CN102411302A - Control method of MEMS (micro-electromechanical system) micro-gyroscope based on direct self-adaptive fuzzy control - Google Patents

Abstract

The invention discloses a control method of an MEMS (micro-electromechanical system) micro-gyroscope based on direct self-adaptive fuzzy control. A control system of the MEMS micro-gyroscope based on direct self-adaptive fuzzy control comprises a direct self-adaptive fuzzy controller, and is characterized in that: the direct self-adaptive fuzzy controller comprises a basic fuzzy controller which is built by a fuzzy logic system and is used for approximating an ideal controller of the MEMS micro-gyroscope, and a D (digital) controller which is used for ensuring that the state of a gyroscope system is bounded. In the control system of the MEMS micro-gyroscope based on direct self-adaptive fuzzy control, the direct self-adaptive fuzzy control method is applied to gyroscope control. The knowledge and the experience of experts can be combined with the fuzzy controller, and parameters in the fuzzy system are self-adaptively adjusted by a Lyapunov-based method, thereby the stability of the fuzzy control system is ensured. The fuzzy controller can be widely applied to the MEMS gyroscope control to improve the stability and the reliability of the system, and has great value in use in industry.

Description

MEMS gyroscope control method based on the direct adaptive fuzzy control

Technical field

The present invention relates to the gyrostatic control system of MEMS, be specifically related to the application of direct adaptive fuzzy control method on the MEMS gyroscope.

Background technology

The MEMS gyroscope is the sensor of measured angular speed the most frequently used in the plurality of applications field, such as Navigation, Guide and Controlling stability.The MEMS gyroscope is to utilize Coriolis force (that is: Coriolis force) that the energy on the axle is transferred to the device on another; Traditional operator scheme lacks the driving gyroscope from the known oscillating motion of a pattern to; And detected Coriolis acceleration is coupled to the perceptual model of vibration; Vibration is vertical with drive pattern, and the response of vibration perceptual model provides the information about practical angular velocity.Because the error in the manufacturing process exists and the influence of environment temperature, causes the difference between original paper characteristic and the design, causes existing the stiffness coefficient and the ratio of damping of coupling, has reduced the sensitivity and the precision of gyroscope.In addition, itself belongs to multi-input multi-output system gyroscope, has the fluctuation that causes to systematic parameter of uncertainty and the external interference of parameter, and the compensation foozle becomes the subject matter that gyroscope is controlled with measured angular speed.And traditional control method concentrates in the control to driving shaft oscillation amplitude and frequency stabilization and diaxon frequency matching, exists not consider the parameter change, and environmental change makes a very bad impression, and can not solve problems such as zero angle speed output.Therefore, advanced control technology is asked to be applied in the control of MEMS gyroscope

Fuzzy control system does not need the mathematical model of controlled device, it with the people to the control experience of controlled device serve as according to and therefore CONTROLLER DESIGN is applicable to that structure confirms unknown parameters or uncertain system.The outstanding advantage of fuzzy control is can be with comparalive ease people's control experience to be incorporated in the controller, if but lack such control experience, be difficult to design high-caliber fuzzy controller.And, because fuzzy controller has adopted the IF-THEN control law, be not easy to the study and the adjustment of controlled variable, and be difficult to guarantee the stability of control system.

Adaptive Fuzzy Control is meant the fuzzy logic system with adaptive learning algorithm, and its learning algorithm is to rely on data message to adjust the parameter of fuzzy logic system, and can guarantee the stability of control system.Compare with traditional adaptive control system, the superiority of Adaptive Fuzzy Control is the language property fuzzy message that it can utilize operating personnel to provide, and traditional adaptive control then can not.This point is even more important to the gyroscope system with height uncertain factor.

At present, Adaptive Fuzzy Control is not applied in the control system of gyroscope as yet.

Summary of the invention

The present invention overcomes the defective that the gyrostatic control system of existing MEMS exists, and a kind of MEMS gyroscope control method based on the direct adaptive fuzzy control is provided.

The object of the invention and solve its technical matters and adopt following technical scheme to realize.The MEMS gyroscope differential equation does

$\stackrel{\·\·}{q}=-(D+2\mathrm{\Ω})\stackrel{\·}{q}-k_{b}q+u---\left(1\right)$

Reference model does

${\stackrel{\·\·}{q}}_m=-k_m{q}_m---\left(2\right)$

If parameter D, Ω, k _bKnown, controller can be designed to

$u^{*}=(D+2\mathrm{\Ω})\stackrel{\·}{q}+k_{b}q+{\stackrel{\·\·}{q}}_m+k^{T}e---\left(3\right)$

Can make $\stackrel{\·\·}{e}+k_1\stackrel{\·}{e}+k_{2}e=0,$ Wherein $e={(e,\stackrel{\·}{e})}^T.$ If select suitable parameters vector k=(k ₂, k ₁) ^TValue can make polynomial expression h (s)=s ²+ k ₁S+k ₂Root on a left side half-open plane, then $\underset{t\→\∞}{\mathrm{Lim}}e\left(t\right)=0,$ Be that control task is accomplished.

Work as D, Ω, k _bWhen unknown, controller (3) can't be used, and therefore needs fuzzy logic system construction direct adaptive fuzzy controller.The fuzzy controller of design is made up of two parts: first is basic fuzzy controller u _c(x| θ) approaches u with it ^*Second portion is D controller u _d(x), guarantee the state bounded of gyroscope system with it.

Be u=u _c(x| θ)+u _d(x) (4)

Wherein basic fuzzy controller $u_c\left(x\right|\mathrm{\θ})=\underset{i}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\θ}}_i{\mathrm{\ξ}}_i\left(x\right)={\mathrm{\θ}}^T\mathrm{\ξ}\left(x\right),$ ξ (x) is fuzzy basis function.

D controller u _d(x)=k _dSgn (e ^TPb _c), (5)

K in the formula _d＞0.

Definition optimized parameter vector:

${\mathrm{\θ}}^{*}=\arg \underset{\underset{\mathrm{\θ}\∈R^{i=1}}{\overset{n}{\mathrm{\Π}}}{m}_i}{\min }\left[\underset{x\∈R^n}{\sup }\right|u_c\left(x\right|\mathrm{\θ})-u^{*}\left|\right]---\left(6\right)$

The least confusion approximate error:

ω＝u _c(x|θ ^*)-u ^* (7)

Design Lyapunov function does $V=\frac{1}{2}{e}^T\mathrm{Pe}+\frac{1}{2\mathrm{\γ}}{\mathrm{\Φ}}^T\mathrm{\Φ},$

The Lyapunov function to the derivative of time is:

$V=-\frac{1}{2}{e}^T\mathrm{Qe}+\frac{1}{\mathrm{\γ}}{({\mathrm{\θ}}^{*}-\mathrm{\θ})}^T[{\mathrm{\γ\; e}}^{T}P{b}_c\mathrm{\ξ}\left(x\right)-\mathrm{\θ}]-e^{T}P{b}_c{u}_d\left(x\right)-e^{T}P{b}_c\mathrm{\ω},$ In order to guarantee $\stackrel{\·}{V}\≤0,$ Get $\stackrel{\·}{\mathrm{\θ}}={\mathrm{\γ\; e}}^{T}P{b}_c\mathrm{\ξ}\left(x\right)=\mathrm{\γ}({\mathrm{Ep}}_{12}+\stackrel{\·}{e}{p}_{22})\mathrm{\ξ}\left(x\right)$ Be the adaptive law of system, γ in the formula＞0 is a law of learning.

By technique scheme, the gyrostatic control system of MEMS that the present invention is based on the direct adaptive fuzzy control has advantage at least:

1. adopting the direct adaptive fuzzy controller that gyroscope system is controlled, is to utilize the advantage of fuzzy controller and the combination of adaptive control advantage to design.This controller can directly utilize fuzzy control rule, and the parameter of self-adaptation adjustment fuzzy controller reduces the influence to systematic error of tracking error and external interference, thereby assurance MEMS gyroscope can be worked normally.

2. compare with traditional fuzzy controller, the direct adaptive fuzzy controller can self-adaptation the parameter of adjustment Fuzzy control system, guaranteed the progressive stability of closed-loop system, and this fuzzy controller has higher robustness.

3. this control system has adopted monitoring controller, can guarantee the state bounded of system.

In sum, the MEMS gyroscope control system based on the direct adaptive fuzzy control of the present invention's design is used the direct adaptive fuzzy control method in gyroscope control.It can be attached to the expertise experience in the fuzzy controller, adopts based on the parameter in the method self-adaptation adjustment fuzzy system of Lyapunov, thus the stability and the accuracy of assurance gyroscope system.This fuzzy controller can be widely used in the control of MEMS gyroscope, and to improve the stability and the reliability of system, it has the value on the industry.

Description of drawings

Fig. 1 is the principle assumption diagram of MEMS gyroscope of the present invention;

Fig. 2 is the The general frame that the present invention is based on the MEMS gyroscope control method of direct adaptive fuzzy control;

Fig. 3 and Fig. 4 are basic fuzzy controller u _cThe aircraft pursuit course of (x| θ);

Fig. 5 and Fig. 6 are basic fuzzy controller u _cThe tracking error of (x| θ);

Fig. 7 and Fig. 8 are controller u=u _c(x| θ)+u _d(x) aircraft pursuit course;

Fig. 9 and Figure 10 are controller u=u _c(x| θ)+u _d(x) tracking error;

Figure 11 and Figure 12 are controller u=u _c(x| θ)+u _d(x) control input curve;

Figure 13 and Figure 14 are controller u=u _c(x| θ)+u _d(x) sliding-mode surface curve.

Embodiment

Following specific embodiments of the invention is described in further detail.

1.MEMS gyroscope kinetics equation

The little gyrotron of MEMS generally comprises three ingredients: by the mass that resilient material supported, and electrostatic drive and sensing apparatus.Static driven circuit major function is the constant of amplitude when driving and keeping little gyrotron vibration; Sensing circuit is used for the position and the speed of perceived quality piece.Gyroscope can be reduced to one has a vibration-damping system by what mass and spring constituted.Fig. 1 has shown little gyrotron model of under cartesian coordinate system, simplifying.As far as the MEMS gyroscope, can think that mass is limited in the x-y plane, to move, and can not move along the Z axle.In fact, because the existence of manufacturing defect and mismachining tolerance can cause the additional dynamic coupling of x axle and y axle, like the stiffness coefficient and the ratio of damping of coupling.Consider foozle, the lumped parameter mathematical model of actual gyroscope is:

$m\stackrel{\·\·}{x}+d_{\mathrm{xx}}\stackrel{\·}{x}+d_{\mathrm{xy}}\stackrel{\·}{y}+k_{\mathrm{xx}}x+k_{\mathrm{xy}}y={\mathrm{\τ}}_x+2m{\mathrm{\Ω}}_z\stackrel{\·}{y}$ (1)

$m\stackrel{\·\·}{y}+d_{\mathrm{xy}}\stackrel{\·}{x}+d_{\mathrm{yy}}\stackrel{\·}{y}+k_{\mathrm{xy}}x+k_{\mathrm{yy}}y={\mathrm{\τ}}_y-2m{\mathrm{\Ω}}_z\stackrel{\·}{x}$

M is the quality of mass, and x, y are the coordinate of mass in rotation system, d _Xx, d _YyBe respectively the ratio of damping of x axle and y axle, k _Xx, k _YyBe respectively the spring constant of x axle and y axle, d _Xy, k _XyBe respectively ratio of damping and the spring constant of coupling of coupling, close and be called quadrature error, τ _x, τ _yBe the control input of diaxon, It is Coriolis force.

The non-guiding principle of model quantizes very valuable when design analysis, and when having big time frame difference, non-guiding principle quantizes numerical simulation is realized easily.Because non-guiding principle amount time t ^*=w ₀T, the both sides of formula (1) are together divided by reference mass m, reference length q ₀, and the resonant frequency of diaxon square

MEMS gyroscope model can be rewritten as:

$\frac{\stackrel{\&CenterDot;\&CenterDot;}{q}}{{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">q</figure-callout>}}_0}+\frac{D}{{\mathrm{mw}}_0}\frac{\stackrel{\&CenterDot;}{q}}{{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">q</figure-callout>}}_0}+\frac{K_a}{{{\mathrm{<figure-callout\; id="0"\; label="mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">mw</figure-callout>}}_0}^2}\frac{\mathrm{<figure-callout\; id="0"\; label="q\; q"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">q</figure-callout>}}{q_{}}=\frac{u}{{{\mathrm{<figure-callout\; id="0"\; label="mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">mw</figure-callout>}}_0}^2{q}_0}-2\frac{\mathrm{\&Omega;}}{w_0}\frac{\stackrel{\&CenterDot;}{q}}{q_0}---\left(2\right)$

Here $q=\left[\begin{array}{c}x\\ y\end{array}\right],$ $u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right],$ $D=\left[\begin{array}{cc}{d}_{\mathrm{Xx}}& d_{\mathrm{Xy}}\\ d_{\mathrm{Xy}}& d_{\mathrm{Yy}}\end{array}\right],$ $K_a=\left[\begin{array}{cc}{k}_{\mathrm{Xx}}& k_{\mathrm{Xy}}\\ k_{\mathrm{Xy}}& k_{\mathrm{Yy}}\end{array}\right]$

It is following to define new parameter:

$q^{*}=\frac{q}{q_0},$ $D^{*}=\frac{D}{{\mathrm{<figure-callout\; id="0"\; label="mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">mw</figure-callout>}}_0},$ ${\mathrm{\&Omega;}}^{*}=\frac{\mathrm{\&Omega;}}{{\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">w</figure-callout>}}_0},$ ${u_x}^{*}=\frac{u_x}{{{\mathrm{<figure-callout\; id="0"\; label="mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">mw</figure-callout>}}_0}^2{q}_0},$ ${u_y}^{*}=\frac{u_{\mathrm{<figure-callout\; id="0"\; label="y\; mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">y</figure-callout>}}}{{{\mathrm{mw}}_{}}^{}}$

${w_x}^2=\frac{k_{\mathrm{xx}}}{{{\mathrm{<figure-callout\; id="0"\; label="mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">mw</figure-callout>}}_0}^2},$ ${w_y}^2=\frac{{\mathrm{<figure-callout\; id="0"\; label="k\; yy\; mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathrm{yy}}}{{{\mathrm{mw}}_{}}^{}},$ $w_{\mathrm{xy}}=\frac{{\mathrm{<figure-callout\; id="0"\; label="k\; xy\; mw"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathrm{xy}}}{{{\mathrm{mw}}_{}}^{}}$

The difference of ignoring symbolic representation, the non-guiding principle quantitative model of MEMS gyroscope can be written as

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

$q=\left[\begin{array}{c}x\\ y\end{array}\right],$ $u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{cc}0& -{\mathrm{\&Omega;}}_z\\ {\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="111107145806.png,111107145851.png"\; state="\{\{state\}\}">z</figure-callout>}}& 0\end{array}\right],$ $D=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],$ $K_b=\left[\begin{array}{cc}{w_x}^2& w_{\mathrm{xy}}\\ w_{\mathrm{xy}}& {w_y}^2\end{array}\right]$

2. direct adaptive The Design of Fuzzy Logic Controller

The MEMS gyroscope differential equation does

$\stackrel{\&CenterDot;\&CenterDot;}{q}=-(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}-k_{b}q+u---(3-1)$

Reference model does

${\stackrel{\&CenterDot;\&CenterDot;}{q}}_m=-k_m{q}_m---(3-2)$

If parameter D, Ω, k _bKnown, controller can be designed to

$u^{*}=(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+k_{b}q+{\stackrel{\&CenterDot;\&CenterDot;}{q}}_m+k^{T}e---(3-3)$

Can make $\stackrel{\&CenterDot;\&CenterDot;}{e}+k_1\stackrel{\&CenterDot;}{e}+k_{2}e=0,$ Wherein $e={(e,\stackrel{\&CenterDot;}{e})}^T.$ If select suitable parameters vector k=(k ₂, k ₁) ^TValue can make polynomial expression h (s)=s ²+ k ₁S+k ₂Root on a left side half-open plane, then $\underset{t\&RightArrow;\&infin;}{\mathrm{Lim}}e\left(t\right)=0,$ Be that control task is accomplished.

Work as D, Ω, k _bWhen unknown, controller (3-3) can't be used, and therefore needs fuzzy logic system construction direct adaptive fuzzy controller.The fuzzy controller of design is made up of two parts: first is basic fuzzy controller u _c(x| θ) approaches u with it ^*Second portion is D controller u _d(x), guarantee the state bounded of system with it.

Promptly

u＝u _c(x|θ)+u _d(x) (3-4)

Wherein basic fuzzy controller $u_c\left(x\right|\mathrm{\&theta;})=\underset{i}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_i{\mathrm{\&xi;}}_i\left(x\right)={\mathrm{\&theta;}}^T\mathrm{\&xi;}\left(x\right),$ ξ (x) is fuzzy basis function.

The D controller

u _d(x)＝k _dsgn(e ^TPb _c)，k _d＞0 (3-5)

Make e=q _m-q,

Then can obtain:

$\stackrel{\&CenterDot;\&CenterDot;}{e}={\stackrel{\&CenterDot;\&CenterDot;}{q}}_m-\stackrel{\&CenterDot;\&CenterDot;}{q}={\stackrel{\&CenterDot;\&CenterDot;}{q}}_m+(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+k_{b}q-u$ (3-6)

$={\stackrel{\&CenterDot;\&CenterDot;}{q}}_m+(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}+k_{b}q-u_c\left(x\right|\mathrm{\&theta;})-u_d\left(x\right)$

Formula (3-5) substitution is obtained:

$\stackrel{\&CenterDot;\&CenterDot;}{e}=-K^{T}e+u^{*}-u_c\left(x\right|\mathrm{\&theta;})-u_c\left(x\right)---(3-7)$

Or be equivalent to

$\stackrel{\&CenterDot;}{e}=\mathrm{\&Lambda;e}+b_c[u^{*}-u_c\left(x\right|\mathrm{\&theta;})-u_d\left(x\right)]---(3-8)$

In the formula: $\mathrm{\&Lambda;}=\left[\begin{array}{cc}0& 1\\ -k_2& -{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111107145923.png,111107150004.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\end{array}\right],$ $b_c=\left[\begin{array}{c}0\\ 1\end{array}\right].$

Because Λ is stable matrix, promptly | sI-Λ |=s ²+ k ₁S+k ₂For stable, therefore certain positive definite symmetric matrices P that has unique 2 * 2 satisfies the Lyapunov equation

Λ ^TP+PΛ＝-Q (3-9)

In the formula $P=\left[\begin{array}{cc}{p}_{11}& p_{12}\\ p_{21}& {\mathrm{<figure-callout\; id="22"\; label="p"\; filenames="111107145806.png"\; state="\{\{state\}\}">p</figure-callout>}}_{22}\end{array}\right],$ Q is 2 * 2 positive definite matrixes arbitrarily.

Provide the adaptive law of parameter θ below.

Definition optimized parameter vector:

${\mathrm{\&theta;}}^{*}=\arg \underset{\underset{\mathrm{\&theta;}\&Element;R^{i=1}}{\overset{n}{\mathrm{\&Pi;}}}{m}_i}{\min }\left[\underset{x\&Element;R^n}{\sup }\right|u_c\left(x\right|\mathrm{\&theta;})-u^{*}\left|\right]---(3-10)$

The least confusion approximate error:

ω＝u _c(x|θ ^*)-u ^* (3-11)

Then error equation (3-8) can be rewritten as

$\stackrel{\&CenterDot;}{e}=\mathrm{\&Lambda;e}+b_c[u_x\left(x\right|{\mathrm{\&theta;}}^{*})-u_c\left(x\right|\mathrm{\&theta;})]-b_c{u}_d\left(x\right)-b_c\mathrm{\&omega;}$ (3-12)

$=\mathrm{\&Lambda;e}+b_c{({\mathrm{\&theta;}}^{*}-\mathrm{\&theta;})}^T\mathrm{\&xi;}\left(x\right)-b_c{u}_d\left(x\right)-b_c\mathrm{\&omega;}$

The adaptive law of getting parameter θ is:

$\stackrel{\&CenterDot;}{\mathrm{\&theta;}}={\mathrm{\&gamma;e}}^{T}P{b}_c\mathrm{\&xi;}\left(x\right)=\mathrm{\&gamma;}({\mathrm{ep}}_{12}+\stackrel{\&CenterDot;}{e}{p}_{22})\mathrm{\&xi;}\left(x\right)---(3-13)$

γ in the formula＞0 is a law of learning.

3. stability and convergence analysis

Getting the Lyapunov function does $V=\frac{1}{2}{e}^T\mathrm{Pe}+\frac{1}{2\mathrm{\&gamma;}}{({\mathrm{\&theta;}}^T-\mathrm{\&theta;})}^T({\mathrm{\&theta;}}^{*}-\mathrm{\&theta;})$

Make M=b _c(θ ^*-θ) ^Tξ (x)-b _cu _d(x)-b _cω, then formula (3-12) becomes

Ask V to the derivative of time, have

$\stackrel{\&CenterDot;}{V}=\frac{1}{2}{\stackrel{\&CenterDot;}{e}}^T\mathrm{Pe}+\frac{1}{2}{e}^{T}P\stackrel{\&CenterDot;}{e}-\frac{1}{\mathrm{\&gamma;}}{({\mathrm{\&theta;}}^{*}-\mathrm{\&theta;})}^T\stackrel{\&CenterDot;}{\mathrm{\&theta;}}$

$=-\frac{1}{2}{e}^T\mathrm{Qe}+\frac{1}{\mathrm{\&gamma;}}{({\mathrm{\&theta;}}^{*}-\mathrm{\&theta;})}^T[{\mathrm{\&gamma;e}}^T{\mathrm{Pb}}_c\mathrm{\&xi;}\left(x\right)-\stackrel{\&CenterDot;}{\mathrm{\&theta;}}]-e^T{\mathrm{Pb}}_c{u}_d\left(x\right)-e^T{\mathrm{Pb}}_c\mathrm{\&omega;}$

(3-13) can get based on formula

$\stackrel{\&CenterDot;}{V}==-\frac{1}{2}{e}^T\mathrm{Qe}-e^{T}P{b}_c{u}_d\left(x\right)-e^T{\mathrm{Pb}}_c\mathrm{\&omega;}\&le;-\frac{1}{2}{e}^T\mathrm{Qe}+\left|e^T{\mathrm{Pb}}_c\right|\left({\sup }_{t\&GreaterEqual;0}\right|\mathrm{\&omega;}|-k_d)$

Get k _d>=sup _T>=0| ω |, then following formula can be changed into

$\stackrel{\&CenterDot;}{V}\&le;-\frac{1}{2}{e}^T\mathrm{Qe}\&le;-{\mathrm{\&lambda;}}_{\min }\left(Q\right){\left|\right|e\left|\right|}^2\&le;0$

Use inequality: λ here _Min(Q) || s|| ²≤s ^TQs≤λ _Max(Q) || s|| ², λ in the formula _Min(Q) be the minimum real part of matrix Q eigenwert.

Because

is negative semidefinite; So can release V, e and θ are bounded.Know by Lhasa your invariant set theorem (LaSalle ' s invariant set theorem), e (t) with asymptotic convergence to zero, promptly $\underset{t\&RightArrow;\&infin;}{\mathrm{Lim}}e\left(t\right)=0.$

4. simulation study

The gyroscope model does $\stackrel{\&CenterDot;\&CenterDot;}{q}=-(D+2\mathrm{\&Omega;})\stackrel{\&CenterDot;}{q}-k_{b}q+u.$ Gyroscope selection of parameter after the non-dimensionization is following:

${\mathrm{\&omega;}}_{x^2}=355.3,$ ${\mathrm{\&omega;}}_{y^2}=532.9,$ ω _xy＝70.99.d _xx＝0.01，d _yy＝0.01，d _xy＝0.002，Ω＝0.1

Go up 6 fuzzy sets of definition in interval [3,3], be respectively:

μ _N3(x)＝1/(1+exp(5(x+2)))μ _N2(x)＝exp(-(x+1.5) ²)μ _N1(x)＝exp(-(x+0.5) ²)μ _P1(x)＝exp(-(x-0.5) ²)，μ _P2(x)＝exp(-(x-1.5) ²)，μ _P3(x)＝1/(1+exp(-5(x-2)))

System initial state is [1,0,0,0], and the initial value of each element is 0 among the θ.X axle disturbance quantity does

The Y axle does

Auto-adaptive parameter γ=300, k ₁=2, k ₂=1, $Q=\left[\begin{array}{cc}50& 0\\ 0& 50\end{array}\right],$ k _d=30.

Because the system that the uncontinuity of sgn function causes is slow excessively, the tan function of using a continuously smooth instead replaces in order to eliminate,

Be u=u _c(x| θ)+u _d(x)=θ ^Tξ (x)+k _dTanh (e ^TPb _c), define sliding-mode surface s=e this moment ^TPb _c

The result of emulation such as Fig. 3 are to shown in Figure 14.

Fig. 3～Figure 10 has compared use u _c(x| θ) and u=u _c(x| θ)+u _d(x) two kinds of tracking errors that controller is different, visible after using the D controller u=u _c(x| θ)+u _d(x) can be in the short period of time better track reference model, and effectively reduced system ambiguous approximate error and external disturbance influence to system's output error, guaranteed the robustness of Fuzzy control system.

Result by above specific embodiment shows; Under abundant input signal situation; The MEMS gyroscope direct adaptive Fuzzy control system of the present invention's design can make the tracking error vector converge to zero soon, simultaneously under the external disturbance situation; System still can well trace model, has good robustness.

Above embodiment is merely the present invention's a kind of embodiment wherein, and it describes comparatively concrete and detailed, but can not therefore be interpreted as the restriction to claim of the present invention.Should be pointed out that for the person of ordinary skill of the art under the prerequisite that does not break away from the present invention's design, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with accompanying claims.

Claims (4)

1. MEMS gyroscope control method based on the direct adaptive fuzzy control; It comprises the direct adaptive fuzzy controller, it is characterized in that: said direct adaptive fuzzy controller comprises two parts: one is the basic fuzzy controller u of fuzzy logic system construction _c(x| θ), it is used for approaching the desirable controller u of said MEMS gyroscope ^*One is D controller u _d(x), be used for guaranteeing the state bounded of said gyroscope system.

2. the MEMS gyroscope control method based on the direct adaptive fuzzy control according to claim 1 is characterized in that: said basic controller satisfies: $u_c\left(x\right|\mathrm{\&theta;})=\underset{i}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_i{\mathrm{\&xi;}}_i\left(x\right)={\mathrm{\&theta;}}^T\mathrm{\&xi;}\left(x\right),$ Wherein ξ (x) is fuzzy basis function; Auto-adaptive parameter in the formula satisfies: $\stackrel{\&CenterDot;}{\mathrm{\&theta;}}={\mathrm{\&gamma;\; e}}^{T}P{b}_c\mathrm{\&xi;}\left(x\right)=\mathrm{\&gamma;}({\mathrm{Ep}}_{12}+\stackrel{\&CenterDot;}{e}{p}_{22})\mathrm{\&xi;}\left(x\right),$ Law of learning in the formula satisfies γ＞0.

3. the MEMS gyroscope control method based on the direct adaptive fuzzy control according to claim 1 is characterized in that: said D controller satisfies: u _d(x)=k _dSgn (e ^TPb _c), k in the formula _d＞0.

4. the MEMS gyroscope control method based on the direct adaptive fuzzy control according to claim 1; It is characterized in that: said direct adaptive fuzzy controller adopts based on method self-adaptation its fuzzy logic system of adjustment of Lyapunov and the parameter in the D controller, to satisfy the control requirement of system.

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