CN106249596A - The indirect self-adaptive of gyroscope fuzzy overall situation fast terminal sliding-mode control - Google Patents

Abstract

The invention discloses the indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control of a kind of gyroscope, it is possible to achieve quickly follow the tracks of the track of upper gyroscope system at short notice.The indirect self-adaptive of the present invention fuzzy overall situation fast terminal sliding-mode control is on the one hand by the unknown in fuzzy close microthrust test system, its advantage is the mathematical models requiring no knowledge about system, can be with fuzzy close parameter uncertainty and the upper dividing value of external disturbance total amount, by upper dividing value is carried out fuzzy close, switching item serialization in sliding mode controller greatly can be reduced buffeting；On the other hand, overall situation fast terminal sliding-mode surface is chosen so that on the basis of ensureing that sliding formwork controls to stablize, make system mode reach the perfect tracking to the expectation state in the finite time specified.The application present invention can make the tracking performance of microthrust test system be greatly improved, and Parameters variation and external disturbance are had stronger robustness.

Description

The indirect self-adaptive of gyroscope fuzzy overall situation fast terminal sliding-mode control

Technical field

The present invention relates to the control method of a kind of gyroscope, the indirect self-adaptive particularly relating to a kind of gyroscope obscures Overall situation fast terminal sliding-mode control.

Background technology

Gyroscope is one of inertia device because it in any environment can independent navigation, so from occur since, Just get more and more people's extensive concerning and obtained universal application in fields such as space flight, navigation, aviation and military affairs.But produce and system There is error and easy temperature influence during making, cause the difference between element characteristic and design, thus cause gyroscope Performance reduce.It addition, gyroscope originally belongs to multi-input multi-output system and systematic parameter exists uncertain and is easily subject to The impact of external environment so that it is unsatisfactory that effect followed the trail of by gyroscope.

Traditional design of Fuzzy Controller accurate model based on microthrust test, and ignore external disturbance impact；Traditional cunning Although mould controls to make tracking error asymptotic convergence to zero, but cannot ensure at Finite-time convergence to zero.

Summary of the invention

It is an object of the invention to overcome deficiency of the prior art, it is provided that the indirect self-adaptive of a kind of gyroscope obscures Overall situation fast terminal sliding-mode control, solves gyroscope control method in prior art and cannot ensure to make in finite time Tracking error converges to the technical problem of zero.

For solving above-mentioned technical problem, the technical solution adopted in the present invention is: the indirect self-adaptive of gyroscope obscures Overall situation fast terminal sliding-mode control, comprises the steps:

1) the dimensionless kinetics equation building gyroscope is:

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

Wherein: q is the position vector of gyroscope x-axis, y-axis；U is the control input of gyroscope；D is damping matrix； K_bContain the natural frequency of two axles and the stiffness coefficient of coupling；Ω is angular speed matrix；D (t) is that systematic uncertainty is with outer Boundary disturbs；

2) reference model determining gyroscope system is:

x_m=A₁sin(ω₁T), y_m=A₂sin(ω₂t) (2)

Wherein: x_m、y_mIt is respectively reference model position vector in x-axis, y-axis；A₁、A₂It is that gyroscope is at x respectively Amplitude on axle, y-axis direction；ω₁、ω₂It is the frequency of vibration that gyroscope is given on x-axis, y-axis direction respectively；T is the time Variable；

Changing into differential equation form is:

Wherein, q_mFor x-axis, y-axis ideal position vector, as reference locus, q_m=[x_m y_m]^T；K_m=diag{ ω₁ ², ω₂ ²}；

3) building overall situation fast terminal sliding-mode surface s is:

$s=\[\begin{array}{cc}{s}_1& s_2\end{array}\]=\stackrel{\·}{e}+\mathrm{\α}e+{\mathrm{\βe}}^{p_2/p_1}---\left(3\right)$

Wherein, s₁,s₂It is the sliding-mode surface on x-axis, y-axis direction respectively；α, β are sliding-mode surface constants, and are normal number；p₁, p₂For positive odd number, p₁＞ p₂；E=q_m-q is tracking error；

4) building indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller control law u is:

$u\left(t\right)={\stackrel{\·\·}{q}}_m-\hat{f}(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{{\mathrm{de}}^{p_2/p_1}}{dt}+\mathrm{\φ}s+\hat{h}\left(s\right)---\left(4\right)$

Wherein, the output of adaptive fuzzy system is usedApproach micro- The unknown f of gyroscope system, with the output of adaptive fuzzy system Approaching sliding formwork switching control item Lsgn (s), L is fixed gain, and φ is normal number, θ_fiForVariable element, ξ isFuzzy Vector, θ_hiForVariable element, Φ isFuzzy vector, i=1,2, represent point vector on x-axis, y-axis direction.

Described indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller uses method self adaptation based on lyapunov Adjust fuzzy parameter θ_fAnd θ_h, θ_fAnd θ_hAdaptive lawWithIt is respectively as follows:

${\stackrel{\·}{\mathrm{\θ}}}_f=-r_1\mathrm{\ξ}\left(x\right)s,{\stackrel{\·}{\mathrm{\θ}}}_h=r_2\mathrm{\Φ}\left(s\right)s$

Designing its lyapunov function is:

Wherein: r₁、r₂For adaptive gain, s is sliding-mode surface function,θ_f ^*、θ_h ^*Respectively For fuzzy systemWithOptimized parameter.

Compared with prior art, the present invention is reached to provide the benefit that: use Fuzzy indirect adaptive control to go to approach The upper dividing value of the unknown, Parameter uncertainties item and external disturbance total amount in gyroscope system, advantage is to require no knowledge about to be The accurate model of system, and the switching item serialization in sliding mode controller can be substantially reduced buffeting；Use overall situation fast terminal Sliding-mode surface, solves the optimal problem of convergence time, in sliding mode design process, combines tradition sliding formwork and terminal sliding mode Advantage, in the stage of arrival, use the concept quickly arrived, make tracking error at shorter Finite-time convergence to zero.Should The tracking performance that can make microthrust test system by the present invention is greatly improved, and has stronger to Parameters variation and external disturbance Robustness.

Accompanying drawing explanation

Fig. 1 is the structured flowchart of indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control.

Fig. 2 is the microthrust test X using indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control, Y-axis tracking effect Figure.

Fig. 3 is the dynamic curve diagram of the sliding-mode surface using indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control.

Fig. 4 is the control input curve figure using indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.Following example are only used for clearly illustrating the present invention Technical scheme, and can not limit the scope of the invention with this.

The indirect self-adaptive of gyroscope fuzzy overall situation fast terminal sliding formwork controls to comprise the following steps:

One, the dimensionless kinetics equation of gyroscope is set up

According to rotate system in Newton's law, it is considered to processing and manufacturing error, then model is carried out nondimensionalization process and etc. After effect conversion, the kinetics equation of the gyroscope obtained is as follows:

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

Wherein:For gyroscope x-axis, the position vector of y-axis；Control for gyroscope inputs；For damping matrix, d_xx,d_yyIt is the damped coefficient of two axles, d_xyFor Coupling Damping coefficient； Wherein,ω₀It is the natural frequency of two axles, k_xx,k_yyIt is the rigidity of two axles Coefficient, k_xyStiffness coefficient for coupling；For angular speed matrix, Ω_zFor the angular velocity on z-axis direction；d(t) Represent systematic uncertainty and external interference, meet uncertainty and the upper bound of external interference that | d (t) |≤L, L are system.

Formula (1) can be write as common version:

$\stackrel{\·\·}{q}=f(q,t)+u+d\left(t\right)=-(D\stackrel{\·}{q}+2\mathrm{\Ω}\stackrel{\·}{q}+K_{b}q)+u+d\left(t\right)---\left(2\right)$

Wherein,

Two, the reference model of gyroscope system is determined

The preferable dynamic characteristic of gyroscope is a kind of noenergy loss, and two between centers shake without the stable sine of Dynamic Coupling Swing, can be described as follows:

x_m=A₁sin(ω₁T), y_m=A₂sin(ω₂t)

Wherein x_m、y_mIt is respectively reference model position vector in x-axis, y-axis；A₁、A₂Gyroscope respectively x-axis, Amplitude on y-axis direction；ω₁、ω₂It is the frequency of vibration that gyroscope is given on x-axis, y-axis direction respectively；T is to become the time Amount.

Changing into differential equation form is:

${\stackrel{\·\·}{q}}_m+K_m{q}_m=0---\left(3\right)$

Wherein, q_mFor x-axis, y-axis ideal position vector, q_m=[x_m y_m]^TFor reference locus, K_m=diag{ ω₁ ²,ω₂ ²}。 Three, design overall situation fast terminal sliding mode controller

Definition tracking error is:

E=q_m-q (4)

Definition overall situation fast terminal sliding-mode surface is:

$s=\[\begin{array}{cc}{s}_1& s_2\end{array}\]=\stackrel{\·}{e}+\mathrm{\α}e+{\mathrm{\βe}}^{p_2/p_1}---\left(5\right)$

In formula, s₁,s₂It is the sliding-mode surface on x-axis, y-axis direction respectively；α, β are sliding-mode surface constants, and are normal number, p₁, p₂(p₁>p₂) it is positive odd number.If sliding formwork controls to be in perfect condition, thenThen

$\begin{array}{c}\stackrel{\·}{s}=\stackrel{\·\·}{e}+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}={\stackrel{\·\·}{q}}_m-\stackrel{\·\·}{q}+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}\\ ={\stackrel{\·\·}{q}}_m+(D\stackrel{\·}{q}+2\mathrm{\Ω}\stackrel{\·}{q}+K_{b}q)-u-d\left(t\right)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}\\ ={\stackrel{\·\·}{q}}_m-f-u-d\left(t\right)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}\end{array}---\left(6\right)$

Do not consider uncertain and additional interference d (t), obtain Equivalent control law

$u_{eq}\left(t\right)=\[{\stackrel{\·\·}{q}}_m-f(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}\]---\left(7\right)$

If in view of uncertain and additional interference d (t), then design control law is

$u=u_{eq}+u_{sw}={\stackrel{\·\·}{q}}_m-f(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{d\left(e^{p_2/p_1}\right)}{dt}+\mathrm{\φ}s+u_{sw}---\left(8\right)$

Wherein: u_sw=Lsgn (s), then

$\begin{array}{c}s\left(t\right)\·\stackrel{\·}{s}\left(t\right)=s\·(-d(t)-\mathrm{\φ}s-u_{sw})\\ =-s\·d\left(t\right)-{\mathrm{\φs}}^2-L\mathrm{sgn}\left(s\right)\·s\\ \≤-{\mathrm{\φs}}^2\≤0\end{array}---\left(9\right)$

Four, design indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller

Use the output of adaptive fuzzy systemApproach the unknown f, with the output of adaptive fuzzy systemApproach and cut Change control item Lsgn (s), then control law becomes

$u\left(t\right)={\stackrel{\·\·}{q}}_m-\hat{f}(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{{\mathrm{de}}^{p_2/p_1}}{dt}+\mathrm{\φ}s+\hat{h}\left(s\right)---\left(10\right)$

$\hat{f}\left(x\right|{\mathrm{\θ}}_f)={\left[\begin{array}{cc}{\hat{f}}_1& {\hat{f}}_2\end{array}\right]}^T={\left[\begin{array}{cc}{{\mathrm{\θ}}_{f1}}^T\mathrm{\ξ}\left(x_1\right)& {{\mathrm{\θ}}_{f2}}^T\mathrm{\ξ}\left(x_2\right)\end{array}\right]}^T---\left(11\right)$

$\hat{h}\left(s\right|{\mathrm{\θ}}_h)={\left[\begin{array}{cc}{\hat{h}}_1& {\hat{h}}_2\end{array}\right]}^T={\left[\begin{array}{cc}{{\mathrm{\θ}}_{f1}}^T\mathrm{\Φ}\left(s_1\right)& {{\mathrm{\θ}}_{f2}}^T\mathrm{\Φ}\left(s_2\right)\end{array}\right]}^T---\left(12\right)$

Wherein, θ_fiForVariable element, ξ isFuzzy vector, θ_hiForVariable element, Φ isMould Stick with paste vectorial, i=1,2, represent point vector on x-axis, y-axis direction.

IfAmbiguity in definition system optimal parameter is:

${{\mathrm{\θ}}_f}^{*}=\arg \underset{{\mathrm{\θ}}_f\∈{\mathrm{\Ω}}_f}{min}\[sup|\hat{f}\left(x\right|{\mathrm{\θ}}_f)-f(x,t)|\]---\left(13\right)$

${{\mathrm{\θ}}_h}^{*}=\arg \underset{{\mathrm{\θ}}_h\∈{\mathrm{\Ω}}_h}{min}\[sup|\hat{h}\left(s\right|{\mathrm{\θ}}_h)-\hat{h}\left(s\right|{{\mathrm{\θ}}_h}^{*})|\]---\left(14\right)$

Wherein Ω_fAnd Ω_hIt is respectively θ_fAnd θ_hSet.

Definition minimum approximation error is:

$\mathrm{\ω}=f(x_i,t)-\hat{f}\left(x_i\right|{{\mathrm{\θ}}^{*}}_{fi})---\left(15\right)$

Indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller output is inputted as the control of gyroscope system, Formula (15) substitutes into formula (6) and obtains

$\begin{array}{c}\stackrel{\·}{s}={\stackrel{\·\·}{q}}_m-f(x,t)-u\left(t\right)-d(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{{\mathrm{de}}^{p_2/p_1}}{dt}\\ =-\[f(x,t)-\hat{f}(x,t)\]-\hat{h}\left(s\right|{\mathrm{\θ}}_h)-d(x,t)-\mathrm{\φ}s\\ =-\[\hat{f}\left(x\right|{{\mathrm{\θ}}_f}^{*})-\hat{f}(x,t)\]-\hat{h}\left(s\right|{\mathrm{\θ}}_h)-d(x,t)-\mathrm{\φ}s+\hat{h}\left(s\right|{{\mathrm{\θ}}_h}^{*})-\hat{h}\left(s\right|{{\mathrm{\θ}}_h}^{*})-\mathrm{\ω}\\ =-{{\widetilde{\mathrm{\θ}}}_f}^T\mathrm{\ξ}\left(x\right)+{{\widetilde{\mathrm{\θ}}}_h}^T\mathrm{\Φ}\left(s\right)-\mathrm{\ω}-d(x,t)-\mathrm{\φ}s-\hat{h}\left(s\right|{{\mathrm{\θ}}_h}^{*})\end{array}---\left(16\right)$

Wherein

Five, based on lyapunov function, the adaptive law of design variable element, make on the track following of gyroscope system The track of reference model, it is ensured that the global stability of system.

Definition lyapunov function

$V=\frac{1}{2}(s^2+\frac{1}{r_1}{{\widetilde{\mathrm{\θ}}}_f}^T{\widetilde{\mathrm{\θ}}}_f+\frac{1}{r_2}{{\widetilde{\mathrm{\θ}}}_h}^T{\widetilde{\mathrm{\θ}}}_h)---\left(17\right)$

Wherein, wherein r₁、r₂For adaptive gain, for normal number.

Its derivation is obtained:

$\begin{array}{c}\stackrel{\·}{V}=s\stackrel{\·}{s}+\frac{1}{r_1}{{\widetilde{\mathrm{\θ}}}_f}^T{\stackrel{\·}{\mathrm{\θ}}}_f+\frac{1}{r_2}{{\widetilde{\mathrm{\θ}}}_h}^T{\stackrel{\·}{\mathrm{\θ}}}_h\\ =s\[-{{\widetilde{\mathrm{\θ}}}_f}^T\mathrm{\ξ}\left(x\right)+{{\widetilde{\mathrm{\θ}}}_h}^T\mathrm{\Φ}\left(s\right)-\mathrm{\ω}-d(x,t)-\mathrm{\φ}s-\hat{h}\left(s\right|{{\mathrm{\θ}}_h}^{*})\]+\frac{1}{r_1}{{\widetilde{\mathrm{\θ}}}_f}^T{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_f+\frac{1}{r_2}{{\widetilde{\mathrm{\θ}}}_h}^T{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_h\\ =\frac{1}{r_1}{{\widetilde{\mathrm{\θ}}}_f}^T(-r_{1}s\mathrm{\ξ}(x)+{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_f)+\frac{1}{r_2}{{\widetilde{\mathrm{\θ}}}_h}^T(-r_{2}s\mathrm{\Φ}(s)+{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_h)-s\mathrm{\ω}-{\mathrm{\φs}}^2-L\left|s\right|\\ \≤\frac{1}{r_1}{{\widetilde{\mathrm{\θ}}}_f}^T(-r_{1}s\mathrm{\ξ}(x)+{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_f)+\frac{1}{r_2}{{\widetilde{\mathrm{\θ}}}_h}^T(-r_{2}s\mathrm{\Φ}(s)+{\stackrel{\·}{\widetilde{\mathrm{\θ}}}}_h)-s\mathrm{\ω}-{\mathrm{\φs}}^2\end{array}---\left(18\right)$

Wherein:

For ensureingMaking above formula Section 1 and Section 2 is zero, then can design θ_fAnd θ_hAdaptive lawWithPoint It is not:

${\stackrel{\·}{\mathrm{\θ}}}_f=-r_1\mathrm{\ξ}\left(x\right)s---\left(19\right)$

${\stackrel{\·}{\mathrm{\θ}}}_h=r_2\mathrm{\Φ}\left(s\right)s---\left(20\right)$

BecauseEnsure that the global stability of system, and make system tracking error at Finite-time convergence to zero.

Six, Computer Simulation

In order to show the indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control that the present invention proposes more intuitively Superiority, at MATLAB/SIMULINK, the present invention is carried out computer simulation experiment.

With reference to existing document, the parameter choosing gyroscope is:

M=1.8 × 10^-7Kg, d_xx=1.8 × 10^-6N s/m, d_yy=1.8 × 10^-6N s/m,

d_xy=3.6 × 10^-7N s/m, k_xx=63.955N/m, k_yy=95.92N/m, k_xy=12.779N/m.

Assuming that unknown input angular velocity is Ω_z=100rad/s.First microthrust test parameter carries out nondimensionalization process.Right In oscillating micro gyroscope, mass of foundation block is chosen along the vibration amplitude of drive shaft and sensitive axis in submicron rank, reference displacement For q₀=1 μm is relatively reasonable.Because the operation frequency of microthrust test is in kHz scope, so selected characteristic frequency is ω₀=1kHz.? Non-dimensionalized parameter to MEMS gyroscope is:

ω_x ²=355.3, ω_y ²=532.9, ω_xy=70.99, d_xx=0.01

d_yy=0.01, d_xy=0.002, Ω_z=0.1

For ξ (x_i), take following 5 kinds of membership functions:

μ_NM(x_i)=exp [-((x_i+π/6)/(π/24))²],

μ_NS(x_i)=exp [-((x_i+π/12)/(π/24))²],

μ_Z(x_i)=exp [-(x_i/(π/24))²],

μ_PS(x_i)=exp [-((x_i-π/12)/(π/24))²],

μ_PM(x_i)=exp [-((x_i-π/6)/(π/24))²],

The fuzzy rule being then used for approaching f has 25.

The membership function of definition sliding-mode surface s is μ_NM(s)=1/ (1+exp (5 (s+3))), μ_ZO(s)=exp (-s²), μ_PM (s)=1/ (1+exp (5 (s-3))).

The original state of controlled device takes [0 00 0], and reference locus is x_m=sin (4.17t), y_m=1.2sin (5.11t), overall situation fast terminal sliding-mode surface parameter takes p₁=5, p₂=3, α=25, β=5；Adaptive gain r₁=50, r₂= 35000.In overall situation fast terminal sliding formwork control law formula (8), take fixed gain L=50.

Indirect self-adaptive fuzzy overall situation fast terminal sliding formwork is used to control simulation figure as shown in Figure 2, Figure 3, Figure 4.

Fig. 2 is the aircraft pursuit course of gyroscope X, Y-axis, as can be seen from the figure uses the fuzzy overall situation of indirect self-adaptive quickly TSM control method, the X of gyroscope, Y-axis track can preferably follow the trail of reference locus.

Fig. 3 is the dynamic curve diagram of sliding-mode surface, it can be seen that in finite time, sliding-mode surface rapidly converges to zero, shows system Arrive diverter surface at short notice and be maintained on sliding-mode surface slip.

Fig. 4 is the control input u of gyroscope_x、u_yCurve chart, it can be seen that use the fuzzy overall situation of indirect self-adaptive quickly Switching item in controller is approached by TSM control method, by switching item serialization, thus can effectively reduce Buffet.

The above, be only presently preferred embodiments of the present invention, and the present invention not makees the biggest any restriction, Although the present invention is disclosed above with preferred embodiments, but and be not used to limit the present invention, any those skilled in the art, In the range of without departing from technical solution of the present invention, when the technology contents of available the disclosure above makes a little change or is modified to With change equivalent example, as long as be for depart from technical scheme content, according to the present invention technical spirit to Any simple modification, equivalent variations and the decoration that upper embodiment is made, all still falls within the range of technical solution of the present invention.

Claims (2)

1. the indirect self-adaptive fuzzy overall situation fast terminal sliding-mode control of gyroscope, it is characterised in that: include walking as follows Rapid:

1) the dimensionless kinetics equation building gyroscope is:

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

Wherein: q is the position vector of gyroscope x-axis, y-axis；U is the control input of gyroscope；D is damping matrix；K_bComprise The natural frequency of two axles and the stiffness coefficient of coupling；Ω is angular speed matrix；D (t) is systematic uncertainty and external interference；

2) reference model determining gyroscope system is:

x_m=A₁sin(ω₁T), y_m=A₂sin(ω₂t) (2)

Wherein: x_m、y_mIt is respectively reference model position vector in x-axis, y-axis；A₁、A₂It is that gyroscope is in x-axis, y-axis respectively Amplitude on direction；ω₁、ω₂It is the frequency of vibration that gyroscope is given on x-axis, y-axis direction respectively；T is time variable；

Changing into differential equation form is:

Wherein, q_mFor x-axis, y-axis ideal position vector, as reference locus, q_m=[x_m y_m]^T；K_m=diag{ ω₁ ²,ω₂ ²}；

3) building overall situation fast terminal sliding-mode surface s is:

$s=\[\begin{array}{cc}{s}_1& s_2\end{array}\]=\stackrel{\·}{e}+\mathrm{\α}e+{\mathrm{\βe}}^{p_2/p_1}---\left(3\right)$

Wherein, s₁,s₂It is the sliding-mode surface on x-axis, y-axis direction respectively；α, β are sliding-mode surface constants, and are normal number；p₁,p₂For Positive odd number, p₁＞ p₂；E=q_m-q is tracking error；

4) the control law u building indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller is:

$u\left(t\right)={\stackrel{\·\·}{q}}_m-\hat{f}(x,t)+\mathrm{\α}\stackrel{\·}{e}+\mathrm{\β}\frac{{\mathrm{de}}^{p_2/p_1}}{dt}+\mathrm{\φ}s+\hat{h}\left(s\right)---\left(4\right)$

Wherein, the output of adaptive fuzzy system is usedApproach gyroscope The unknown f of system, with the output of adaptive fuzzy systemApproach cunning Cross cutting changes control item Lsgn (s), and L is fixed gain, and φ is normal number, θ_fiForVariable element, ξ isFuzzy vector, θ_hiForVariable element, Φ isFuzzy vector, i=1,2, represent point vector on x-axis, y-axis direction.

The indirect self-adaptive of gyroscope the most according to claim 1 fuzzy overall situation fast terminal sliding-mode control, its It is characterised by: described indirect self-adaptive fuzzy overall situation fast terminal sliding mode controller uses method self adaptation based on lyapunov Adjust fuzzy parameter θ_fAnd θ_h, θ_fAnd θ_hAdaptive lawWithIt is respectively as follows:

${\stackrel{\·}{\mathrm{\θ}}}_f=-r_1\mathrm{\ξ}\left(x\right)s,{\stackrel{\·}{\mathrm{\θ}}}_h=r_2\mathrm{\Φ}\left(s\right)s$

Designing its lyapunov function is:

Wherein: r₁、r₂For adaptive gain, s is sliding-mode surface function,θ_f ^*、θ_h ^*It is respectively mould Paste systemWithOptimized parameter.