x, i _ybe respectively the electric current of bidimensional torquer, for sensor can be measured;

θ _z, represent gyroscope flywheel motor shaft corner and rotating speed respectively, being sensor can measure;

θ in equation _x, θ _y, φ _z, I ₁, I ₂, β ₁, β ₂, η is intermediate variable, and concrete form is as follows respectively:

$\begin{array}{cc}{\mathrm{\θ}}_x=arcsin(C_{{\mathrm{\φ}}_x}{S}_{{\mathrm{\φ}}_y}{S}_{{\mathrm{\φ}}_z}+S_{{\mathrm{\φ}}_x}{C}_{{\mathrm{\φ}}_z});& {\mathrm{\θ}}_y=arcsin(S_{{\mathrm{\φ}}_y}{C}_{{\mathrm{\θ}}_z}-S_{{\mathrm{\φ}}_x}{C}_{{\mathrm{\φ}}_y}{S}_{{\mathrm{\θ}}_z})\end{array}$

$\begin{array}{cc}{\stackrel{\·}{\mathrm{\θ}}}_x=\frac{1}{C_{{\mathrm{\θ}}_y}}(C_{{\mathrm{\φ}}_y}{C}_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\φ}}}_x+S_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\φ}}}_y+C_{{\mathrm{\θ}}_x}{S}_{{\mathrm{\θ}}_y}{\stackrel{\·}{\mathrm{\θ}}}_z)& ;{\stackrel{\·}{\mathrm{\θ}}}_y=C_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\φ}}}_y-C_{{\mathrm{\φ}}_y}{S}_{{\mathrm{\φ}}_z}{\stackrel{\·}{\mathrm{\φ}}}_x-S_{{\mathrm{\θ}}_x}{\stackrel{\·}{\mathrm{\θ}}}_z\end{array}$

${\mathrm{\φ}}_z=arctan\frac{C_{{\mathrm{\φ}}_x}{S}_{{\mathrm{\θ}}_z}}{C_{{\mathrm{\φ}}_y}{C}_{{\mathrm{\θ}}_z}+S_{{\mathrm{\φ}}_x}{S}_{{\mathrm{\φ}}_y}{S}_{{\mathrm{\θ}}_z}};$ I ₁＝I _gx+I _rxcos ²θ _y+I _rzsin ²θ _y

I ₂＝I _gz-I _gy-I _ry+I _rxsin ²θ _y+I _rzcos ²θ _y； $\begin{array}{ccc}{\mathrm{\β}}_1=\frac{C_{{\mathrm{\φ}}_z}{C}_{{\mathrm{\θ}}_y}}{C_{{\mathrm{\φ}}_y}}& \mathrm{\η}=\frac{S_{{\mathrm{\φ}}_z}}{C_{{\mathrm{\φ}}_y}}& {\mathrm{\β}}_2=C_{{\mathrm{\θ}}_y}{S}_{{\mathrm{\φ}}_z}\end{array}$

Step 2, the gyroscope flywheel system state equation of basis containing unknown disturbance, utilize bidimensional canting sensor to measure φ _x, φ _y, design expansion High-gain observer;

For utilizing measurement equation y=Cx, realize state variable x and nonlinear disturbance item σ _dthe accurate estimation of (x, t), design expands High-gain observer as follows:

$\left\{\begin{array}{c}\stackrel{\·}{\hat{x}}=A\hat{x}+B\[f\left(\hat{x},t\right)+g\left(\hat{x},t\right)u-\widehat{\mathrm{\σ}}\]+H\left(\mathrm{\ϵ}\right)\left(y-C\hat{x}\right)\\ \stackrel{\·}{\widehat{\mathrm{\σ}}}=F\left(\mathrm{\ϵ}\right)\left(y-C\hat{x}\right)\end{array}\right.---\left(4\right)$

Wherein, for High-gain observer state variable; $\widehat{\mathrm{\σ}}={\left[\begin{array}{cc}{\widehat{\mathrm{\σ}}}_x& {\widehat{\mathrm{\σ}}}_y\end{array}\right]}^T$ For expansion High-gain observer state variable;

The gain matrix that H (ε), F (ε) they are observer, and its concrete form is as follows:

$\begin{array}{cc}H\left(\mathrm{\ϵ}\right)=\left[\begin{array}{cc}{h}_1& 0\\ h_2& 0\\ 0& h_3\\ 0& h_4\end{array}\right]=\left[\begin{array}{cc}\frac{{\mathrm{\α}}_{11}}{\mathrm{\ϵ}}& 0\\ \frac{{\mathrm{\α}}_{21}}{{\mathrm{\ϵ}}^2}& 0\\ 0& \frac{{\mathrm{\α}}_{12}}{\mathrm{\ϵ}}\\ 0& \frac{{\mathrm{\α}}_{22}}{{\mathrm{\ϵ}}^2}\end{array}\right]& F\left(\mathrm{\ϵ}\right)=\left[\begin{array}{cc}-h_5& 0\\ 0& -h_6\end{array}\right]=\left[\begin{array}{cc}-\frac{{\mathrm{\α}}_{31}}{{\mathrm{\ϵ}}^3}& 0\\ 0& -\frac{{\mathrm{\α}}_{32}}{{\mathrm{\ϵ}}^3}\end{array}\right]\end{array}---\left(5\right)$

Wherein, design parameter ε >0 is little design parameter; Design parameter α _ij, i=1,2,3, j=1,2 are all chosen as real number;

The checking of step 3, observational error convergence and Design of Observer parameter ε regulate;

The observational error convergence of the gyroscope flywheel expansion High-gain observer designed by analysis, according to accuracy of observation demand, adjusts and provides applicable expansion High-gain observer design parameter;

Definition error vector namely $\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\tilde{x}}_3\\ {\tilde{x}}_4\end{array}\right]=\left[\begin{array}{c}{x}_1-{\hat{x}}_1\\ x_2-{\hat{x}}_2\\ x_3-{\hat{x}}_3\\ x_4-{\hat{x}}_4\end{array}\right],$ First formula in formula (3) and formula (4) first formula are done difference, and the nonlinear terms after doing difference in gained equation are carried out integral extension is state formula (6) is obtained after arrangement:

$\left\{\begin{array}{c}{\stackrel{\·}{\tilde{x}}}_1=-h_1{\tilde{x}}_1+{\tilde{x}}_2\\ {\stackrel{\·}{\tilde{x}}}_2=-h_2{\tilde{x}}_1+n_{{\widehat{\mathrm{\σ}}}_x}\\ {\stackrel{\·}{n}}_{{\widehat{\mathrm{\σ}}}_x}={\stackrel{\·}{\widehat{\mathrm{\σ}}}}_x+{\widehat{\mathrm{\σ}}}_x(x,t)+{\stackrel{\·}{f}}_1(x,t)-{\stackrel{\·}{f}}_1(\hat{x},t)+{\stackrel{\·}{g}}_{ex}^1(x,t)u_x+{\stackrel{\·}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\·}{\tilde{x}}}_3=-h_3{\tilde{x}}_3+{\tilde{x}}_4\\ {\stackrel{\·}{\tilde{x}}}_4=-h_4{\tilde{x}}_3+n_{{\widehat{\mathrm{\σ}}}_y}\\ {\stackrel{\·}{n}}_{{\widehat{\mathrm{\σ}}}_y}={\stackrel{\·}{\widehat{\mathrm{\σ}}}}_y+{\widehat{\mathrm{\σ}}}_y(x,t)+{\stackrel{\·}{f}}_2(x,t)-{\stackrel{\·}{f}}_2(\hat{x},t)+{\stackrel{\·}{g}}_{ex}^2(x,t)u_x+{\stackrel{\·}{g}}_{ey}^2(x,t)u_y\end{array}\right.---\left(6\right)$

Wherein, $\begin{array}{c}{g}_{ex}^1(x,t)=g_{x1}(x,t)-g_{x1}(\hat{x},t)\\ g_{ey}^1(x,t)=g_{y1}(x,t)-g_{y1}(\hat{x},t)\\ g_{ex}^2(x,t)=g_{x2}(x,t)-g_{x2}(\hat{x},t)\\ g_{ey}^2(x,t)=g_{y2}(x,t)-g_{y2}(\hat{x},t)\end{array};$

$\begin{array}{c}{\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_x}={\widehat{\mathrm{\σ}}}_x+{\mathrm{\σ}}_x(x,t)+f_1(x,t)-f_1(\hat{x},t)+g_{ex}^1(x,t)u_x+g_{ey}^1(x,t)u_y\\ {\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_y}={\widehat{\mathrm{\σ}}}_y+{\mathrm{\σ}}_y(x,t)+f_2(x,t)-f_2(\hat{x},t)+g_{ex}^2(x,t)u_x+g_{ey}^2(x,t)u_y\end{array}$ For the nonlinear terms of formula (7);

By equation (4) second formula be brought into the 3rd formula and the 6th formula of equation (6), and be organized into matrix form, as formula (7):

$\left[\begin{array}{c}{\stackrel{\·}{\tilde{x}}}_1\\ {\stackrel{\·}{\tilde{x}}}_2\\ {\stackrel{\·}{\mathrm{\η}}}_{{\widehat{\mathrm{\σ}}}_1}\\ {\stackrel{\·}{\tilde{x}}}_3\\ {\stackrel{\·}{\tilde{x}}}_4\\ {\stackrel{\·}{\mathrm{\η}}}_{{\widehat{\mathrm{\σ}}}_2}\end{array}\right]=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_5& 0& 0\end{array}\right]\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_1}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_2}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{\mathrm{\δ}}_1\left(x\right)\\ {\mathrm{\δ}}_2\left(x\right)\end{array}\right]---\left(7\right)$

Formula (7) can be abbreviated as further:

$\stackrel{\·}{\tilde{x}}=\tilde{A}\tilde{x}+\tilde{B}\mathrm{\δ}---\left(8\right)$

Wherein,

$\begin{array}{cccc}\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_x}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\η}}_{{\widehat{\mathrm{\σ}}}_y}\end{array}\right];& \tilde{A}=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_5& 0& 0\end{array}\right];& \tilde{B}=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right];& \mathrm{\δ}=\left[\begin{array}{c}{\mathrm{\δ}}_1\left(x\right)\\ {\mathrm{\δ}}_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\σ}}}_x(x,t)+{\stackrel{\·}{f}}_1(x,t)-{\stackrel{\·}{f}}_1(\hat{x},t)+\\ {\stackrel{\·}{g}}_{ex}^1(x,t)u_x+{\stackrel{\·}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\·}{\mathrm{\σ}}}_y(x,t)+{\stackrel{\·}{f}}_2(x,t)-{\stackrel{\·}{f}}_2(\hat{x},t)+\\ {\stackrel{\·}{g}}_{ex}^2(x,t)u_x+{\stackrel{\·}{g}}_{ey}^2(x,t)u_y\end{array}\right];\end{array}$

According to state equation (8), nonlinear terms δ can be considered the disturbance input of system, state the system that is considered as exports, then expect middle h _i, the design of i=1,2...6 can offset δ couple impact, realize the asymptotic convergence of state observation error, consider by disturbance input δ to State-output transport function, Laplace transformation is carried out to (8), obtains formula (9):

$\frac{\tilde{x}\left(s\right)}{\mathrm{\δ}\left(s\right)}={(sI-\tilde{A})}^{-1}\tilde{B}---\left(9\right)$

Formula (9) expands into further:

$\frac{\tilde{x}\left(s\right)}{\mathrm{\δ}\left(s\right)}=\left[\begin{array}{cc}{G}_{11}\left(s\right)& 0\\ G_{21}\left(s\right)& 0\\ G_{31}\left(s\right)& 0\\ 0& G_{42}\left(s\right)\\ 0& G_{52}\left(s\right)\\ 0& G_{62}\left(s\right)\end{array}\right]---\left(10\right)$

Wherein,

$\begin{array}{ccc}{G}_{11}\left(s\right)=\frac{1}{s^3+h_1{s}^2+h_{2}s+h_5};& G_{21}\left(s\right)=\frac{h_1+s}{s^3+h_1{s}^2+h_{2}s+h_5};& G_{31}\left(s\right)=\frac{s^2+h_{1}s+h_2}{s^3+h_1{s}^2+h_{2}s+h_5};\end{array}$

$\begin{array}{ccc}{G}_{42}\left(s\right)=\frac{1}{s^3+h_3{s}^2+h_{4}s+h_6};& G_{52}\left(s\right)=\frac{h_3+s}{s^3+h_3{s}^2+h_{4}s+h_6};& G_{62}\left(s\right)=\frac{s^2+h_{3}s+h_4}{s^3+h_3{s}^2+h_{4}s+h_6};\end{array}$

Remember respectively $\left\{\begin{array}{c}{G}_1\left(s\right)=\left[\begin{array}{c}{G}_{11}\left(s\right)\\ G_{21}\left(s\right)\\ G_{31}\left(s\right)\end{array}\right]\\ G_2\left(s\right)=\left[\begin{array}{c}{G}_{42}\left(s\right)\\ G_{52}\left(s\right)\\ G_{62}\left(s\right)\end{array}\right]\end{array}\right.,$ According to equation (9), if transport function G ₁(s), G ₂s () be identically vanishing all, then offset nonlinear disturbance input δ completely to State-output error impact, accurately realize the estimation of gyroscope flywheel system total state; Select design parameter h ₁~ h ₆, to ω ∈ R, make the Infinite Norm shown in formula (11) simultaneously arbitrarily small;

$\left\{\begin{array}{c}\left|\right|G_1\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{1<i\&le;3}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i1}\left(j\mathrm{\&omega;}\right)|\\ \left|\right|G_2\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{4<i\&le;6}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i2}\left(j\mathrm{\&omega;}\right)|\end{array}\right.---\left(11\right)$

If $\left\{\begin{array}{c}{h}_5>>h_2>>h_1\\ h_6>>h_3>>h_4\end{array}\right.,$ Choose $\left\{\begin{array}{ccc}{h}_1=\frac{{\mathrm{\&alpha;}}_{11}}{\mathrm{\&epsiv;}}& h_2=\frac{{\mathrm{\&alpha;}}_{21}}{{\mathrm{\&epsiv;}}^2}& h_5=\frac{{\mathrm{\&alpha;}}_{31}}{{\mathrm{\&epsiv;}}^3}\\ h_3=\frac{{\mathrm{\&alpha;}}_{12}}{\mathrm{\&epsiv;}}& h_4=\frac{{\mathrm{\&alpha;}}_{22}}{{\mathrm{\&epsiv;}}^2}& h_6=\frac{{\mathrm{\&alpha;}}_{32}}{{\mathrm{\&epsiv;}}^3}\end{array}\right.$

Wherein, α _ij, i=1,2,3; J=1,2 meet following Hurwitz polynomial expression shown in (12); ε is normal number, and ε < < 1;

s ³+α _1js ²+α _2js+α _3j,j＝1,2(12)

By h ₁~ h ₆bring into G _jin (s), can obtain:

$G_j\left(s\right)=\frac{\mathrm{\&epsiv;}}{P\left(s\right)}\left[\begin{array}{c}{\mathrm{\&epsiv;}}^2\\ \mathrm{\&epsiv;}s+{\mathrm{\&alpha;}}_{1j}\\ {\left(\mathrm{\&epsiv;}s\right)}^2+{\mathrm{\&alpha;}}_{1j}\left(\mathrm{\&epsiv;}s\right)+{\mathrm{\&alpha;}}_{2j}\end{array}\right]---\left(13\right)$

Wherein, P (s)=(ε s) ³+ α _1j(ε s) ²+ α _2j(ε s)+α _3j, j=1,2; $\left\{\begin{array}{c}\underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_1\left(s\right)=0\\ \underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_2\left(s\right)=0\end{array}\right.,$ According to formula (13), design expansion High-gain observer, by reducing the value of ε, improves disturbance estimated accuracy, the precision index needed for realization;

Step 4, realize gyroscope flywheel system disturbance estimate;

The High-gain observer after expansion is utilized to carry out the disturbance observation of gyroscope flywheel system, integrating step three adjusted design parameter ε, the disturbance characterized utilizing multivariate regression model is estimated, the estimated accuracy index until observation data meets the expectation, obtain the disturbance estimation test data sequence that the large rolling motion of gyroscope flywheel system produces, realize the disturbance term σ of the non-modeling of gyroscope flywheel system _dx(x, t), σ _dythe estimation of (x, t).

Beneficial effect of the present invention:

1, the inventive method utilizes designed expansion High-gain observer, utilizes the error of bidimensional canting sensor measurement information and observation information fully, weakens the adverse effect that calculus of differences produces largely, improve observation degree of accuracy;

2, compared with the inventive method adopts static error method with traditional mechanical gyroscope, the present invention is directed the disturbance caused by the large angle of heel of gyroscope flywheel rotor moves is estimated, for the dynamic error estimation of one, be used on static error demarcation basis and further gyroscope flywheel measurement equation carried out disturbance estimation and compensated, for the one of existing error calibration technology supplements technology.

Accompanying drawing explanation

Fig. 1 is the schematic process flow diagram of the gyroscope flywheel system disturbance method of estimation based on expansion High-gain observer;

When Fig. 2 is design parameter ε=0.1, gyroscope flywheel is at the disturbance estimated value figure of x-axis;

When Fig. 3 is design parameter ε=0.1, gyroscope flywheel is at the disturbance estimated value figure of y-axis;

When Fig. 4 is design parameter ε=0.1, gyroscope flywheel is at the disturbance evaluated error figure of x-axis;

When Fig. 5 is design parameter ε=0.1, gyroscope flywheel is at the disturbance evaluated error figure of y-axis;

When Fig. 6 is design parameter ε=0.001, gyroscope flywheel is at the disturbance estimated value figure of x-axis;

When Fig. 7 is design parameter ε=0.001, gyroscope flywheel is at the disturbance estimated value figure of y-axis;

When Fig. 8 is design parameter ε=0.001, gyroscope flywheel is at x-axis disturbance evaluated error figure;

When Fig. 9 is design parameter ε=0.001, gyroscope flywheel is at the disturbance evaluated error figure of y-axis.

Embodiment

Embodiment one: present embodiment realizes according to following steps based on the gyroscope flywheel system disturbance method of estimation of expansion High-gain observer:

Step one, kinetics equation according to gyroscope flywheel system, set up the gyroscope flywheel system state equation containing unknown disturbance;

Step 2, the gyroscope flywheel system state equation of basis containing unknown disturbance, design expansion High-gain observer;

Step 3, observational error convergence and Design of Observer parameter ε regulate;

Step 4, realize gyroscope flywheel system disturbance estimate.

Embodiment two: present embodiment and embodiment one unlike: it is characterized in that, the gyroscope flywheel system state equation of described step one containing unknown disturbance realizes according to following steps:

Gyroscope flywheel rotor is at the angle of heel (φ of two-dimensional direction _x, φ _y) and angle of heel speed as state variable x: $x={\left[\begin{array}{cccc}{x}_1& x_2& x_3& x_4\end{array}\right]}^T={\left[\begin{array}{cccc}{\mathrm{\&phi;}}_x& {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x& {\mathrm{\&phi;}}_y& {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y\end{array}\right]}^T,$ Gyroscope flywheel system state equation then containing non-modeling disturbance is as shown in formula (1):

$\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=f_1(x,t)+g_{x1}(x,t)u_x+g_{y1}(x,t)u_y+{\mathrm{\&sigma;}}_x(x,t)\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=f_2(x,t)+g_{x2}(x,t)u_x+g_{y2}(x,t)u_y+{\mathrm{\&sigma;}}_y(x,t)\end{array}---\left(1\right)$

Measurement equation is as shown in formula (2):

$y={\left[\begin{array}{cc}{y}_1& y_2\end{array}\right]}^T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]---\left(2\right)$

Wherein, f ₁(x, t), f ₂(x, t) represents ideally, the Nonlinear Mechanism item of gyroscope flywheel; u _x, u _yrepresent the control moment of bidimensional torquer, g _x1(x, t), g _x2(x, t), g _y1(x, t), g _y2(x, t) represents that the nonlinear system of bidimensional torquer is several;

σ _x(x, t), σ _y(x, t) represents the non-modeling disturbance term of system; y ₁, y ₂represent measurable gyroscope flywheel rotor bidimensional angle of heel (φ respectively _x, φ _y);

After being arranged by formula (1) (2), formula (3) can be obtained:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=Ax+B\&lsqb;f(x,t)+{\mathrm{\&sigma;}}_d(x,t)+g(x,t)u\&rsqb;\\ y=Cx\end{array}\right.---\left(3\right)$

Wherein, σ _dthe non-modeling nonlinear disturbance item that (x, t) is the continuous bounded of gyroscope flywheel system; U is the continuous bounded control input of bidimensional, and namely bidimensional torquer exports; F (x, t), g (x, t) are nominal model, and are twice continuously differentiable bounded nonlinear function;

Wherein, $\begin{array}{cccc}A=\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right];& B=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 0\\ 0& 1\end{array}\right];& C=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right];& u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right]=\left[\begin{array}{c}{T}_{cx}\\ T_{cy}\end{array}\right];\end{array}$

$\begin{array}{ccc}f(x,t)=\left[\begin{array}{c}{f}_1(x,t)\\ f_2(x,t)\end{array}\right];& {\mathrm{\&sigma;}}_d(x,t)=\left[\begin{array}{c}{\mathrm{\&sigma;}}_x(x,t)\\ {\mathrm{\&sigma;}}_y(x,t)\end{array}\right];& g(x,t)=\left[\begin{array}{cc}{g}_{x1}(x,t)& g_{y1}(x,t)\\ g_{x2}(x,t)& g_{y2}(x,t)\end{array}\right];\end{array}$

$\begin{array}{c}{f}_1(x,y)=\frac{{\mathrm{\&phi;}}_y{S}_{{\mathrm{\&phi;}}_y}}{C_{{\mathrm{\&phi;}}_y}^2}\&lsqb;C_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\left(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\&rsqb;\\ +\frac{1}{C_{{\mathrm{\&phi;}}_y}}\left[\begin{array}{c}\left(-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&phi;}}_z}{S}_{{\mathrm{\&theta;}}_y}\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\left(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}\right){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_z\\ +\left({\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}-C_{{\mathrm{\&phi;}}_z}\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&phi;}}_z}-C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\end{array}\right]\\ +\frac{{\mathrm{\&beta;}}_1}{I_1}\left(-c_{gx}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-k_x{\mathrm{\&theta;}}_x+-\frac{1}{2}{I}_2{S}_{2{\mathrm{\&theta;}}_x}\&CenterDot;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2-\&lsqb;\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\&lsqb;\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;S_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\right)\\ -\frac{\mathrm{\&eta;}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-k_y{\mathrm{\&theta;}}_y-\&lsqb;\frac{1}{2}\left(I_{rz}-I_{rx}\right)C_{{\mathrm{\&theta;}}_x}^2{S}_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2\\ +\&lsqb;\frac{1}{2}\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x^2+\&lsqb;\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z{S}_{{\mathrm{\&theta;}}_x}\end{array}\right)\end{array};$

$\begin{array}{c}{f}_2(x,t)=\left({\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{S}_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\left(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}-S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}\right){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_z\\ -\&lsqb;{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&phi;}}_z}\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}\right)-\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{C}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&phi;}}_z}-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}\right)\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\\ +\frac{{\mathrm{\&beta;}}_2}{I_1}\left(-c_{gx}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-k_x{\mathrm{\&theta;}}_x-\frac{1}{2}{I}_2{S}_{2{\mathrm{\&theta;}}_x}\&CenterDot;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2-\&lsqb;\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\&lsqb;\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;C_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\right)\\ +\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-k_y{\mathrm{\&theta;}}_y-\&lsqb;\frac{1}{2}\left(I_{rz}-I_{rx}\right)C_{{\mathrm{\&theta;}}_x}^2{S}_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2+\\ \&lsqb;\frac{1}{2}\left(I_{rz}-I_{rx}\right)S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x^2+\&lsqb;\left(I_{rz}-I_{rx}\right)C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z{C}_{{\mathrm{\&theta;}}_x}\end{array}\right)\end{array};$

$\begin{array}{cc}{g}_{x1}(x,t)=\frac{{\mathrm{\&beta;}}_1}{I_1}{C}_{{\mathrm{\&theta;}}_z}+\frac{\mathrm{\&eta;}}{I_{ry}}{S}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}& g_{y1}(x,t)=\frac{{\mathrm{\&beta;}}_1}{I_1}{S}_{{\mathrm{\&theta;}}_z}-\frac{\mathrm{\&eta;}}{I_{ry}}{C}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}\end{array};$

$\begin{array}{cc}{g}_{x2}(x,t)=\frac{{\mathrm{\&beta;}}_2}{I_1}{C}_{{\mathrm{\&theta;}}_z}-\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}{S}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}& g_{y2}(x,t)=\frac{{\mathrm{\&beta;}}_2}{I_1}{S}_{{\mathrm{\&theta;}}_z}+\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}{C}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}\end{array};$

Wherein, C _θwith S _θexpression formula be respectively cosine value cos θ and the sine value sin θ of rotational angle theta;

I _rx, I _ry, I _rzbeing respectively rotor at rotor block coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

I _gx, I _gy, I _gzbeing respectively gimbal at balance ring body coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

K _x, k _ybe respectively known flexible support torsion bar torsional rigidity; c _gx, c _gybe respectively known flexible support ratio of damping;

T _cx=k _tyi _y, T _cy=k _txi _xbe respectively the control moment that bidimensional torquer exports rotor to, the u namely in equation (1) _x, u _y;

K _tx, k _tybe respectively the scaling factor of known sensor, i _x, i _ybe respectively the electric current of bidimensional torquer, for sensor can be measured;

θ _z, represent gyroscope flywheel motor shaft corner and rotating speed respectively, being sensor can measure;

θ in equation _x, θ _y, φ _z, I ₁, I ₂, β ₁, β ₂, η is intermediate variable, and concrete form is as follows respectively:

$\begin{array}{cc}{\mathrm{\&theta;}}_x=arcsin(C_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&phi;}}_x}{C}_{{\mathrm{\&phi;}}_z});& {\mathrm{\&theta;}}_y=arcsin(S_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&theta;}}_z}-S_{{\mathrm{\&phi;}}_x}{C}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&theta;}}_z})\end{array}$

$\begin{array}{cc}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x=\frac{1}{C_{{\mathrm{\&theta;}}_y}}(C_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x+S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y+C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z)& ;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y=C_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y-C_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x-S_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\end{array}$

${\mathrm{\&phi;}}_z=arctan\frac{C_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&theta;}}_z}}{C_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&theta;}}_z}+S_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&theta;}}_z}};$ I ₁＝I _gx+I _rxcos ²θ _y+I _rzsin ²θ _y。

I ₂＝I _gz-I _gy-I _ry+I _rxsin ²θ _y+I _rzcos ²θ _y； $\begin{array}{ccc}{\mathrm{\&beta;}}_1=\frac{C_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}}{C_{{\mathrm{\&phi;}}_y}}& \mathrm{\&eta;}=\frac{S_{{\mathrm{\&phi;}}_z}}{C_{{\mathrm{\&phi;}}_y}}& {\mathrm{\&beta;}}_2=C_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}\end{array}$

Embodiment three: present embodiment and embodiment one or two unlike: it is characterized in that, described step 2 design expansion High-gain observer realizes according to following steps:

Utilize measurement equation y=Cx, realize state variable x and nonlinear disturbance item σ _dthe estimation of (x, t), design expands High-gain observer as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=A\hat{x}+B\&lsqb;f\left(\hat{x},t\right)+g\left(\hat{x},t\right)u-\widehat{\mathrm{\&sigma;}}\&rsqb;+H\left(\mathrm{\&epsiv;}\right)\left(y-C\hat{x}\right)\\ \stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}=F\left(\mathrm{\&epsiv;}\right)\left(y-C\hat{x}\right)\end{array}\right.---\left(4\right)$

Wherein, for High-gain observer state variable; $\widehat{\mathrm{\&sigma;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&sigma;}}}_x& {\widehat{\mathrm{\&sigma;}}}_y\end{array}\right]}^T$ For expansion High-gain observer state variable;

The gain matrix that H (ε), F (ε) they are observer, and its concrete form is as follows:

$\begin{array}{cc}H\left(\mathrm{\&epsiv;}\right)=\left[\begin{array}{cc}{h}_1& 0\\ h_2& 0\\ 0& h_3\\ 0& h_4\end{array}\right]=\left[\begin{array}{cc}\frac{{\mathrm{\&alpha;}}_{11}}{\mathrm{\&epsiv;}}& 0\\ \frac{{\mathrm{\&alpha;}}_{21}}{{\mathrm{\&epsiv;}}^2}& 0\\ 0& \frac{{\mathrm{\&alpha;}}_{12}}{\mathrm{\&epsiv;}}\\ 0& \frac{{\mathrm{\&alpha;}}_{22}}{{\mathrm{\&epsiv;}}^2}\end{array}\right];& F\left(\mathrm{\&epsiv;}\right)=\left[\begin{array}{cc}-h_5& 0\\ 0& -h_6\end{array}\right]=\left[\begin{array}{cc}-\frac{{\mathrm{\&alpha;}}_{31}}{{\mathrm{\&epsiv;}}^3}& 0\\ 0& -\frac{{\mathrm{\&alpha;}}_{32}}{{\mathrm{\&epsiv;}}^3}\end{array}\right]\end{array}---\left(5\right)$

Wherein, design parameter ε >0 is little design parameter; Design parameter α _ij, i=1,2,3, j=1,2 are all chosen as real number, and should meet following Hurwitz polynomial expression:

s ³+α _1js ²+α _2js+α _3j,j＝1,2

Other step and parameter identical with one of embodiment one to two.

Embodiment four: one of present embodiment and embodiment one to three unlike: it is characterized in that, described step 3 observational error convergence and Design of Observer parameter ε regulate and realize according to following steps:

The observational error convergence of the gyroscope flywheel expansion High-gain observer designed by analysis, according to accuracy of observation demand, adjusts and provides applicable expansion High-gain observer design parameter;

Definition error vector namely $\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\tilde{x}}_3\\ {\tilde{x}}_4\end{array}\right]=\left[\begin{array}{c}{x}_1-{\hat{x}}_1\\ x_2-{\hat{x}}_2\\ x_3-{\hat{x}}_3\\ x_4-{\hat{x}}_4\end{array}\right],$ First formula in formula (3) and formula (4) first formula are done difference, and the nonlinear terms after doing difference in gained equation are carried out integral extension is state formula (6) is obtained after arrangement:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{x}}}_1=-h_1{\tilde{x}}_1+{\tilde{x}}_2\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_2=-h_2{\tilde{x}}_1+n_{{\widehat{\mathrm{\&sigma;}}}_x}\\ {\stackrel{\&CenterDot;}{n}}_{{\widehat{\mathrm{\&sigma;}}}_x}={\stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}}_x+{\widehat{\mathrm{\&sigma;}}}_x(x,t)+{\stackrel{\&CenterDot;}{f}}_1(x,t)-{\stackrel{\&CenterDot;}{f}}_1(\hat{x},t)+{\stackrel{\&CenterDot;}{g}}_{ex}^1(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_3=-h_3{\tilde{x}}_3+{\tilde{x}}_4\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_4=-h_4{\tilde{x}}_3+n_{{\widehat{\mathrm{\&sigma;}}}_y}\\ {\stackrel{\&CenterDot;}{n}}_{{\widehat{\mathrm{\&sigma;}}}_y}={\stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}}_y+{\widehat{\mathrm{\&sigma;}}}_y(x,t)+{\stackrel{\&CenterDot;}{f}}_2(x,t)-{\stackrel{\&CenterDot;}{f}}_2(\hat{x},t)+{\stackrel{\&CenterDot;}{g}}_{ex}^2(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^2(x,t)u_y\end{array}\right.---\left(6\right)$

Wherein, $\begin{array}{c}{g}_{ex}^1(x,t)=g_{x1}(x,t)-g_{x1}(\hat{x},t)\\ g_{ey}^1(x,t)=g_{y1}(x,t)-g_{y1}(\hat{x},t)\\ g_{ex}^2(x,t)=g_{x2}(x,t)-g_{x2}(\hat{x},t)\\ g_{ey}^2(x,t)=g_{y2}(x,t)-g_{y2}(\hat{x},t)\end{array};$

$\begin{array}{c}{\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_x}={\widehat{\mathrm{\&sigma;}}}_x+{\mathrm{\&sigma;}}_x(x,t)+f_1(x,t)-f_1(\hat{x},t)+g_{ex}^1(x,t)u_x+g_{ey}^1(x,t)u_y\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_y}={\widehat{\mathrm{\&sigma;}}}_y+{\mathrm{\&sigma;}}_y(x,t)+f_2(x,t)-f_2(\hat{x},t)+g_{ex}^2(x,t)u_x+g_{ey}^2(x,t)u_y\end{array}$ For the nonlinear terms of formula (7);

By equation (4) second formula be brought into the 3rd formula and the 6th formula of equation (6), and be organized into matrix form, as formula (7):

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{x}}}_1\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_2\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_1}\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_3\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_4\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_2}\end{array}\right]=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_5& 0& 0\end{array}\right]\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_1}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_2}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{\mathrm{\&delta;}}_1\left(x\right)\\ {\mathrm{\&delta;}}_2\left(x\right)\end{array}\right]---\left(7\right)$

Formula (7) can be abbreviated as further:

$\stackrel{\&CenterDot;}{\tilde{x}}=\tilde{A}\tilde{x}+\tilde{B}\mathrm{\&delta;}---\left(8\right)$

Wherein,

$\begin{array}{cccc}\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_x}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_y}\end{array}\right];& \tilde{A}=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_5& 0& 0\end{array}\right];& \tilde{B}=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right];& \mathrm{\&delta;}=\left[\begin{array}{c}{\mathrm{\&delta;}}_1\left(x\right)\\ {\mathrm{\&delta;}}_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_x(x,t)+{\stackrel{\&CenterDot;}{f}}_1(x,t)-{\stackrel{\&CenterDot;}{f}}_1(\hat{x},t)+\\ {\stackrel{\&CenterDot;}{g}}_{ex}^1(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_y(x,t)+{\stackrel{\&CenterDot;}{f}}_2(x,t)-{\stackrel{\&CenterDot;}{f}}_2(\hat{x},t)+\\ {\stackrel{\&CenterDot;}{g}}_{ex}^2(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^2(x,t)u_y\end{array}\right];\end{array}$

According to state equation (8), nonlinear terms δ can be considered the disturbance input of system, state the system that is considered as exports, then expect middle h _i, the design of i=1,2...6 can offset δ couple impact, realize the asymptotic convergence of state observation error, consider by disturbance input δ to State-output transport function, Laplace transformation is carried out to (8), obtains formula (9):

$\frac{\tilde{x}\left(s\right)}{\mathrm{\&delta;}\left(s\right)}={(sI-\tilde{A})}^{-1}\tilde{B}---\left(9\right)$

Formula (9) expands into further:

$\frac{\tilde{x}\left(s\right)}{\mathrm{\&delta;}\left(s\right)}=\left[\begin{array}{cc}{G}_{11}\left(s\right)& 0\\ G_{21}\left(s\right)& 0\\ G_{31}\left(s\right)& 0\\ 0& G_{42}\left(s\right)\\ 0& G_{52}\left(s\right)\\ 0& G_{62}\left(s\right)\end{array}\right]---\left(10\right)$

Wherein,

$\begin{array}{ccc}{G}_{11}\left(s\right)=\frac{1}{s^3+h_1{s}^2+h_{2}s+h_5};& G_{21}\left(s\right)=\frac{h_1+s}{s^3+h_1{s}^2+h_{2}s+h_5};& G_{31}\left(s\right)=\frac{s^2+h_{1}s+h_2}{s^3+h_1{s}^2+h_{2}s+h_5};\end{array}$

$\begin{array}{ccc}{G}_{42}\left(s\right)=\frac{1}{s^3+h_3{s}^2+h_{4}s+h_6};& G_{52}\left(s\right)=\frac{h_3+s}{s^3+h_3{s}^2+h_{4}s+h_6};& G_{62}\left(s\right)=\frac{s^2+h_{3}s+h_4}{s^3+h_3{s}^2+h_{4}s+h_6};\end{array}$

Remember respectively $\left\{\begin{array}{c}{G}_1\left(s\right)=\left[\begin{array}{c}{G}_{11}\left(s\right)\\ G_{21}\left(s\right)\\ G_{31}\left(s\right)\end{array}\right]\\ G_2\left(s\right)=\left[\begin{array}{c}{G}_{42}\left(s\right)\\ G_{52}\left(s\right)\\ G_{62}\left(s\right)\end{array}\right]\end{array}\right.,$ According to equation (9), if transport function G ₁(s), G ₂s () be identically vanishing all, then offset nonlinear disturbance input δ completely to State-output error impact, accurately realize the estimation of gyroscope flywheel system total state; Select design parameter h ₁~ h ₆, to ω ∈ R, make the Infinite Norm shown in formula (11) simultaneously arbitrarily small;

$\left\{\begin{array}{c}\left|\right|G_1\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{1<i\&le;3}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i1}\left(j\mathrm{\&omega;}\right)|\\ \left|\right|G_2\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{4<i\&le;6}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i2}\left(j\mathrm{\&omega;}\right)|\end{array}\right.---\left(11\right)$

If $\left\{\begin{array}{c}{h}_5>>h_2>>h_1\\ h_6>>h_3>>h_4\end{array}\right.,$ Choose $\left\{\begin{array}{ccc}{h}_1=\frac{{\mathrm{\&alpha;}}_{11}}{\mathrm{\&epsiv;}}& h_2=\frac{{\mathrm{\&alpha;}}_{21}}{{\mathrm{\&epsiv;}}^2}& h_5=\frac{{\mathrm{\&alpha;}}_{31}}{{\mathrm{\&epsiv;}}^3}\\ h_3=\frac{{\mathrm{\&alpha;}}_{12}}{\mathrm{\&epsiv;}}& h_4=\frac{{\mathrm{\&alpha;}}_{22}}{{\mathrm{\&epsiv;}}^2}& h_6=\frac{{\mathrm{\&alpha;}}_{32}}{{\mathrm{\&epsiv;}}^3}\end{array}\right.$

Wherein, α _ij, i=1,2,3; J=1,2 meet following Hurwitz polynomial expression shown in (12); ε is normal number, and ε < < 1;

s ³+α _1js ²+α _2js+α _3j,j＝1,2(12)

By h ₁~ h ₆bring into G _jin (s), can obtain:

$G_j\left(s\right)=\frac{\mathrm{\&epsiv;}}{P\left(s\right)}\left[\begin{array}{c}{\mathrm{\&epsiv;}}^2\\ \mathrm{\&epsiv;}s+{\mathrm{\&alpha;}}_{1j}\\ {\left(\mathrm{\&epsiv;}s\right)}^2+{\mathrm{\&alpha;}}_{1j}\left(\mathrm{\&epsiv;}s\right)+{\mathrm{\&alpha;}}_{2j}\end{array}\right]---\left(13\right)$

Wherein P (s)=(ε s) ³+ α _1j(ε s) ²+ α _2j(ε s)+α _3j, j=1,2; $\left\{\begin{array}{c}\underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_1\left(s\right)=0\\ \underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_2\left(s\right)=0\end{array}\right.,$ According to formula (13), design expansion High-gain observer, by reducing the value of ε, improves disturbance estimated accuracy, the precision index needed for realization;

Other step and parameter identical with one of embodiment one to three.

Embodiment five: one of present embodiment and embodiment one to four unlike: it is characterized in that, described step 4 gyroscope flywheel system disturbance is estimated to realize according to following steps:

The High-gain observer after the expansion designed by step 2 is utilized to carry out the disturbance observation of gyroscope flywheel system, integrating step three adjusted design parameter ε, the disturbance of the gyroscope flywheel system characterized utilizing multivariate regression model is estimated, observation data is met the expectation estimated accuracy index, obtain the disturbance estimation test data sequence that the large rolling motion of gyroscope flywheel system produces, realize the disturbance term σ of the non-modeling of gyroscope flywheel system _dx(x, t), σ _dythe estimation of (x, t);

Other step and parameter identical with one of embodiment one to four.

Embodiment

If gyroscope flywheel system disturbance σ _kmathematical description is as shown in formula (14):

${\mathrm{\&sigma;}}_k=a\&CenterDot;\sin (2\mathrm{\&pi;f}\&CenterDot;t)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{b}_i{\mathrm{\&phi;}}_x^i+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_j{\mathrm{\&phi;}}_y^j---\left(14\right)$

Wherein, a, b _i, c _jbe constant value undetermined coefficient, m, n are the exponent number selected of multivariate regression model, f=ω _m/ (2 π) for time become motor rotation frequency, ω _mfor motor speed; During emulation, gyroscope flywheel physical system mathematical model is as σ in formula (1) _x, σ _ybe expressed as shown in formula (15):

$\begin{array}{c}{\mathrm{\&sigma;}}_x=1\&times;{10}^{-4}\&CenterDot;\sin (2\mathrm{\&pi;f}\&CenterDot;t)+1.5\&CenterDot;{\mathrm{\&phi;}}_x+0.6\&CenterDot;{\mathrm{\&phi;}}_x^2+0.15\&CenterDot;{\mathrm{\&phi;}}_x^3\\ {\mathrm{\&sigma;}}_y=1\&times;{10}^{-4}\&CenterDot;\sin (2\mathrm{\&pi;f}\&CenterDot;t)+2.1\&CenterDot;{\mathrm{\&phi;}}_x+1.5\&CenterDot;{\mathrm{\&phi;}}_x^2+0.8\&CenterDot;{\mathrm{\&phi;}}_x^3\end{array}---\left(15\right)$

Formula (15) expands the estimating target of High-gain observer in namely testing;

The moment of inertia J of gyroscope flywheel system rotor, gimbal _r, J _gbe given as respectively:

$J_r=\left[\begin{array}{ccc}1106.49& J_{\mathrm{rxy}}& J_{\mathrm{rxz}}\\ J_{\mathrm{rxy}}& 1106.49& J_{\mathrm{ryz}}\\ J_{\mathrm{rxz}}& J_{\mathrm{ryz}}& 1963.51\end{array}\right]\mathrm{kg}\&CenterDot;{\mathrm{mm}}^2;J_g=\left[\begin{array}{ccc}16.11& & \\ & 16.11& \\ & & 23.9\end{array}\right]\mathrm{kg}\&CenterDot;{\mathrm{mm}}^2$

Wherein, J _rxy, J _rxz, J _ryzrepresent the disturbance factor caused by rotor unbalance, its impact is presented as σ in gyroscope flywheel system equation is as formula (1) _x(x, t), σ _y(x, t) unknown disturbance item, in emulation, disturbing influence is characterized by formula (15);

The torsional rigidity k of two pairs of torsion bars and ratio of damping c in gyroscope flywheel system _gbe set to respectively:

k＝0.092N·m/rad；c _g＝2.5e-4N·m·s/rad

If gyroscope flywheel is all in moment output state at spacecraft three direction of principal axis, gyroscope flywheel three axle input instruction is respectively motor driving shaft rotary speed instruction: ω ' _m=23sin (0.2 π t)+157rad/s, rotor is x-axis radially, and the bidimensional angle of heel instruction of y-axis is respectively:

φ' _y＝1·sin(0.2π·t)°

Expansion High-gain observer design parameter α _ij, i=1,2,3, j=1,2 is as follows:

α _1j＝12.6；α _2j＝312.1；α _3j＝3225.3；j＝1,2

According to gyroscope flywheel optimum configurations and input instruction, when not considering measurement noise in sensor, ε gets 0.1 respectively, when 0.001, and system disturbance (σ _x, σ _y) observation effect respectively as shown in Fig. 2-Fig. 9.

Known according to Fig. 2-Fig. 9, when ε=0.1, observational error is positioned at 10 ^-3in the order of magnitude; When ε=0.001, observational error is positioned at 10 ^-4in the order of magnitude, observational error improves an order of magnitude; High-gain observer designed by utilization is estimated the disturbance of gyroscope flywheel two radial axle all reach good observation effect, the estimated accuracy of disturbance improves with the reduction of ε value.

Claims (5)

1. based on the gyroscope flywheel system disturbance method of estimation of expansion High-gain observer, it is characterized in that, the described gyroscope flywheel system disturbance method of estimation based on expansion High-gain observer realizes according to following steps:

Step one, kinetics equation according to gyroscope flywheel system, set up the gyroscope flywheel system state equation containing unknown disturbance;

Step 2, the gyroscope flywheel system state equation of basis containing unknown disturbance, design expansion High-gain observer;

The checking of step 3, observational error convergence and Design of Observer parameter ε regulate;

Step 4, realize gyroscope flywheel system disturbance estimate.

2. according to the gyroscope flywheel system disturbance method of estimation of claim 1 based on expansion High-gain observer, it is characterized in that, the gyroscope flywheel system state equation of described step one containing unknown disturbance realizes according to following steps:

Gyroscope flywheel rotor is at the angle of heel (φ of bidimensional radial direction _x, φ _y) and angle of heel speed as state variable x: $x={\left[\begin{array}{cccc}{x}_1& x_2& x_3& x_4\end{array}\right]}^T={\left[\begin{array}{cccc}{\mathrm{\&phi;}}_x& {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x& {\mathrm{\&phi;}}_y& {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y\end{array}\right]}^T,$ Gyroscope flywheel system state equation then containing non-modeling disturbance is as shown in formula (1):

$\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=f_1(x,t)+g_{x1}(x,t)u_x+g_{y1}(x,t)u_y+{\mathrm{\&sigma;}}_x(x,t)\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=f_2(x,t)+g_{x2}(x,t)u_x+g_{y2}(x,t)u_y+{\mathrm{\&sigma;}}_y(x,t)\end{array}---\left(1\right)$

System measurements equation is as shown in formula (2):

$y={\left[\begin{array}{cc}{y}_1& y_2\end{array}\right]}^T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]---\left(2\right)$

Wherein, f ₁(x, t), f ₂(x, t) represents ideally, the Nonlinear Mechanism item of gyroscope flywheel; u _x, u _yrepresent the control moment of bidimensional torquer, g _x1(x, t), g _x2(x, t), g _y1(x, t), g _y2(x, t) represents that the nonlinear system of bidimensional torquer is several; σ _x(x, t), σ _y(x, t) represents the non-modeling disturbance term of system; y ₁, y ₂represent measurable gyroscope flywheel rotor bidimensional angle of heel (φ respectively _x, φ _y);

After being arranged by formula (1) (2), formula (3) can be obtained:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=Ax+B\&lsqb;f(x,t)+{\mathrm{\&sigma;}}_d(x,t)+g(x,t)u\&rsqb;\\ y=Cx\end{array}\right.---\left(3\right)$

Wherein, σ _dthe non-modeling nonlinear disturbance item that (x, t) is the continuous bounded of gyroscope flywheel system; U is the continuous bounded control input of bidimensional, and namely bidimensional torquer exports; F (x, t), g (x, t) are nominal model, and are twice continuously differentiable bounded nonlinear function;

Wherein, $A=\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right];B=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 0\\ 0& 1\end{array}\right];C=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\end{array}\right];u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right]=\left[\begin{array}{c}{T}_{cx}\\ T_{cy}\end{array}\right];$

$f(x,t)=\left[\begin{array}{c}{f}_1(x,t)\\ f_2(x,t)\end{array}\right];{\mathrm{\&sigma;}}_d(x,t)=\left[\begin{array}{c}{\mathrm{\&sigma;}}_x(x,t)\\ {\mathrm{\&sigma;}}_y(x,t)\end{array}\right];g(x,t)=\left[\begin{array}{cc}{g}_{x1}(x,t)& g_{y1}(x,t)\\ g_{x2}(x,t)& g_{y2}(x,t)\end{array}\right];$

$\begin{array}{c}{f}_1(x,t)=\frac{{\mathrm{\&phi;}}_y{S}_{{\mathrm{\&phi;}}_y}}{C_{{\mathrm{\&phi;}}_y}^2}\&lsqb;C_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\&rsqb;\\ =\frac{1}{C_{{\mathrm{\&phi;}}_y}}\left[\begin{array}{c}(-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&phi;}}_z}{S}_{{\mathrm{\&theta;}}_y}){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_z\\ +({\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}-C_{{\mathrm{\&phi;}}_z}({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y})-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&phi;}}_z}-C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\end{array}\right]\\ +\frac{{\mathrm{\&beta;}}_1}{I_1}(-c_{gx}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-k_x{\mathrm{\&theta;}}_x+-\frac{1}{2}{I}_2{S}_{2{\mathrm{\&theta;}}_x}\&CenterDot;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2-\&lsqb;(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}\mathrm{\&rsqb;}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\&lsqb;(I_{rz}-I_{rx})C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;S_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z)\\ -\frac{\mathrm{\&eta;}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-k_y{\mathrm{\&theta;}}_y-\&lsqb;\frac{1}{2}(I_{rz}-I_{rx})C_{{\mathrm{\&theta;}}_x}^2{S}_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2\\ +\&lsqb;\frac{1}{2}(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x^2+\&lsqb;(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z{S}_{{\mathrm{\&theta;}}_x}\end{array}\right)\end{array};$

$\begin{array}{c}{f}_2(x,t)=({\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{S}_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-(C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}-S_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_z\\ -\&lsqb;{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{C}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{C}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&phi;}}_z}({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{C}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&theta;}}_y}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z})-({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{C}_{{\mathrm{\&theta;}}_x}{C}_{{\mathrm{\&phi;}}_z}-{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_z{S}_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&phi;}}_z}){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z\\ +\frac{{\mathrm{\&beta;}}_2}{I_1}(-c_{gx}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x-k_x{\mathrm{\&theta;}}_x-\frac{1}{2}{I}_2{S}_{2{\mathrm{\&theta;}}_x}\&CenterDot;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2-\&lsqb;(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}\mathrm{\&rsqb;}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-\&lsqb;(I_{rz}-I_{rx})C_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;S_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z)\\ -\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}\left(\begin{array}{c}-c_{gy}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y-k_y{\mathrm{\&theta;}}_y-\&lsqb;\frac{1}{2}(I_{rz}-I_{rx})C_{{\mathrm{\&theta;}}_x}^2{S}_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z^2+\\ \&lsqb;\frac{1}{2}(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x^2+\&lsqb;(I_{rz}-I_{rx})S_{2{\mathrm{\&theta;}}_y}-I_{ry}\&rsqb;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z{C}_{{\mathrm{\&theta;}}_x}\end{array}\right)\end{array};$

$\begin{array}{cc}{g}_{x1}(x,t)=\frac{{\mathrm{\&beta;}}_1}{I_1}{C}_{{\mathrm{\&theta;}}_z}+\frac{\mathrm{\&eta;}}{I_{ry}}{S}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}& g_{y1}(x,t)=\frac{{\mathrm{\&beta;}}_1}{I_1}{S}_{{\mathrm{\&theta;}}_z}-\frac{\mathrm{\&eta;}}{I_{ry}}{C}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}\end{array};$

$\begin{array}{cc}{g}_{x2}(x,t)=\frac{{\mathrm{\&beta;}}_2}{I_1}{C}_{{\mathrm{\&theta;}}_z}-\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}{S}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}& g_{y2}(x,t)=\frac{{\mathrm{\&beta;}}_2}{I_1}{S}_{{\mathrm{\&theta;}}_z}+\frac{C_{{\mathrm{\&phi;}}_z}}{I_{ry}}{C}_{{\mathrm{\&theta;}}_z}{C}_{{\mathrm{\&theta;}}_x}\end{array};$

Wherein, C _θwith S _θexpression formula be respectively cosine value cos θ and the sine value sin θ of rotational angle theta;

I _rx, I _ry, I _rzbeing respectively rotor at rotor block coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

I _gx, I _gy, I _gzbeing respectively gimbal at balance ring body coordinate system three principal axis of inertia direction moment of inertia, is known quantity;

K _x, k _ybe respectively known flexible support torsion bar torsional rigidity; c _gx, c _gybe respectively known flexible support ratio of damping;

T _cx=k _tyi _y, T _cy=k _txi _xbe respectively the control moment that bidimensional torquer exports rotor to, the u namely in equation (1) _x, u _y;

K _tx, k _tybe respectively the scaling factor of known sensor, i _x, i _ybe respectively the electric current of bidimensional torquer, for sensor can be measured;

θ _z, represent gyroscope flywheel motor shaft corner and rotating speed respectively, being sensor can measure;

θ in equation _x, θ _y, φ _z, I ₁, I ₂, β ₁, β ₂, η is intermediate variable, and concrete form is as follows respectively:

${\mathrm{\&theta;}}_x=arcsin(C_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&phi;}}_z}+S_{{\mathrm{\&phi;}}_x}{C}_{{\mathrm{\&phi;}}_z});{\mathrm{\&theta;}}_y=arcsin(S_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&theta;}}_z}-S_{{\mathrm{\&phi;}}_x}{C}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&theta;}}_z})$

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x=\frac{1}{C_{{\mathrm{\&theta;}}_y}}(C_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x+S_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y+C_{{\mathrm{\&theta;}}_x}{S}_{{\mathrm{\&theta;}}_y}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z);{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y=C_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_y-C_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&phi;}}_z}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_x-S_{{\mathrm{\&theta;}}_x}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_z$

${\mathrm{\&phi;}}_z=arctan\frac{C_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&theta;}}_z}}{C_{{\mathrm{\&phi;}}_y}{C}_{{\mathrm{\&theta;}}_z}+S_{{\mathrm{\&phi;}}_x}{S}_{{\mathrm{\&phi;}}_y}{S}_{{\mathrm{\&theta;}}_z}};$ I ₁＝I _gx+I _rxcos ²θ _y+I _rzsin ²θy。

I ₂＝I _gz-I _gy-I _ry+I _rxsin ²θ _y+I _rzcos ²θ _y； $\begin{array}{ccc}{\mathrm{\&beta;}}_1=\frac{C_{{\mathrm{\&phi;}}_z}{C}_{{\mathrm{\&theta;}}_y}}{C_{{\mathrm{\&phi;}}_y}}& \mathrm{\&eta;}=\frac{S_{{\mathrm{\&phi;}}_z}}{C_{{\mathrm{\&phi;}}_y}}& {\mathrm{\&beta;}}_2=C_{{\mathrm{\&theta;}}_y}{S}_{{\mathrm{\&phi;}}_z}\end{array}$

3. according to the gyroscope flywheel system disturbance method of estimation of claim 2 based on expansion High-gain observer, it is characterized in that, described step 2 design expansion High-gain observer realizes according to following steps:

Utilize measurement equation y=Cx, realize state variable x and nonlinear disturbance item σ _dthe estimation of (x, t), design expands High-gain observer as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=A\hat{x}+B\&lsqb;f(\hat{x},t)+g(\hat{x},t)u-\widehat{\mathrm{\&sigma;}}\&rsqb;+H\left(\mathrm{\&epsiv;}\right)(y-C\hat{x})\\ \stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}=F\left(\mathrm{\&epsiv;}\right)(y-C\hat{x})\end{array}\right.---\left(4\right)$

Wherein, for High-gain observer state variable; $\widehat{\mathrm{\&sigma;}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&sigma;}}}_x& {\widehat{\mathrm{\&sigma;}}}_y\end{array}\right]}^T$ For expansion High-gain observer state variable;

The gain matrix that H (ε), F (ε) they are observer, and its concrete form is as follows:

$H\left(\mathrm{\&epsiv;}\right)=\left[\begin{array}{cc}{h}_1& 0\\ h_2& 0\\ 0& h_3\\ 0& h_4\end{array}\right]=\left[\begin{array}{cc}\frac{{\mathrm{\&alpha;}}_{11}}{\mathrm{\&epsiv;}}& 0\\ \frac{{\mathrm{\&alpha;}}_{21}}{{\mathrm{\&epsiv;}}^2}& 0\\ 0& \frac{{\mathrm{\&alpha;}}_{12}}{\mathrm{\&epsiv;}}\\ 0& \frac{{\mathrm{\&alpha;}}_{22}}{{\mathrm{\&epsiv;}}^2}\end{array}\right];F\left(\mathrm{\&epsiv;}\right)=\left[\begin{array}{cc}-h_5& 0\\ 0& -h_6\end{array}\right]=\left[\begin{array}{cc}-\frac{{\mathrm{\&alpha;}}_{31}}{{\mathrm{\&epsiv;}}^3}& 0\\ 0& -\frac{{\mathrm{\&alpha;}}_{32}}{{\mathrm{\&epsiv;}}^3}\end{array}\right]---\left(5\right)$

Wherein, design parameter ε >0 is little design parameter; Design parameter α _ij, i=1,2,3, j=1,2 are all chosen as real number.

4. according to the gyroscope flywheel system disturbance method of estimation of claim 3 based on expansion High-gain observer, it is characterized in that, described step 3 observational error convergence checking and Design of Observer parameter ε regulate and realize according to following steps:

The observational error convergence of the gyroscope flywheel expansion High-gain observer of Observation Design, according to accuracy of observation demand, adjustment obtains the expansion High-gain observer design parameter be suitable for;

Definition error vector namely $\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\tilde{x}}_3\\ {\tilde{x}}_4\end{array}\right]=\left[\begin{array}{c}{x}_1-{\tilde{x}}_1\\ x_2-{\tilde{x}}_2\\ x_3-{\tilde{x}}_3\\ x_4-{\tilde{x}}_4\end{array}\right],$ First formula in formula (3) and formula (4) first formula are done difference, and the nonlinear terms after doing difference in gained equation are carried out integral extension is state formula (6) is obtained after arrangement:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{x}}}_1=-h_1{\tilde{x}}_1+{\tilde{x}}_2\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_2=-h_2{\tilde{x}}_1+{\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_x}\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_x}={\stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}}_x+{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_x(x,t)+{\stackrel{\&CenterDot;}{f}}_1(x,t)-{\stackrel{\&CenterDot;}{f}}_1(\hat{x},t)+{\stackrel{\&CenterDot;}{g}}_{ex}^1(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_3=-h_3{\tilde{x}}_3+{\tilde{x}}_4\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_4=-h_4{\tilde{x}}_3+{\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_y}\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_y}={\stackrel{\&CenterDot;}{\widehat{\mathrm{\&sigma;}}}}_y+{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_y(x,t)+{\stackrel{\&CenterDot;}{f}}_2(x,t)-{\stackrel{\&CenterDot;}{f}}_2(\hat{x},t)+{\stackrel{\&CenterDot;}{g}}_{ex}^2(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^2(x,t)u_y\end{array}\right.---\left(6\right)$

Wherein, $\begin{array}{c}{g}_{ex}^1(x,t)=g_{x1}(x,t)-g_{x1}(\hat{x},t)\\ g_{ey}^1(x,t)=g_{y1}(x,t)-g_{y1}(\hat{x},t)\\ g_{ex}^2(x,t)=g_{x2}(x,t)-g_{x2}(\hat{x},t)\\ g_{ey}^2(x,t)=g_{y2}(x,t)-g_{y2}(\hat{x},t)\end{array};$

$\begin{array}{c}{\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_x}={\widehat{\mathrm{\&sigma;}}}_x+{\mathrm{\&sigma;}}_x(x,t)+f_1(x,t)-f_1(\hat{x},t)+g_{ex}^1(x,t)u_x+g_{ey}^1(x,t)u_y\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_y}={\widehat{\mathrm{\&sigma;}}}_y+{\mathrm{\&sigma;}}_y(x,t)+f_2(x,t)-f_2(\hat{x},t)+g_{ex}^2(x,t)u_x+g_{ey}^2(x,t)u_y\end{array}$ For the nonlinear terms of formula (7);

By equation (4) second formula be brought into the 3rd formula and the 6th formula of equation (6), and be organized into matrix form, as formula (7):

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\tilde{x}}}_1\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_2\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_1}\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_3\\ {\stackrel{\&CenterDot;}{\tilde{x}}}_4\\ {\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{{\widehat{\mathrm{\&sigma;}}}_2}\end{array}\right]=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_6& 0& 0\end{array}\right]\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_1}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_2}\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{\mathrm{\&delta;}}_1\left(x\right)\\ {\mathrm{\&delta;}}_2\left(x\right)\end{array}\right]---\left(7\right)$

Formula (7) can be abbreviated as further:

$\stackrel{\&CenterDot;}{\tilde{x}}=\tilde{A}\tilde{x}+\tilde{B}\mathrm{\&delta;}---\left(8\right)$

Wherein,

$\tilde{x}=\left[\begin{array}{c}{\tilde{x}}_1\\ {\tilde{x}}_2\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_x}\\ {\tilde{x}}_3\\ {\tilde{x}}_4\\ {\mathrm{\&eta;}}_{{\widehat{\mathrm{\&sigma;}}}_y}\end{array}\right];\tilde{A}=\left[\begin{array}{cccccc}-h_1& 1& 0& 0& 0& 0\\ -h_2& 0& 1& 0& 0& 0\\ -h_5& 0& 0& 0& 0& 0\\ 0& 0& 0& -h_3& 1& 0\\ 0& 0& 0& -h_4& 0& 1\\ 0& 0& 0& -h_6& 0& 0\end{array}\right];\tilde{B}=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 0\\ 0& 0\\ 0& 1\end{array}\right];\mathrm{\&delta;}=\left[\begin{array}{c}{\mathrm{\&delta;}}_1\left(x\right)\\ {\mathrm{\&delta;}}_2\left(x\right)\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_x(x,t)+{\stackrel{\&CenterDot;}{f}}_1(x,t)-{\stackrel{\&CenterDot;}{f}}_1(\hat{x},t)+\\ {\stackrel{\&CenterDot;}{g}}_{ex}^1(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^1(x,t)u_y\\ {\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_y(x,t)+{\stackrel{\&CenterDot;}{f}}_2(x,t)-{\stackrel{\&CenterDot;}{f}}_2(\hat{x},t)+\\ {\stackrel{\&CenterDot;}{g}}_{ex}^2(x,t)u_x+{\stackrel{\&CenterDot;}{g}}_{ey}^2(x,t)u_y\end{array}\right];$

According to state equation (8), nonlinear terms δ can be considered the disturbance input of system, state the system that is considered as exports, then expect middle h _i, the design of i=1,2...6 can offset δ couple impact, realize the asymptotic convergence of state observation error, consider by disturbance input δ to State-output transport function, Laplace transformation is carried out to (8), obtains formula (9):

$\frac{\tilde{x}\left(s\right)}{\mathrm{\&delta;}\left(s\right)}={(sI-\tilde{A})}^{-1}\tilde{B}---\left(9\right)$

Formula (9) expands into further:

$\frac{\tilde{x}\left(s\right)}{\mathrm{\&delta;}\left(s\right)}=\left[\begin{array}{cc}{G}_{11}\left(s\right)& 0\\ G_{21}\left(s\right)& 0\\ G_{31}\left(s\right)& 0\\ 0& G_{42}\left(s\right)\\ 0& G_{52}\left(s\right)\\ 0& G_{62}\left(s\right)\end{array}\right]---\left(10\right)$

Wherein,

$G_{11}\left(s\right)=\frac{1}{s^3+h_1{s}^2+h_{2}s+h_5};G_{21}\left(s\right)=\frac{h_1+s}{s^3+h_1{s}^2+h_{2}s+h_5};G_{31}\left(s\right)=\frac{s^2+h_{1}s+h_2}{s^3+h_1{s}^2+h_{2}s+h_5};$

$G_{42}\left(s\right)=\frac{1}{s^3+h_3{s}^2+h_{4}s+h_6};G_{52}\left(s\right)=\frac{h_3+s}{s^3+h_3{s}^2+h_{4}s+h_6};G_{62}\left(s\right)=\frac{s^2+h_{3}s+h_4}{s^3+h_3{s}^2+h_{4}s+h_6};$

Remember respectively $\left\{\begin{array}{c}{G}_1\left(s\right)=\left[\begin{array}{c}{G}_{11}\left(s\right)\\ G_{21}\left(s\right)\\ G_{31}\left(s\right)\end{array}\right]\\ G_2\left(s\right)=\left[\begin{array}{c}{G}_{42}\left(s\right)\\ G_{52}\left(s\right)\\ G_{62}\left(s\right)\end{array}\right]\end{array}\right.,$ According to equation (9), if transport function G ₁(s), G ₂s () be identically vanishing all, then offset nonlinear disturbance input δ completely to State-output error impact, accurately realize the estimation of gyroscope flywheel system total state; Select design parameter h ₁~ h ₆, to ω ∈ R, make the Infinite Norm shown in formula (11) simultaneously arbitrarily small;

$\left\{\begin{array}{c}\left|\right|G_1\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{1<i\&le;3}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i1}\left(j\mathrm{\&omega;}\right)|\\ \left|\right|G_2\left(j\mathrm{\&omega;}\right)|{|}_{\mathrm{\&infin;}}=\underset{4<i\&le;6}{max}\underset{\mathrm{\&omega;}}{\sup }|G_{i2}\left(j\mathrm{\&omega;}\right)|\end{array}\right.---\left(11\right)$

If $\left\{\begin{array}{c}{h}_5>>h_2>>h_1\\ h_6>>h_3>>h_4\end{array}\right.,$ Choose $\left\{\begin{array}{ccc}{h}_1=\frac{{\mathrm{\&alpha;}}_{11}}{\mathrm{\&epsiv;}}& h_2=\frac{{\mathrm{\&alpha;}}_{21}}{{\mathrm{\&epsiv;}}^2}& h_5=\frac{{\mathrm{\&alpha;}}_{31}}{{\mathrm{\&epsiv;}}^3}\\ h_3=\frac{{\mathrm{\&alpha;}}_{12}}{\mathrm{\&epsiv;}}& h_4=\frac{{\mathrm{\&alpha;}}_{22}}{{\mathrm{\&epsiv;}}^2}& h_6=\frac{{\mathrm{\&alpha;}}_{32}}{{\mathrm{\&epsiv;}}^3}\end{array}\right.$

Wherein, α _ij, i=1,2,3; J=1,2 meet following Hurwitz polynomial expression shown in (12); ε is normal number, and ε <<1;

s ³+α _1js ²+α _2js+α _3j,j＝1,2(12)

By h ₁~ h ₆bring into G _jin (s), can obtain:

$G_j\left(s\right)=\frac{\mathrm{\&epsiv;}}{P\left(s\right)}\left[\begin{array}{c}{\mathrm{\&epsiv;}}^2\\ \mathrm{\&epsiv;}s+{\mathrm{\&alpha;}}_{1j}\\ {\left(\mathrm{\&epsiv;}s\right)}^2+{\mathrm{\&alpha;}}_{1j}\left(\mathrm{\&epsiv;}s\right)+{\mathrm{\&alpha;}}_{2j}\end{array}\right]---\left(13\right)$

Wherein P (s)=(ε s) ³+ α _1j(ε s) ²+ α _2j(ε s)+α _3j, j=1,2; $\left\{\begin{array}{c}\underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_1\left(s\right)=0\\ \underset{\mathrm{\&epsiv;}\&RightArrow;0}{\lim }{G}_2\left(s\right)=0\end{array}\right.,$ According to formula (13), design expansion High-gain observer, by reducing the value of ε, improves disturbance estimated accuracy, the precision index needed for realization.

5. according to the gyroscope flywheel system disturbance method of estimation of claim 4 based on expansion High-gain observer, it is characterized in that, described step 4 gyroscope flywheel system disturbance is estimated to realize according to following steps:

High-gain observer after the expansion utilizing step 2 to design carries out the disturbance observation of gyroscope flywheel system, integrating step three adjusted design parameter ε, the disturbance of the gyroscope flywheel system characterized utilizing multivariate regression model is estimated, observation data is met the expectation estimated accuracy index, obtain the disturbance estimation test data sequence that the large rolling motion of gyroscope flywheel system produces, realize the disturbance term σ of the non-modeling of gyroscope flywheel system _dx(x, t), σ _dythe estimation of (x, t).