CN103197558B - Microgyroscope fuzzy self-adaptation control method based on T-S model - Google Patents

Abstract

The invention discloses a microgyroscope fuzzy self-adaptation control method based on a T-S model. The microgyroscope fuzzy self-adaptation control method based on the T-S model comprises the following steps: establishing a T-S fuzzy module based on a microgyroscope nonlinearity model, and acquiring an fuzzy dynamic system model through single point fuzzification, product reasoning and center equal-weighted defuzzification; designing a reference model based on controlling tracks, designing a local linear state feedback controller to each T-S fuzzy submodel based on a parallel distribution compensation method, and enabling the fuzzy dynamic system model tracks to track the reference model tracks; and designing a parameter estimator due to the facts that both manufacturing errors and environmental interference exist and the parameters of the T-S fuzzy model are unknown. An improved type self-adaptation control algorithm is designed based on a Lyapunov theory for enabling an overall situation of both track control errors and parameter estimating errors to be gradual and stable. The microgyroscope fuzzy self-adaptation control method based on the T-S model is applied to the microgyroscope nonlinearity model, tests and verifies feasibility and effectiveness of the microgyroscop nonlinearity model which is controlled on a microgyroscope track control module.

Description

Based on the gyroscope Fuzzy Adaptive Control Scheme of T-S model

Technical field:

The invention belongs to gyroscope control technology field, be specifically related to a kind of gyroscope Fuzzy Adaptive Control Scheme based on T-S model.

Background technology:

Gyroscope is the fundamental measurement element of inertial navigation and guidance, compared with conventional gyro, gyroscope has huge advantage on volume and cost, measuring accuracy also there is huge raising, therefore wide application market is had, such as in navigational guidance, consumer electronics, navigation and national defence.But actually, foozle in manufacturing process and the impact of environment temperature cause the existence of stiffness coefficient and the ratio of damping be coupled, thus produce the intrinsic interference of system of machinery and electrostatic force form, cause the difference between original paper characteristic and design, reduce sensitivity and the precision of gyroscope.In addition, gyroscope itself belongs to multi-input multi-output system, and the uncertain and external interference of parameter can cause fluctuation to systematic parameter.Compensation foozle and TRAJECTORY CONTROL become the subject matter that gyroscope controls.And common gyroscope controls to be control on the basis of its linear model, do not examine the problem of the controlled model of reality closer to nonlinear model, the present invention sets up its T-S fuzzy model on the basis of gyroscope nonlinear model, then carries out TRAJECTORY CONTROL to its T-S fuzzy model.

The essence of T-S fuzzy model is the fuzzy close that a non-linear dynamic model can regard many Local Linear Models as, T-S fuzzy model describes nonlinear system by one group of if-then rule, each rule represents a subsystem, and whole fuzzy system is the linear combination of subsystems.Fuzzy control is a kind of intelligent control method based on fuzzy set theory, Fuzzy Linguistic Variable and fuzzy logic inference, first operating personnel or expertise are become fuzzy rule by it, then the live signal obfuscation will come by sensor, obfuscation is obtained the input of signal as fuzzy rule, complete fuzzy reasoning, the output quantity obtained after reasoning is the most at last added on actuator, realizes the fuzzy control of system.Adaptive Fuzzy Control is the fuzzy logic system with adaptive learning, it can the initial value of setup control image parameter arbitrarily, then by the adaptive algorithm of CONTROLLER DESIGN parameter, regulate auto-adaptive parameter, real-time online update controller parameter, ensures rapidity and the stability of Systematical control under arbitrary initial value.

Summary of the invention:

There are differences to solve between the control object of common gyroscope control method and actual controlled device, make the more progressive reality of the TRAJECTORY CONTROL of gyroscope, the present invention sets up its T-S model on the basis of gyroscope nonlinear model, then on the basis of its T-S model, based on Lyapunov method design Adaptive Fuzzy Control algorithm, ensure that the Globally asymptotic of whole control system, improve the robustness of system to Parameters variation, compensate for foozle.

In order to solve the problem, the technical solution used in the present invention is:

Based on the gyroscope Fuzzy Adaptive Control Scheme of T-S model, comprise the following steps

1) the dimensionless nonlinear motion vector equation of gyroscope is set up;

2) on the basis of gyroscope dimensionless nonlinear motion vector equation, set up its T-S fuzzy model, and obtain gyroscope fuzzifying dynamic system model by single-point obfuscation, product inference and center average weighted anti fuzzy method;

3) design the local linear state feedback controller of the fuzzy submodel of each T-S according to parallel distribution compensation method, and obtain controller output by single-point obfuscation, product inference and center average weighted anti fuzzy method;

4) design reference model, allows gyroscope fuzzifying dynamic system model track following reference model track;

5) according to Lyapunov function theory design adaptive control algorithm, line stabilization analysis of going forward side by side;

Abovementioned steps 1) dimensionless nonlinear motion vector equation complete as follows,

1-1) consider the existence of foozle and non-linear spring effect, the nonlinear mathematical model of actual gyroscope can simplify and is approximately:

$m\stackrel{\·\·}{x}+d_{\mathrm{xx}}\stackrel{\·}{x}+(d_{\mathrm{xy}}-2m{\mathrm{\Ω}}_z)\stackrel{\·}{y}+(k_{\mathrm{xx}}-m{\mathrm{\Ω}}_z^2)x+k_{\mathrm{xy}}y+k_{x^3}{x}^3=u_x$ （1）

$m\stackrel{\·\·}{y}+d_{\mathrm{yy}}\stackrel{\·}{y}+(d_{\mathrm{xy}}+2m{\mathrm{\Ω}}_z)\stackrel{\·}{x}+(k_{\mathrm{yy}}-m{\mathrm{\Ω}}_z^2)y+k_{\mathrm{xy}}x+k_{y^3}{y}^3=u_y$

Wherein m is mass quality, and x, y are mass state variables in the rotated coordinate system, d _xx, d _yydiaxon ratio of damping, k _xx, k _yydiaxon spring constant, diaxon non-linear spring coefficient, d _xycoupling Damping coefficient, k _xycoupling spring coefficient, u _x, u _ythe control inputs of diaxon, Ω _zit is the input angular velocity of z-axis.

1-2) because the displacement range of mass is in sub-millimeter meter range, therefore to get reference length be 1 μm; The natural frequency of the diaxon of gyroscope is in kilohertz range, therefore to get reference frequency be 1KHz, non-dimension time t ^*=ω ₀t, by described equation (1) both sides with square ω divided by diaxon natural frequency ₀ ², reference length q ₀with mass quality m, obtain the dimensionless nonlinear motion vector equation of gyroscope

${\stackrel{\·\·}{q}}^{*}=({2S}^{*}-D^{*}){\stackrel{\·}{q}}^{*}+({\mathrm{\Ω}}_z^{*2}-k_1)q^{*}-k_3{q}^{{*}^3}+u^{*}---\left(2\right)$

Wherein, track state $q^{*}=\frac{q_n}{q_0},$ ${\stackrel{\·}{q}}^{*}=\frac{q_n}{{\mathrm{\ω}}_0{q}_0},$ ${\stackrel{\·\·}{q}}^{*}=\frac{q_n}{{\mathrm{\ω}}_0^2{q}_{0,}}$ $q_n=\left[\begin{array}{c}x\\ y\end{array}\right],$ $u^{*}=\frac{u_m}{m{{\mathrm{\ω}}_0}^2{q}_0},$ $u_m=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],$ ${{\mathrm{\Ω}}^{*}}_z=\frac{{\mathrm{\Ω}}_z}{{\mathrm{\ω}}_0},$ $S^{*}=\left[\begin{array}{cc}0& {\mathrm{\Ω}}_z^{*}\\ {-\mathrm{\Ω}}_Z^{*}& 0\end{array}\right],$ $D^{*}=\frac{D}{m{\mathrm{\ω}}_0},$ $D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],$ $k_1=\left[\begin{array}{cc}{w_x}^2& w_{\mathrm{xy}}\\ w_{\mathrm{xy}}& {w_y}^2\end{array}\right],$ ${w_x}^2=\frac{k_{\mathrm{xx}}}{m{{\mathrm{\ω}}_0}^2},$ ${w_y}^2=\frac{k_{\mathrm{yy}}}{m{{\mathrm{\ω}}_0}^2},$ $w_{\mathrm{xy}}=\frac{k_{\mathrm{xy}}}{m{{\mathrm{\ω}}_0}^2},$ $k_3=\left[\begin{array}{cc}{k_{x^3}}^{*}& 0\\ 0& {k_{y^3}}^{*}\end{array}\right],$ ${k_{x^3}}^{*}=\frac{k_{x^3}{q}_0^2}{m{\mathrm{\ω}}_0^2},$ ${k_{x^3}}^{*}=\frac{k_{x^3}{q}_0^2}{m{\mathrm{\ω}}_0^2},$

Q ^*represent track state.

Abovementioned steps 2) in T-S fuzzy model be made up of 9 IF-THEN rules, described rule is

Rule i:IF x is about M _i1and y is about M _i2and is about M _i3 is about M _i4。

$\mathrm{THEN}\stackrel{\·}{q}=A_i*q+B_i*u$ i＝1,2,…,9

Abovementioned steps 2) in gyroscope fuzzifying dynamic system model be

$\stackrel{\·}{q}=\frac{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)[A_{i}q+B_{i}u]}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}---\left(3\right)$

Wherein A _ifor gating matrix $A_i=\left[\begin{array}{cccc}{a}_{11}^i& a_{12}^i& a_{13}^i& a_{14}^i\\ a_{21}^i& a_{22}^i& a_{23}^i& a_{24}^i\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ B _ifor input matrix $B_i=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\\ 0& 0\end{array}\right],$ State variable $q=\left[\begin{array}{c}\stackrel{\·}{x}\\ \stackrel{\·}{y}\\ x\\ y\end{array}\right],$ Input $u=\left[\begin{array}{c}{u}_x\\ u_y\\ 0\\ 0\end{array}\right],$ Weighting membership function ${\mathrm{\μ}}_i\left(\mathrm{\η}\right)=M_{\mathrm{il}}\left(x\right)M_{i2}\left(y\right)M_{i3}\left(\stackrel{\·}{x}\right)M_{i4}\left(\stackrel{\·}{y}\right);$ M _i1(x), M _i2(y), with be respectively state variable x, y, with about fuzzy set M _i1, M _i2, M _i3and M _i4membership function.

Abovementioned steps 3) in local linear state feedback controller be made up of 9 IF-THEN rules, described rule is

Rule i:IF x is about M _j1and y is about M _j2and is about M _j3 is about M _j4

THEN S(t)＝-K _j(t)*x(t)+l _j(t)*r(t),j＝1,2,…,9

Output S (t) of local linear state feedback controller is

$s\left(t\right)=\frac{{\∑}_{j=1}^9{\mathrm{\μ}}_j\left(\mathrm{\η}\right)[-k_j\left(t\right)q\left(t\right)+l_j\left(t\right)r\left(t\right)]}{{\mathrm{\Σ}}_{j=1}^9{\mathrm{\μ}}_j\left(\mathrm{\η}\right)}---\left(4\right)$

Wherein matrix $K_j\left(t\right)\left[\begin{array}{cccc}{a}_{11}^i-a_{11}^m& a_{12}^i-a_{12}^m& a_{13}^i-a_{13}^m& a_{14}^i-a_{14}^m\\ a_{21}^i-a_{21}^m& a_{22}^i-a_{22}^m& a_{23}^i-a_{23}^m& a_{24}^i-a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ R(t) for expecting input $r\left(t\right)=\left[\begin{array}{c}{A}_x{\mathrm{\ω}}_x\cos \left({\mathrm{\ω}}_{x}t\right)\\ A_y{\mathrm{\ω}}_y\cos \left({\mathrm{\ω}}_{y}t\right)\end{array}\right],$ Parameter l _j(t)=1, A _mfor expecting gating matrix $A_m=\left[\begin{array}{cccc}{a}_{11}^m& a_{12}^m& a_{13}^m& a_{14}^m\\ a_{21}^m& a_{22}^m& a_{23}^m& a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ A _x, A _ybe respectively the amplitude of x-axis and y-axis vibration, ω _x, ω _xbe respectively the vibration frequency of diaxon, t is the time.

Abovementioned steps 4) in definition reference model refer to output S (t) of local linear state feedback controller in described step 3) brought in gyroscope fuzzifying dynamic system modular form (3), obtain reference model:

${\stackrel{\·}{q}}_m=A_{m}q+B_{m}r---\left(5\right)$

Wherein desired control matrix A _mvalue is, $A_m=\left[\begin{array}{cccc}{a}_{11}^m& a_{12}^m& a_{13}^m& a_{14}^m\\ a_{21}^m& a_{22}^m& a_{23}^m& a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]=\left[\begin{array}{cccc}-1& 0& -{\mathrm{\ω}}_x^2& 0\\ 0& -1& 0& -{\mathrm{\ω}}_y^2\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ Expect input matrix B _mvalue is, $B_m=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\\ 0& 0\end{array}\right],$ Expect input ^rbe taken as, $r=\left[\begin{array}{c}{A}_x{\mathrm{\ω}}_x\cos \left({\mathrm{\ω}}_{x}t\right)\\ A_y{\mathrm{\ω}}_y\cos \left({\mathrm{\ω}}_{y}t\right)\end{array}\right],$ State

Variable q is taken as, $q=\left[\begin{array}{c}\stackrel{\·}{x}\\ \stackrel{\·}{y}\\ x\\ y\end{array}\right]=\left[\begin{array}{c}{A}_x{\mathrm{\ω}}_x\cos \left({\mathrm{\ω}}_{x}t\right)\\ A_y{\mathrm{\ω}}_y\cos \left({\mathrm{\ω}}_{y}t\right)\\ A_x\sin \left({\mathrm{\ω}}_{x}t\right)\\ A_y\sin \left({\mathrm{\ω}}_{y}t\right)\end{array}\right].$

In output S (t) of aforementioned local linear state feedback controller, the gating matrix A of gyroscope T-S fuzzy model _iunknown with state variable q, in order to make fuzzy system formula (3) at gating matrix A _iwhen unknown, track reference modular form (5), is adjusted to output S (t) of local linear state feedback controller

$s\left(t\right)=\frac{{\∑}_{j=1}^9{\mathrm{\μ}}_j\left(\mathrm{\η}\right)[-{\hat{K}}_{j}q\left(t\right)+l_j\left(t\right)r\left(t\right)]}{{\mathrm{\Σ}}_{j=1}^9{\mathrm{\μ}}_j\left(\mathrm{\η}\right)}$

Wherein, for estimated matrix, ${\hat{K}}_j=\left[\begin{array}{cccc}{\hat{a}}_{11}^i-a_{11}^m& {\hat{a}}_{12}^i-a_{12}^m& {\stackrel{i}{a}}_{13}^{^}-a_{13}^m& {\hat{a}}_{14}^i-a_{14}^m\\ {\hat{a}}_{21}^i-a_{21}^m& {\hat{a}}_{22}^i-a_{22}^m& {\hat{a}}_{23}^i-a_{23}^m& {\hat{a}}_{24}^i-a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ for estimating control

Matrix processed, ${\hat{A}}_i=\left[\begin{array}{cccc}{\hat{a}}_{11}^i& {\hat{a}}_{12}^i& {\hat{a}}_{13}^i& {\hat{a}}_{14}^i\\ {\hat{a}}_{21}^i& {\hat{a}}_{22}^i& {\hat{a}}_{23}^i& {\hat{a}}_{24}^i\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

Gyroscope fuzzifying dynamic system model after adjustment is

$\stackrel{\·}{q}\left(t\right)=A_{m}q\left(t\right)+\frac{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)[(A_i-A_m)q\left(t\right)+B_{i}u\left(t\right)]}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}$

In order to obtain the state variable q of gyroscope, design parameter estimator

$\stackrel{\stackrel{\·}{^}}{q}\left(t\right)=A_m\hat{q}\left(t\right)+\frac{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)[({\hat{A}}_i-A_m)q\left(t\right)+B_{i}u\left(t\right)]}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}---\left(7\right)$

Wherein, for estimated state variable.

Abovementioned steps 5) according to Lyapunov function theory design adaptive control algorithm, be specially,

5-1) defining Lyapunov function V (t) is:

$V\left(t\right)=V(e,{\tilde{a}}_{1i},{\tilde{a}}_{2i})=e^T\left(t\right)\mathrm{Pe}\left(t\right)+{\mathrm{\Σ}}_{i=1}^9\frac{{\tilde{a}}_{1i}^T{\tilde{a}}_{1i}}{{\mathrm{\γ}}_{1i}}+{\mathrm{\Σ}}_{i=1}^9\frac{{\tilde{a}}_{2i}^T{\tilde{a}}_{2i}}{{\mathrm{\γ}}_{2i}}$

5-2) to Lyapunov function V (t) differentiate, obtain

$\stackrel{\·}{V}\left(t\right)=-e^T\left(t\right)(A_s^{T}P+{\mathrm{PA}}_s)e\left(t\right)-2\frac{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right){P_1}^{T}e\left(t\right)q^T\left(t\right){\tilde{a}}_{2i}}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}$

$-2\frac{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right){P_2}^{T}e\left(t\right)q^T\left(t\right){\tilde{a}}_{2i}}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}+{\mathrm{\Σ}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\·}{~}}{a}}_{1i}^T{\tilde{a}}_{1i}}{{\mathrm{\γ}}_{1i}}+{\mathrm{\Σ}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\·}{~}}{a}}_{2i}^T{\tilde{a}}_{2i}}{{\mathrm{\γ}}_{2i}}$

5-3) get adaptive law for

${\stackrel{\stackrel{\·}{~}}{a}}_i^T={\mathrm{\γ}}_i\frac{{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}{{\mathrm{\Σ}}_{i=1}^9{\mathrm{\μ}}_i\left(\mathrm{\η}\right)}\left[{P_1}^T{P_2}^T\right]e\left(t\right)q^T\left(t\right)-\mathrm{\ρsgn}\left({\tilde{a}}_i\right)\mathrm{\ρ}>0$

Then $\stackrel{\&CenterDot;}{V}\left(t\right)=-e^T\left(t\right)e\left(t\right)-2\mathrm{\&rho;}{\mathrm{\&Sigma;}}_{i=1}^9\frac{\mathrm{sgn}\left({\tilde{a}}_{1i}\right){\tilde{a}}_{1i}}{{\mathrm{\&gamma;}}_{1i}}-2\mathrm{\&rho;}{\mathrm{\&Sigma;}}_{i=1}^9\frac{\mathrm{sgn}\left({\tilde{a}}_{2i}\right){\tilde{a}}_{2i}}{{\mathrm{\&gamma;}}_{2i}}<0,$ According to Lyapunov stability theory, track following error and parameter estimating error asymptotically stability,

Wherein, γ _i=γ _1i=γ _2ibe adaptive gain parameter, ρ is auto-adaptive parameter, A _sstablize arbitrarily quadravalence matrix, parameter estimating error parameter estimating error the first row ${\tilde{a}}_{1i}={\hat{a}}_{1i}-a_{1i},{\hat{a}}_{1i}=\left[\begin{array}{cccc}{\hat{a}}_{11}^i& {\hat{a}}_{12}^i& {\hat{a}}_{13}^i& {\hat{a}}_{14}^i\end{array}\right],$ $a_{1i}=\left[\begin{array}{cccc}{a}_{11}^i& a_{12}^i& a_{13}^i& a_{14}^i\end{array}\right],$ Parameter estimating error second row ${\tilde{a}}_{2i}={\hat{a}}_{2i}-a_{2i},{\hat{a}}_{2i}=\left[\begin{array}{cccc}{\hat{a}}_{21}^i& {\hat{a}}_{22}^i& {\hat{a}}_{23}^i& {\hat{a}}_{24}^i\end{array}\right],$ $a_{2i}=\left[\begin{array}{cccc}{a}_{21}^i& a_{22}^i& a_{23}^i& a_{24}^i\end{array}\right],$ P meets $A_s^{T}P+{\mathrm{PA}}_s=-I,P=\left[\begin{array}{cccc}{P}_1& P_2& P_3& P_4\end{array}\right],$ for track following error function, for predicted state variable.

Technique scheme can find out that usefulness of the present invention is: the present invention can when gyroscope T-S fuzzy model unknown parameters, accurate trajectory track control is carried out to the non-linear controlled device of gyroscope, and can ensure TRAJECTORY CONTROL error and parameter estimating error Globally asymptotic, the Adaptive Fuzzy Control after improvement can improve system to the robustness of Parameters variation and compensate foozle.

Accompanying drawing illustrates:

Fig. 1 is gyroscope simplified model structural drawing in instantiation of the present invention;

Fig. 2 is the schematic diagram of micro-gyroscope control system of the present invention;

Fig. 3 is T-S model track following error e in instantiation of the present invention _t-Stime-domain response curve figure;

Fig. 4 is the nonlinear model track following error e in instantiation of the present invention _nONtime-domain response curve figure;

Fig. 5 is the T-S fuzzy model partial parameters matrix A in instantiation of the present invention ₁time-domain response curve figure;

Fig. 6 is the T-S fuzzy model partial parameters matrix A in instantiation of the present invention ₄time-domain response curve figure;

Fig. 7 is the T-S fuzzy model partial parameters matrix A in instantiation of the present invention ₇time-domain response curve figure.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention will be further described:

As shown in Figure 2, based on the gyroscope Fuzzy Adaptive Control Scheme of T-S model, mainly comprise the following steps

One, the dimensionless nonlinear motion vector equation of gyroscope is set up

Micro-gyrotron generally comprises three ingredients: the mass, electrostatic drive and the sensing apparatus that support by resilient material.The major function of electrostatic drive is the constant of amplitude when driving and maintain the vibration of micro-gyrotron; Sensing apparatus is used for the position of perceived quality block and speed.Gyroscope can regard a damping vibrition system be made up of mass and spring as.Fig. 1 shows the micro-gyrotron model simplified under cartesian coordinate system.Z axis represents gyroscope, can think that mass is limited to move in x-y plane, and can not move along Z axis.Non-linear spring effect can be there is in actual mass spring damping vibrition system, due to the existence of gyroscope manufacturing defect and mismachining tolerance, rigidity Dynamic Coupling and the damping Dynamic Coupling of x-axis and y-axis can be caused, consider the existence of foozle and non-linear spring effect, the nonlinear mathematical model of actual gyroscope can simplify and is approximately:

$m\stackrel{\&CenterDot;\&CenterDot;}{x}+d_{\mathrm{xx}}\stackrel{\&CenterDot;}{x}+(d_{\mathrm{xy}}-2m{\mathrm{\&Omega;}}_z)\stackrel{\&CenterDot;}{y}+(k_{\mathrm{xx}}-m{\mathrm{\&Omega;}}_z^2)x+k_{\mathrm{xy}}y+k_{x^3}{x}^3=u_x$ （1）

$m\stackrel{\&CenterDot;\&CenterDot;}{y}+d_{\mathrm{yy}}\stackrel{\&CenterDot;}{y}+(d_{\mathrm{xy}}+2m{\mathrm{\&Omega;}}_z)\stackrel{\&CenterDot;}{x}+(k_{\mathrm{yy}}-m{\mathrm{\&Omega;}}_z^2)y+k_{\mathrm{xy}}x+k_{y^3}{y}^3=u_y$

Wherein m is mass quality, and x, y are mass variablees in the rotated coordinate system, d _xx, d _yythe ratio of damping of x-axis and y-axis, k _xx, k _yythe spring constant of x-axis and y-axis, the non-linear spring coefficient of x-axis and y-axis, d _xycoupling Damping coefficient, k _xycoupling spring coefficient, u _x, u _ybe x-axis and y-axis control inputs, Ω _zit is the input angular velocity of Z axis.

The natural frequency scope of micro-gyrotron diaxon is generally in KHz (KHz) scope, and input angular velocity may only in the several years scope per second to the several years per hour, and both exist large time frame difference, not easily realize numerical simulation.In order to overcome the above problems, non-dimension process is carried out to model, because the displacement range of mass is in sub-millimeter meter range, therefore rational reference length q ₀desirable 1 μm, the natural frequency ω of the diaxon of gyroscope ₀desirable 1KHz, defines non-dimension time t ^*=ω ₀t.Equation (1) both sides are with square ω divided by diaxon natural frequency ₀ ², reference length q ₀with mass quality m, the new number of definition is as follows: $q^{*}=\frac{q_n}{q_0},$ ${\stackrel{\&CenterDot;}{q}}^{*}=\frac{q_n}{{\mathrm{\&omega;}}_0{q}_0},$ ${\stackrel{\&CenterDot;\&CenterDot;}{q}}^{*}=\frac{q_n}{{\mathrm{\&omega;}}_0^2{q}_0},$ $u^{*}=\frac{u_m}{m{{\mathrm{\&omega;}}_0}^2{q}_0},$ ${{\mathrm{\&Omega;}}^{*}}_z=\frac{{\mathrm{\&Omega;}}_z}{{\mathrm{\&omega;}}_0},$ $S^{*}=\left[\begin{array}{cc}0& {\mathrm{\&Omega;}}_z^{*}\\ {-\mathrm{\&Omega;}}_Z^{*}& 0\end{array}\right],$ $D^{*}=\frac{D}{m{\mathrm{\&omega;}}_0},$ ${w_x}^2=\frac{k_{\mathrm{xx}}}{m{{\mathrm{\&omega;}}_0}^2},$ ${w_y}^2=\frac{k_{\mathrm{yy}}}{m{{\mathrm{\&omega;}}_0}^2},$ $w_{\mathrm{xy}}=\frac{k_{\mathrm{xy}}}{m{{\mathrm{\&omega;}}_0}^2},$ ${k_{x^3}}^{*}=\frac{k_{x^3}{q}_0^2}{m{\mathrm{\&omega;}}_0^2},$ ${k_{x^3}}^{*}=\frac{k_{x^3}{q}_0^2}{m{\mathrm{\&omega;}}_0^2},$

Obtain the vector form of the dimensionless Nonlinear Equations of Motion of gyroscope as (2):

${\stackrel{\&CenterDot;\&CenterDot;}{q}}^{*}=({2S}^{*}-D^{*}){\stackrel{\&CenterDot;}{q}}^{*}+({\mathrm{\&Omega;}}_z^{*2}-k_1)q^{*}-k_3{q}^{{*}^3}+u^{*}---\left(2\right)$

Wherein $q_n=\left[\begin{array}{c}x\\ y\end{array}\right],$ $u_m=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],$ $D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],$ $k_1=\left[\begin{array}{cc}{w_x}^2& w_{\mathrm{xy}}\\ w_{\mathrm{xy}}& {w_y}^2\end{array}\right],$ $k_3=\left[\begin{array}{cc}{k_{x^3}}^{*}& 0\\ 0& {k_{y^3}}^{*}\end{array}\right].$

Q ^*represent track state.

Two, on the basis of gyroscope dimensionless nonlinear motion vector equation, set up its T-S fuzzy model, and obtain gyroscope fuzzifying dynamic system model by single-point obfuscation, product inference and center average weighted anti fuzzy method

On the basis of gyroscope dimensionless nonlinear motion vector equation (2), set up its T-S fuzzy model, this model is made up of 9 IF-THEN rules, and rule format is as follows:

Rule i:IF x is about M _i1and y is about M _i2and is about Mi3 is about M _i4

$\mathrm{THEN}\stackrel{\&CenterDot;}{q}=A_i*q+B_i*u,i=\mathrm{1,2},...,9$

Obtaining gyroscope fuzzifying dynamic system model by single-point obfuscation, product inference and center average weighted anti fuzzy method is

$\stackrel{\&CenterDot;}{q}=\frac{{\&Sum;}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)[A_{i}q+B_{i}u]}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}---\left(3\right)$

Wherein A _ifor gating matrix $A_i=\left[\begin{array}{cccc}{a}_{11}^i& a_{12}^i& a_{13}^i& a_{14}^i\\ a_{21}^i& a_{22}^i& a_{23}^i& a_{24}^i\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ B _ifor input matrix $B_i=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\\ 0& 0\end{array}\right],$ State variable $q=\left[\begin{array}{c}\stackrel{\&CenterDot;}{x}\\ \stackrel{\&CenterDot;}{y}\\ x\\ y\end{array}\right],$ Input $u=\left[\begin{array}{c}{u}_x\\ u_y\\ 0\\ 0\end{array}\right],$ Weighting membership function ${\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)=M_{\mathrm{il}}\left(x\right)M_{i2}\left(y\right)M_{i3}\left(\stackrel{\&CenterDot;}{x}\right)M_{i4}\left(\stackrel{\&CenterDot;}{y}\right);$ with be respectively state variable x, y, with about fuzzy set M _i1, M _i2, M _i3and M _i4membership function.

Three, design local linear state feedback control device

According to parallel distribution compensation method to each T-S fuzzy submodel design local linear state feedback control device, controller is made up of 9 IF-THEN rules, and form is as follows:

Rule i:IF x is about M _j1and y is about M _j2and is about M _j3 is about M _j4

THEN S(t)＝-K _j(t)*x(t)+l _j(t)*r(t),j＝1,2,…,9

Obtaining controller output S (t) by single-point obfuscation, product inference and center average weighted anti fuzzy method is

$s\left(t\right)=\frac{{\&Sum;}_{j=1}^9{\mathrm{\&mu;}}_j\left(\mathrm{\&eta;}\right)[-k_j\left(t\right)q\left(t\right)+l_j\left(t\right)r\left(t\right)]}{{\mathrm{\&Sigma;}}_{j=1}^9{\mathrm{\&mu;}}_j\left(\mathrm{\&eta;}\right)}---\left(4\right)$

Wherein matrix $K_j\left(t\right)\left[\begin{array}{cccc}{a}_{11}^i-a_{11}^m& a_{12}^i-a_{12}^m& a_{13}^i-a_{13}^m& a_{14}^i-a_{14}^m\\ a_{21}^i-a_{21}^m& a_{22}^i-a_{22}^m& a_{23}^i-a_{23}^m& a_{24}^i-a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ Expect input $r\left(t\right)=\left[\begin{array}{c}{A}_x{\mathrm{\&omega;}}_x\cos \left({\mathrm{\&omega;}}_{x}t\right)\\ A_y{\mathrm{\&omega;}}_y\cos \left({\mathrm{\&omega;}}_{y}t\right)\end{array}\right],$ Parameter l _j(t)=1, desired control matrix $A_m=\left[\begin{array}{cccc}{a}_{11}^m& a_{12}^m& a_{13}^m& a_{14}^m\\ a_{21}^m& a_{22}^m& a_{23}^m& a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ A _x, A _ybe respectively the amplitude of x-axis and y-axis vibration, ω _x, ω _xbe respectively the vibration frequency of diaxon, t is the time.

Four, define reference model, allow gyroscope fuzzifying dynamic system model track following reference model track

The control objectives of gyroscope allows mass in x-axis and y-axis with given amplitude and frequency vibration, and form is x=A _xsin (ω _xt), y=A _ysin (ω _yt),

In order to ensure reference model track asymptotically stability, output S (t) of local linear state feedback controller being brought into gyroscope fuzzifying dynamic system modular form (3) and obtains reference model:

${\stackrel{\&CenterDot;}{q}}_m=A_{m}q+B_{m}r---\left(5\right)$

Wherein desired control matrix A _mvalue is, $A_m=\left[\begin{array}{cccc}-1& 0& -{\mathrm{\&omega;}}_x^2& 0\\ 0& -1& 0& -{\mathrm{\&omega;}}_y^2\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ Expect input matrix B _mvalue

For, $B_m=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\\ 0& 0\end{array}\right],$ Expect that input r is, $r=\left[\begin{array}{c}{A}_x{\mathrm{\&omega;}}_x\cos \left({\mathrm{\&omega;}}_{x}t\right)\\ A_y{\mathrm{\&omega;}}_y\cos \left({\mathrm{\&omega;}}_{y}t\right)\end{array}\right],$ State variable q is taken as

$q=\left[\begin{array}{c}\stackrel{\&CenterDot;}{x}\\ \stackrel{\&CenterDot;}{y}\\ x\\ y\end{array}\right]=\left[\begin{array}{c}{A}_x{\mathrm{\&omega;}}_x\cos \left({\mathrm{\&omega;}}_{x}t\right)\\ A_y{\mathrm{\&omega;}}_y\cos \left({\mathrm{\&omega;}}_{y}t\right)\\ A_x\sin \left({\mathrm{\&omega;}}_{x}t\right)\\ A_y\sin \left({\mathrm{\&omega;}}_{y}t\right)\end{array}\right].$

Due to the existence of the actual foozle of gyroscope and external environmental interference, the gating matrix A of gyroscope T-S model _iunknown with state variable q, in order to make fuzzy system track at gating matrix A _iwhen unknown, track reference model, is adjusted to the output type (4) of controller

$s\left(t\right)=\frac{{\&Sum;}_{j=1}^9{\mathrm{\&mu;}}_j\left(\mathrm{\&eta;}\right)[-{\hat{K}}_{j}q\left(t\right)+l_j\left(t\right)r\left(t\right)]}{{\mathrm{\&Sigma;}}_{j=1}^9{\mathrm{\&mu;}}_j\left(\mathrm{\&eta;}\right)},---\left(6\right)$

Wherein, for estimated matrix, ${\hat{K}}_j=\left[\begin{array}{cccc}{\hat{a}}_{11}^i-a_{11}^m& {\hat{a}}_{12}^i-a_{12}^m& {\stackrel{i}{a}}_{13}^{^}-a_{13}^m& {\hat{a}}_{14}^i-a_{14}^m\\ {\hat{a}}_{21}^i-a_{21}^m& {\hat{a}}_{22}^i-a_{22}^m& {\hat{a}}_{23}^i-a_{23}^m& {\hat{a}}_{24}^i-a_{24}^m\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ for estimating gating matrix, ${\hat{A}}_i=\left[\begin{array}{cccc}{\hat{a}}_{11}^i& {\hat{a}}_{12}^i& {\hat{a}}_{13}^i& {\hat{a}}_{14}^i\\ {\hat{a}}_{21}^i& {\hat{a}}_{22}^i& {\hat{a}}_{23}^i& {\hat{a}}_{24}^i\\ 1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

Gyroscope fuzzifying dynamic system model after adjustment is

$\stackrel{\&CenterDot;}{q}\left(t\right)=A_{m}q\left(t\right)+\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)[(A_i-A_m)q\left(t\right)+B_{i}u\left(t\right)]}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}$

In order to obtain the state variable q of gyroscope, design parameter estimator

$\stackrel{\stackrel{\&CenterDot;}{^}}{q}\left(t\right)=A_m\hat{q}\left(t\right)+\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)[({\hat{A}}_i-A_m)q\left(t\right)+B_{i}u\left(t\right)]}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}---\left(7\right)$

Wherein, for estimated state variable.

Five, according to Lyapunov function theory design adaptive control algorithm, line stabilization analysis of going forward side by side, is specially,

5-1) define Lyapunov function $V\left(t\right)=V(e,{\tilde{a}}_{1i},{\tilde{a}}_{2i})=e^T\left(t\right)\mathrm{Pe}\left(t\right)+{\mathrm{\&Sigma;}}_{i=1}^9\frac{{\tilde{a}}_{1i}^T{\tilde{a}}_{1i}}{{\mathrm{\&gamma;}}_{1i}}+{\mathrm{\&Sigma;}}_{i=1}^9\frac{{\tilde{a}}_{2i}^T{\tilde{a}}_{2i}}{{\mathrm{\&gamma;}}_{2i}}$

In formula, for track following error function, meet

$\stackrel{\&CenterDot;}{e}\left(t\right)=A_{s}e\left(t\right)+\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)(A_i-{\hat{A}}_i)q\left(t\right)}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}=A_{s}e\left(t\right)-\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right){\left[\begin{array}{cccc}{\tilde{a}}_{1i}& {\tilde{a}}_{2i}& 0& 0\end{array}\right]}^{T}q\left(t\right)}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)},---\left(8\right)$

${\stackrel{\&CenterDot;}{e}}^T\left(t\right)=e\left(t\right)A_s^T-\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)q^T\left(t\right){\left[\begin{array}{cccc}{\tilde{a}}_{1i}& {\tilde{a}}_{2i}& 0& 0\end{array}\right]}^{T}q\left(t\right)}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)},$

5-2) to Lyapunov function V (t) differentiate,

$\stackrel{\&CenterDot;}{V}\left(t\right)={\stackrel{\&CenterDot;}{e}}^T\left(t\right)\mathrm{Pe}\left(t\right)+e^T\left(t\right)P\stackrel{\&CenterDot;}{e}\left(t\right)+{\mathrm{\&Sigma;}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\&CenterDot;}{~}}{a}}_{1i}^T{\tilde{a}}_{1i}}{{\mathrm{\&gamma;}}_{1i}}+{\mathrm{\&Sigma;}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\&CenterDot;}{~}}{a}}_{2i}^T{\tilde{a}}_{2i}}{{\mathrm{\&gamma;}}_{2i}},$

(8) and (9) are substituted in (10), obtains

$\stackrel{\&CenterDot;}{V}\left(t\right)=-e^T\left(t\right)(A_s^{T}P+{\mathrm{PA}}_s)e\left(t\right)-2\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right){P_1}^{T}e\left(t\right)q^T\left(t\right){\tilde{a}}_{2i}}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}$ （11）

$-2\frac{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right){P_2}^{T}e\left(t\right)q^T\left(t\right){\tilde{a}}_{2i}}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}+{\mathrm{\&Sigma;}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\&CenterDot;}{~}}{a}}_{1i}^T{\tilde{a}}_{1i}}{{\mathrm{\&gamma;}}_{1i}}+{\mathrm{\&Sigma;}}_{i=1}^{9}2\frac{{\stackrel{\stackrel{\&CenterDot;}{~}}{a}}_{2i}^T{\tilde{a}}_{2i}}{{\mathrm{\&gamma;}}_{2i}}$

5-3) get adaptive law for

${\stackrel{\stackrel{\&CenterDot;}{~}}{a}}_i^T={\mathrm{\&gamma;}}_i\frac{{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}{{\mathrm{\&Sigma;}}_{i=1}^9{\mathrm{\&mu;}}_i\left(\mathrm{\&eta;}\right)}\left[{P_1}^T{P_2}^T\right]e\left(t\right)q^T\left(t\right)-\mathrm{\&rho;sgn}\left({\tilde{a}}_i\right)\mathrm{\&rho;}>0---\left(12\right)$

ρ＞0

Then $\stackrel{\&CenterDot;}{V}\left(t\right)=-e^T\left(t\right)e\left(t\right)-2\mathrm{\&rho;}{\mathrm{\&Sigma;}}_{i=1}^9\frac{\mathrm{sgn}\left({\tilde{a}}_{1i}\right){\tilde{a}}_{1i}}{{\mathrm{\&gamma;}}_{1i}}-2\mathrm{\&rho;}{\mathrm{\&Sigma;}}_{i=1}^9\frac{\mathrm{sgn}\left({\tilde{a}}_{2i}\right){\tilde{a}}_{2i}}{{\mathrm{\&gamma;}}_{2i}}<0.$ According to

Lyapunov stability theory, track following error and parameter estimating error asymptotically stability.

Wherein, γ _i=γ _1i=γ _2ibe adaptive gain parameter, ρ is auto-adaptive parameter, A _sstablize arbitrarily quadravalence matrix, for parameter estimating error, parameter estimating error the first row ${\hat{a}}_{1i}=\left[\begin{array}{cccc}{\hat{a}}_{11}^i& {\hat{a}}_{12}^i& {\hat{a}}_{13}^i& {\hat{a}}_{14}^i\end{array}\right],$ $a_{1i}=\left[\begin{array}{cccc}{a}_{11}^i& a_{12}^i& a_{13}^i& a_{14}^i\end{array}\right],$ Parameter estimating error second row ${\hat{a}}_{2i}=\left[\begin{array}{cccc}{\hat{a}}_{21}^i& {\hat{a}}_{22}^i& {\hat{a}}_{23}^i& {\hat{a}}_{24}^i\end{array}\right],$ $a_{2i}=\left[\begin{array}{cccc}{a}_{21}^i& a_{22}^i& a_{23}^i& a_{24}^i\end{array}\right],$ P meets $A_s^{T}P+{\mathrm{PA}}_s=-I,$ $P=\left[\begin{array}{cccc}{P}_1& P_2& P_3& P_4\end{array}\right],$ $e\left(t\right)=q\left(t\right)-\hat{q}\left(t\right)$ For track following error function, for predicted state variable.

In the emulation of the present embodiment, definition gyroscope parameter is as follows:

m＝0.57e-8kg,ω ₀＝1KHz,q ₀＝10e-6m,d _xx＝0.429e-6Nsm，

d _yy＝0.0429e-6Nsm，d _xy＝0.0429e-6Nsm，k _xx＝80.98Nm，

k _yy＝71.62Nm，k _xy＝5Nm， $k_{x^3}=3.56e6N/m,$ $k_{y^3}=3.56e6N/m,$

Ω _z＝5.0rads，ω _x＝6.71KHz,ω _y＝5.11KHz，A _x＝1，A _y＝1.2，

T-S model track following error e _t-Swith nonlinear model track following error e _nONtime domain change curve respectively as shown in Figure 3 and Figure 4, show that T-S model trajectory error can converge to zero soon, the track of gyroscope nonlinear model can follow the trail of desired trajectory, whole control system asymptotically stability.Fig. 5, Fig. 6 and Fig. 7 are respectively T-S fuzzy model partial parameters matrix A ₁, A ₄and A ₇time-domain response curve figure, result show estimates of parameters can asymptotic convergence in stable, regulating time is short.

The result display of instantiation, the gyroscope Fuzzy Adaptive Control Scheme based on T-S model of the present invention's design, controller effectively can control gyroscope nonlinear model in the uncertain situation of T-S model parameter, effectively estimates model parameter.

Below disclose the present invention with preferred embodiment, so it is not intended to limiting the invention, and all employings are equal to replacement or the technical scheme that obtains of equivalent transformation mode, all drop within protection scope of the present invention.

Claims (5)

1., based on the gyroscope Fuzzy Adaptive Control Scheme of T-S model, it is characterized in that, comprise the following steps:

1) the dimensionless nonlinear motion vector equation of gyroscope is set up; Described dimensionless nonlinear motion vector equation completes as follows,

1-1) consider the existence of foozle and non-linear spring effect, the nonlinear mathematical model of actual gyroscope can simplify and is approximately:

Wherein m is mass quality, and x, y are mass state variables in the rotated coordinate system, d _xx, d _yydiaxon ratio of damping, k _xx, k _yydiaxon spring constant, diaxon non-linear spring coefficient, d _xycoupling Damping coefficient, k _xycoupling spring coefficient, u _x, u _ythe control inputs of diaxon, Ω _zit is the input angular velocity of z-axis;

1-2) because the displacement range of mass is in sub-millimeter meter range, therefore to get reference length be 1 μm; The natural frequency of the diaxon of gyroscope is in kilohertz range, therefore to get reference frequency be 1KHz, non-dimension time t ^*=ω ₀t, by described equation (1) both sides with square ω divided by diaxon natural frequency ₀ ², reference length q ₀with mass quality m, obtain the dimensionless nonlinear motion vector equation of gyroscope

Wherein,

Q ^*represent track state;

2) on the basis of gyroscope dimensionless nonlinear motion vector equation, set up its T-S fuzzy model, and obtain gyroscope fuzzifying dynamic system model by single-point obfuscation, product inference and center average weighted anti fuzzy method;

3) design the local linear state feedback controller of the fuzzy submodel of each T-S according to parallel distribution compensation method, and obtain controller output by single-point obfuscation, product inference and center average weighted anti fuzzy method;

4) design reference model, allows gyroscope fuzzifying dynamic system model track following reference model track;

5) according to Lyapunov function theory design adaptive control algorithm, line stabilization analysis of going forward side by side; Described according to Lyapunov function theory design adaptive control algorithm, be specially,

5-1) defining Lyapunov function V (t) is:

5-2) to Lyapunov function V (t) differentiate, obtain

5-3) get adaptive law for

Then according to Lyapunov stability theory, track following error and parameter estimating error asymptotically stability,

Wherein, γ _i=γ _1i=γ _2ibe adaptive gain parameter, ρ is auto-adaptive parameter, A _sstablize arbitrarily quadravalence matrix,

Parameter estimating error parameter estimating error the first row parameter estimating error second row for estimating gating matrix four elements of the first row, for estimating gating matrix four elements of the second row, for gating matrix A _ifour elements of the first row, for gating matrix A _ifour elements of the second row, P meets p=[P ₁p ₂p ₃p ₄], for track following error function, q (t) is state variable, for predicted state variable, μ _i(η) be weighting membership function.

2. the gyroscope Fuzzy Adaptive Control Scheme based on T-S model according to claim 1, is characterized in that, described step 2) in T-S fuzzy model be made up of 9 IF-THEN rules, described rule is:

Rule i: if x is M _i1and y is M _i2and m _i3and m _i4,

Then

Described gyroscope fuzzifying dynamic system model is

Wherein A _ifor gating matrix b _ifor input matrix state variable input μ _i(η) be weighting membership function,

m _i1(x) _,m _i2(y) _, with be respectively state variable x, y, with about fuzzy set M _i1, M _i2, M _i3and M _i4membership function.

3. the gyroscope Fuzzy Adaptive Control Scheme based on T-S model according to claim 1 and 2, is characterized in that, described step 3) in local linear state feedback controller be made up of 9 IF-THEN rules, described rule is:

Rule i: if x is M _j1and y is M _j2and m _j3and m _j4,

Then S (t)=-K _j(t) * x (t)+l _j(t) * r (t) _,j=1,2 ..., 9,

Output S (t) of described local linear state feedback controller is

Wherein matrix r (t) inputs for expecting, parameter l _j(t)=1, A _mfor expecting gating matrix a _x, A _ybe respectively the amplitude of x-axis and y-axis vibration, ω _x, ω _ybe respectively the vibration frequency of diaxon, t is the time.

4. the gyroscope Fuzzy Adaptive Control Scheme based on T-S model according to claim 3, it is characterized in that, described step 4) in definition reference model refer to described step 3) output S (t) of middle local linear state feedback controller brings in gyroscope fuzzifying dynamic system modular form (3), obtains reference model:

Wherein desired control matrix A _mvalue is, expect input matrix B _mvalue is, expect that input r is taken as, state variable q is taken as,

5. the gyroscope Fuzzy Adaptive Control Scheme based on T-S model according to claim 4, is characterized in that, in output S (t) of described local linear state feedback controller, and the gating matrix A of gyroscope T-S fuzzy model _iunknown with state variable q, in order to make fuzzy system formula (3) at gating matrix A _iwhen unknown, track reference modular form (5), is adjusted to output S (t) of local linear state feedback controller

Wherein, for estimated matrix, for estimating gating matrix,

Gyroscope fuzzifying dynamic system model after adjustment is

In order to obtain the state variable q of gyroscope, design parameter estimator

Wherein, for estimated state variable.