CN104281056B - The gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound - Google Patents

Abstract

The invention discloses a kind of gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound, comprise the following steps：Set up ideal kinetics model and gyroscope kinetic model, design sliding formwork function simultaneously obtains control law based on sliding formwork function, plus feedback term and robust on the basis of this control law, using RBF neural Estimation of Upper-Bound value as robust item gain.Based on liapunov's method design parameter adaptive law and network weight adaptive law.The present invention adds feedback term in control law, the shaft vibration track following of microthrust test two and parameter Estimation speed is greatly improved, and vibration amplitude reduces；The robust learnt based on the RBF neural upper bound is added in control law, is solved because external interference is larger and the caused uncertainty buffeted and dynamic characteristic compromises, eliminate structural formula and unstructured of fluctuation, further the robustness of raising system.

Description

The gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound

Technical field

The present invention relates to a kind of gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound, belong to micro- Gyroscope control technology field.

Background technology

Micro-mechanical gyroscope (MEMS Gyroscope) is the use processed using microelectric technique and micro-processing technology To sense the inertial sensor of angular speed.It detects angular speed by the micromechanical component of a vibration being made up of silicon, because This micro-mechanical gyroscope is very easy to miniaturization and produced in batches, with cost is low and the features such as small volume.In recent years, micromechanics Gyroscope is nearly paid close attention in many applications, for example, gyroscope coordinates micro-machine acceleration transducer to be led for inertia Navigate, be used to stablize image, for wireless inertial mouse of computer etc. in digital camera.But, due to manufacturing process In inevitably mismachining tolerance and environment temperature influence, the difference between original paper characteristic and design can be caused, caused micro- There is parameter uncertainty in gyroscope, it is difficult to set up accurate mathematical modeling.Along with the external disturbance effect in working environment It can not ignore so that the trajectory track control of gyroscope is difficult to, and robustness is relatively low.The complete base of traditional control method In the nominal value parameter designing of gyroscope, and ignore the effect of quadrature error and external disturbance, although in most cases System is still stable, but tracking effect is far undesirable, this to have very big use for the controller that single environment is designed Limitation.

In terms of the domestic research for gyroscope is concentrated mainly on structure design and manufacturing technology at present, and it is above-mentioned Mechanical compensation technology and drive circuit research, seldom appearance advanced control method compensation foozle are shaken with control mass Dynamic rail mark, to reach the complete control and the measurement of angular speed to gyroscope.The typical mechanism of studies in China gyroscope is Southeast China University's instrumental science and engineering college and Southeast China University's micro inertial instrument and advanced navigation techniques key lab.

International article, which has, is applied to various advanced control methods among the control of gyroscope, typically there is adaptive It should control and sliding-mode control.On the one hand these advanced methods compensate for quadrature error caused by fabrication error, on the other hand Realize the TRAJECTORY CONTROL to gyroscope.But the robustness that Self Adaptive Control is disturbed to external world is very low, easily system is become not It is stable.

As can be seen here, existing gyroscope is using upper, it is clear that has still suffered from inconvenience and defect, and has urgently been entered one Step is improved.

The content of the invention

It is an object of the present invention to which the defect for overcoming existing gyroscope control method to exist, particularly improves micro- top There is model uncertain, Parameter Perturbation and external disturbance is larger and fluctuation is caused chattering phenomenon etc. is various dry in spiral shell instrument system In the case of disturbing, the robustness of tracking performance and whole system to ideal trajectory is learnt there is provided one kind based on the neutral net upper bound Gyroscope Robust Adaptive Control method.

What the present invention was realized using following technical scheme：

The gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound, is comprised the following steps：

(1) ideal kinetics equation is set up；

(2) the dimensionless kinetics equation of gyroscope is set up；

(3) sliding formwork function design control law is based on, is comprised the following steps：

(3-1) defines sliding formwork function s：

Wherein, c is sliding-mode surface parameter, and e is tracking error；

(3-2) is organized into the form with parameter error vector to sliding formwork function derivation：

Wherein,

(3-3) design control lawFor：

Wherein, K_sWithIt is constant square Battle array, K_sFor linear feedback gain,It is θ^*Estimate,For the upper bound of external interference,

u_s1=-K_sS is feedback term,

For robust；

(4) robust that design is learnt based on the RBF neural upper bound, be specially：Disturbed to external world with RBF neural The upper boundLearnt, the output of RBF neural is the upper bound of external interferenceEstimate

Wherein, W is the network weight of RBF neural,For optimal network weights W^*Estimate, x be RBF nerve nets The input signal of network, φ₁(x) it is RBF neural hidden node output vector；

(5) by the output of RBF neuralIt is used as the upper bound of external interferenceBring into formula (16), obtain new control Rule

By control lawGyroscope is controlled as the control input u of gyroscope；

(6) based on Lyapunov design robust adaptive rules and network weight adaptive law,

The Lyapunov functions V is designed as：

Wherein, m=m^T, η=η^TIt is positive definite symmetric matrices,For network weight evaluated error,

The robust adaptive rule is designed as：

M is representedAdaptive law gain；

The network weight adaptive law is designed as：

In foregoing step (1), ideal kinetics equation is the sine wave of two different frequencies：

x_m=A₁sin(w₁T), y_m=A₂sin(w₂T),

Wherein w₁≠w₂, and be all not zero, A₁、A₂Respectively amplitude of the gyroscope on two direction of principal axis, t is time, w₁、 w₂It is vibration frequency of the micro, slight gyroscope on two direction of principal axis respectively；

Being write as vector form is：

Wherein

In foregoing step (2), the process for setting up the dimensionless kinetics equation of gyroscope is：

2-1) take into account foozle and external interference effect, the kinetics equation of two axle micro-mechanical gyroscopes is：

In formula, m is the quality of mass；X, y are respectively position of the mass along drive shaft and sensitive axis；d_xx,d_xy,d_yy For the damped coefficient of gyroscope, k_xx,k_xy,k_yyFor the coefficient of elasticity of gyroscope, unknown and slow time-varying；Ω_zIt is micro- top Angular speed in spiral shell instrument working environment, is also unknown quantity；u_x,u_yIt is the control input of two axles；ρ_x,ρ_yIt is the external interference of two axles Effect；

2-2) by the both sides of formula (1) with divided by gyroscope quality m, reference length q₀, the resonant frequency of two axles it is flat SideDimensionless transformation is carried out again, obtains nondimensionalization model as follows：

Now, all amounts are nondimensional pure values in formula (3), and the expression formula of each characteristic is：

Characteristic is represented on the right of arrow, the arrow left side indicates dimensional quantity；

2-3) form for being write gyroscope dimensionless kinetic simulation pattern (3) as dimensionless vector is：

In formula,

Q is the movement locus of gyroscope, and ρ is the external interference of gyroscope, and D is the damped coefficient square of gyroscope Battle array, K is the elastic coefficient matrix of gyroscope, and Ω is input angular velocity matrix, and u is control input.

In foregoing step (3), tracking error e is：

E=q-q_m,

Wherein, q is the movement locus of gyroscope, q_mFor the ideal movements track of gyroscope.

Compared with prior art, advantage is the present invention：

(1) dynamic characteristic of gyroscope is a kind of idealized model, compensate for foozle and and environmental disturbances.

(2) the parameter θ adaptive algorithm and the adaptive algorithm of network weight designed based on Lyapunov methods can be protected Demonstrate,prove the Global asymptotic stability of whole closed-loop system.

(3) present invention adds feedback term in control algolithm, substantially increases the shaft vibration track following of gyroscope two Speed and parameter Estimation speed, while reducing oscillation amplitude.

(4) present invention adds robust in control algolithm, counteracts the parameter of environmental disturbances and gyroscope in itself not Certainty, improves the robustness and dynamic characteristic of system.

(5) the Estimation of Upper-Bound value using RBF neural of the invention as robust gain, reduction by external interference compared with Buffeted caused by big and fluctuation, eliminate the influence of system architecture formula and unstructured interference, further increase the Shandong of system Rod.

(6) control of the present invention to gyroscope need not be set up on the basis of object Accurate Model, save modeling Expense, with the value in industry.

Brief description of the drawings

Fig. 1 is the simplified model schematic diagram of micro-vibration gyroscope；

Fig. 2 is the gyroscope Robust Adaptive Control method schematic learnt based on the neutral net upper bound of the invention；

Fig. 3 is x, y-axis tracking response curve in the specific embodiment of the invention；

Fig. 4 is x, y-axis trajectory track error curve in the specific embodiment of the invention；

Fig. 5 is estimated angular rate Ω in the specific embodiment of the invention_zResponse curve；

Fig. 6 is in the specific embodiment of the inventionw_xy、d_xx、d_yy、d_xyParameter Estimation response curve；

Fig. 7 is the upper bound of the external interference of the present inventionTrace plot.

Embodiment

Further to illustrate the present invention to reach the technological means and effect that predetermined goal of the invention is taken, below in conjunction with Accompanying drawing and preferred embodiment, to according to proposed by the present invention a kind of based on micro- top that robust and feedback term are added in control law Spiral shell Robust Adaptive Control method is described in detail as rear.

As shown in Fig. 2 the microthrust test Robust Adaptive Control method learnt based on the neutral net upper bound, including following step Suddenly：

(1) ideal kinetics model is set up

Design reference model is the sine wave of two different frequencies：x_m=A₁sin(w₁T), y_m=A₂sin(w₂T), wherein w₁ ≠w₂And be all not zero,

x_m, y_mIt is gyroscope respectively along the position in drive shaft and sensing direction of principal axis, A₁, A₂It is gyroscope respectively Amplitude on two direction of principal axis, t is time, w₁And w₂The vibration frequency that respectively gyroscope gives on two direction of principal axis；

Being write as vector form is：Wherein

(2) gyroscope system dynamics model is set up

The simplified model of microthrust test according to Fig. 1, it is considered to enter foozle and external interference effect, two axle micromechanics The kinetics equation of gyroscope is：

In formula, m is the quality of mass；X, y are respectively position of the mass along drive shaft and sensitive axis；d_xx,d_xy,d_yy For the damped coefficient of gyroscope, k_xx,k_xy,k_yyFor the coefficient of elasticity of gyroscope, unknown and slow time-varying；Ω_zIt is micro- top Angular speed in spiral shell instrument working environment, is also unknown quantity；u_x,u_yIt is the control input of two axles；ρ_x,ρ_yIt is the external interference of two axles Effect.

By the both sides of formula (1) with divided by the quality of gyroscope obtain：

Both sides with divided by a reference length q₀, square of the resonant frequency of two axlesDimensionless transformation is carried out again, is obtained Nondimensionalization model is as follows：

Now, all amounts are nondimensional pure values in formula (3), and the conversion process of each characteristic is：

Characteristic is represented on the right of arrow, the arrow left side indicates dimensional quantity.

Because mass obtains displacement range in sub-millimeter meter range, therefore rational reference length q₀Desirable 1m, gyroscope Two axle resonant frequencies it is general in kilohertz range, therefore reference frequency w₀Desirable 1KHz.

Being write gyroscope kinetic simulation pattern (3) as dimensionless vectorial form is：

In formula,

(3) it is based on sliding formwork function design control law

For gyroscope, we can make following standard hypothesis：

I. the quality m of mass keeps constant in whole work process and working environment, i.e.,

II. the damped coefficient d of gyroscope_xx,d_xy,d_yyMeet relation：d_xx＞ ＞ d_xy,d_yy＞ ＞ d_xy, so D matrix is Positive definite symmetric matrices.

The control targe of gyroscope is that the oscillation trajectory of the axle of mass two follows the trail of given reference locus q_m=[x_m, y_m]^T, defining tracking error e is：

E (t)=q (t)-q_m(t) (5)

Designing sliding formwork function s is：

In formula,It is sliding-mode surface parameter for positive definite symmetric matrices.

To sliding formwork function derivation：

Will Bring formula (7) into, have：

Formula (8) is organized into the form with parameter error vector, this is also the conventional change of one kind of Self Adaptive Control analysis Change method.

Definition：

So, formula (9) can be write as：

In formulaBe known to a parameter 2 × 7 matrix, θ^*Be one comprising 7 unknown system parameters 7 × 1 parameter error vector.

MakeTo obtain Equivalent control law u_eqHave：

u_eq=Y θ^*-Q-ρ (14)

ρ is external interference, bounded, set its upper bound as

Value can be obtained by some prioris, or obtained by certain off-line strategyA conservative estimation Value, then we are in control signal addition robust, elimination ρ interference, it is ensured that track progressive tracking.

Design control lawFor：

Wherein, K_sWithIt is constant square Battle array, K_sFor linear feedback gain,It isEstimate, define evaluated error be：

u_s1=-K_sS is feedback term,

For robust.

By the control law of formula (16)Formula (13) is brought into as the control input u of gyroscope, obtains closed-loop system equation：

Formula (16) brings formula (13) into,

In formula,Meet

(4) robust that design is learnt based on the RBF neural upper bound

The upper bound for adaptive learning external interferenceRBF neural outputFor：

In formula, W is network weight,For optimal network weights W^*Estimate, x be RBF neural input signal, φ₁(x) it is RBF neural hidden node output vector, is fixed by center vector and sound stage width, i.e. φ₁(x) it is known signal.

The upper bound disturbed to external world for RBF neuralLearnt, the output of RBF neural is extraneous dry The upper bound disturbedEstimateUsing the estimate asThe then control law of formula (16)It can be written as：

By the control law of formula (19)Formula (13) is brought into as the control input u of gyroscope to obtain：

Wherein,Meet

(5) based on Lyapunov design robust adaptive rules and network weight adaptive law

Designing Lyapunov functions V is：

Wherein, m=m^T, η=η^TIt is positive definite symmetric matrices,

For network weight evaluated error, satisfaction has

Lyapunov function V derivations are obtained：

For RBF neural, planned network Weight number adaptively learning algorithm is：

η is neural network learning speed.

Assuming that 1：In the presence of one group of optimal network weights W^*So that the RBF neural with enough concealed nodes expires The following relational expression of foot：

Wherein, ε₂(x) bounded,

|ε₂(x)|≤ε^*

In formula, ε^*For ε₂(x) the upper bound, ε^*For the positive number of very little.

Assuming that 2：Between meet following relation：

Definition：

Network weight adaptive law (23) is brought into formula (22) to obtain：

DesignAdaptive law be：

M is symmetric positive definite matrix, is representedAdaptive law gain, selected by actual conditions oneself.Robust is adaptive Formula (25) should be restrained to bring into formula (24), obtained：

Negative definite, then can ensure s and0 is leveled off to, system enters sliding formwork surface state, so that tracking error is received Hold back to zero, system realizes progressive tracking performance, the angular speed and unknown system parameter of gyroscope also can be estimated correctly.

(6) computer simulation experiment

In order to more intuitively show proposed by the present invention added in control law based on the study of the RBF neural upper bound The microthrust test Robust Adaptive Control method of robust and feedback term, now using perceptive construction on mathematics/SIMULINK to this hair Bright carry out computer simulation experiment.With reference to existing literature, the parameter for choosing gyroscope is：

M=1.8 × 10^-7Kg, k_xx=63.955N/m, k_yy=95.92N/m, k_xy=12.779N/m

d_xx=1.8 × 10^-6N s/m, d_yy=1.8 × 10^-6N s/m,d_xy=3.6 × 10^-7N s/m,Ω_z=0.1

Unknown angular speed is assumed to Ω_z=100rad/s.

Reference locus is described as：x_m=0.1*cos (6.17t), y_m=0.1*cos (5.11t).

Gyroscope is zero original state.Consider that external interference act as the noise resonated with ideal trajectory, external interference Take ρ=[randn (1,1), randn (1,1)]^TμN。

In l-G simulation test, linear feedback gain is taken as K_s=10*I, I are unit matrix.

Sliding-mode surface parameter c=diag (150,150).

It is 45 to choose node in hidden layer for RBF neural, and learning rate is η=10.

M is taken as m=10000*I, and I is unit vector.

Taken for fixed gain robust adaptive compensation scheme

Simulated program is run, the simulation result curve of the specific embodiment of the invention is obtained as shown in Fig. 3-7.

Fig. 3 illustrates two track shaft tracking effect curves of the gyroscope under control method proposed by the present invention.Figure In, solid line is reference locus, and curve is actual motion track.From accompanying drawing as can be seen that control system enables to gyroscope Output, do not know gyroscope parameter and structure and exist external interference effect in the case of, can promptly track Upper given ideal trajectory, whole closed-loop system asymptotically stability has reached satisfied effect.

Fig. 4 illustrates X, the tracking error curve in Y direction.It can be seen that by very short time-tracking Error curve converges to zero substantially, and keeps this motion.

Fig. 5 illustrates Attitude rate estimator value changes curve, as a result show angular speed estimate can asymptotic convergence in true Value, and regulating time is shorter.

Fig. 6 illustrates gyroscope parameterw_xy、d_xx、d_yy、d_xyParameter Estimation response curve, as a result shows it Can converge to respective true value, and regulating time is shorter.

Fig. 7 illustrates the upper bound change curve of the external interference of control system.Upper bound change is by neural network learning Result, according to the different external environment condition of system to the upper bound carry out adaptive learning, enable it to be well adapted for robust adaptive Control system, while reducing the generation that control system is buffeted.

Can be seen that control method proposed by the present invention from above analogous diagram has very well to the track following of gyroscope Control effect, eliminate buffet, substantially increase the tracking performance and robustness of gyroscope system, the axle of gyroscope two shaken The high-precision control of dynamic rail mark provides theoretical foundation and Math.

The content not being described in detail in description of the invention belongs to technological know-how known to professional and technical personnel in the field.

The above described is only a preferred embodiment of the present invention, not make any formal big limitation to the present invention, Although the present invention is disclosed above with preferred embodiment, but is not limited to the present invention, any to be familiar with this professional technology Personnel, without departing from the scope of the present invention, when the technology contents using the disclosure above make a little change or repair The equivalent embodiment for equivalent variations is adornd, as long as being the content without departing from technical solution of the present invention, the technology according to the present invention is real Any simple modification, equivalent variations and modification that confrontation above example is made, still fall within the scope of our bright technical scheme It is interior.

Claims (2)

1. the gyroscope Robust Adaptive Control method learnt based on the neutral net upper bound, it is characterised in that including following step Suddenly：

(1) ideal kinetics equation is set up；

The ideal kinetics equation is the sine wave of two different frequencies：

x_m=A₁sin(w₁T), y_m=A₂sin(w₂T),

Wherein w₁≠w₂, and be all not zero, A₁、A₂Respectively amplitude of the gyroscope on two direction of principal axis, t is time, w₁、w₂Point It is not vibration frequency of the micro, slight gyroscope on two direction of principal axis；

Being write as vector form is：

${\stackrel{\·\·}{q}}_m+k_m{q}_m=0,$

Wherein

(2) the dimensionless kinetics equation of gyroscope is set up, process is：

2-1) take into account foozle and external interference effect, the kinetics equation of two axle micro-mechanical gyroscopes is：

$\begin{array}{c}m\stackrel{\·\·}{x}+d_{xx}\stackrel{\·}{x}+d_{xy}\stackrel{\·}{y}+k_{xx}x+k_{xy}y=u_x+{\mathrm{\ρ}}_x+2{\mathrm{m\Ω}}_z\stackrel{\·}{y}\\ m\stackrel{\·\·}{y}+d_{xy}\stackrel{\·}{x}+d_{yy}\stackrel{\·}{y}+k_{xy}x+k_{yy}y=u_y+{\mathrm{\ρ}}_y-2{\mathrm{m\Ω}}_z\stackrel{\·}{x}\end{array}---\left(1\right)$

In formula, m is the quality of mass；X, y are respectively position of the mass along drive shaft and sensitive axis；d_xx,d_xy,d_yyTo be micro- The damped coefficient of gyroscope, k_xx,k_xy,k_yyFor the coefficient of elasticity of gyroscope, unknown and slow time-varying；Ω_zIt is gyroscope Angular speed in working environment, is also unknown quantity；u_x,u_yIt is the control input of two axles；ρ_x,ρ_yIt is the external interference effect of two axles；

2-2) by the both sides of formula (1) with divided by gyroscope quality m, reference length q₀, square of the resonant frequency of two axles Dimensionless transformation is carried out again, obtains nondimensionalization model as follows：

$\begin{array}{c}\stackrel{\·\·}{x}+d_{xx}\stackrel{\·}{x}+d_{xy}\stackrel{\·}{y}+w_x^{2}x+w_{xy}y=u_x+{\mathrm{\ρ}}_x+2{\mathrm{\Ω}}_z\stackrel{\·}{y}\\ \stackrel{\·\·}{y}+d_{xy}\stackrel{\·}{x}+d_{yy}\stackrel{\·}{y}+w_{xy}x+w_y^{2}y=u_y+{\mathrm{\ρ}}_y-2{\mathrm{\Ω}}_z\stackrel{\·}{x}\end{array}---\left(3\right)$

Now, all amounts are nondimensional pure values in formula (3), and the expression formula of each characteristic is：

$\frac{d_{xx}}{{\mathrm{mw}}_0}\→d_{xx},\frac{d_{xy}}{{\mathrm{mw}}_0}\→d_{xy},\frac{d_{yy}}{{\mathrm{mw}}_0}\→d_{yy},\frac{{\mathrm{\Ω}}_z}{w_0}\→{\mathrm{\Ω}}_z,\sqrt{\frac{k_{xx}}{{{\mathrm{mw}}_0}^2}}\→w_x,\sqrt{\frac{k_{yy}}{{{\mathrm{mw}}_0}^2}}\→w_y$

Characteristic is represented on the right of arrow, the arrow left side indicates dimensional quantity；

2-3) form for being write gyroscope dimensionless kinetic simulation pattern (3) as dimensionless vector is：

$\stackrel{\·\·}{q}+(D+2\mathrm{\Ω})\stackrel{\·}{q}+Kq=u+\mathrm{\ρ}---\left(4\right)$

In formula,

Q is the movement locus of gyroscope, and ρ is the external interference of gyroscope, and D is the damped coefficient matrix of gyroscope, and K is The elastic coefficient matrix of gyroscope, Ω is input angular velocity matrix, and u is control input；

(3) sliding formwork function design control law is based on, is comprised the following steps：

(3-1) defines sliding formwork function s：

$s=\stackrel{\·}{e}+ce---\left(6\right)$

Wherein, c is sliding-mode surface parameter, and e is tracking error；

(3-2) is organized into the form with parameter error vector to sliding formwork function derivation：

$\stackrel{\·}{s}=u+\mathrm{\ρ}-{\mathrm{Y\θ}}^{*}+Q---\left(13\right)$

Wherein,

${\mathrm{\θ}}^{*}={\left[\begin{array}{ccccccc}{d}_{xx}& d_{xy}& d_{yy}& {\mathrm{\Ω}}_z& w_x^2& w_{xy}& w_y^2\end{array}\right]}^T---\left(11\right)$

$Q=c(\stackrel{\·}{q}-{\stackrel{\·}{q}}_m)+k_m{q}_m---\left(12\right);$

(3-3) design control lawFor：

Wherein,K_sWithIt is constant matrices, K_s For linear feedback gain,It is θ^*Estimate,For the upper bound of external interference,

u_s1=-K_sS is feedback term,

For robust；

(4) robust that design is learnt based on the RBF neural upper bound, be specially：That is disturbed to external world with RBF neural is upper BoundaryLearnt, the output of RBF neural is the upper bound of external interferenceEstimate

$\widehat{\stackrel{\‾}{\mathrm{\ρ}}}(W,x)={\hat{W}}^T{\mathrm{\φ}}_1\left(x\right)---\left(18\right)$

Wherein, W is the network weight of RBF neural,For optimal network weights W^*Estimate, x is RBF neural Input signal, φ₁(x) it is RBF neural hidden node output vector；

(5) by the output of RBF neuralIt is used as the upper bound of external interferenceBring into formula (16), obtain new control law

By control lawGyroscope is controlled as the control input u of gyroscope；

(6) based on Lyapunov design robust adaptive rules and network weight adaptive law,

The Lyapunov functions V is designed as：

$V=\frac{1}{2}{s}^{T}s+\frac{1}{2}{\widetilde{\mathrm{\θ}}}^T{m}^{-1}\widetilde{\mathrm{\θ}}+\frac{1}{2}tr\left({\tilde{W}}^T{\mathrm{\η}}^{-1}\tilde{W}\right)---\left(21\right)$

Wherein, m=m^T, η=η^TIt is positive definite symmetric matrices,For network weight evaluated error,

The robust adaptive rule is designed as：

$\stackrel{\·}{\widehat{\mathrm{\θ}}}=-{\mathrm{mY}}^{T}s---\left(25\right)$

M is representedAdaptive law gain；

The network weight adaptive law is designed as：

$\stackrel{\·}{\hat{W}}={\mathrm{\η\φ}}_1\left(x\right)\left|\right|s\left|\right|---\left(23\right)$

η is neural network learning speed.

2. the gyroscope Robust Adaptive Control method according to claim 1 learnt based on the neutral net upper bound, its It is characterised by, in the step (3), tracking error e is：

E=q-q_m,

Wherein, q is the movement locus of gyroscope, q_mFor the ideal movements track of gyroscope.