CN104049534B - Self-adaption iterative learning control method for micro-gyroscope - Google Patents

Abstract

The invention discloses a self-adaption iterative learning control method for a micro-gyroscope. The method includes the following steps that firstly, a non-dimensional kinetic model of the micro-gyroscope is established; secondly, a reference trajectory module outputs reference trajectories of x axis vibration and y axis vibration of the micro-gyroscope, wherein the reference trajectories include position signals and speed signals; thirdly, a self-adaption law module receives the reference trajectories and output of a micro-gyroscope system and estimates the increments of parameters according to the self-adaption law; fourthly, a controller module receives new parameter estimation and acts together with trajectory tracking errors and speed tracking errors to generate control signal output of the self-adaption iterative learning control method; fifthly, output signals of the controller module are received, and position information and speed information of vibrating parts of the micro-gyroscope are output; sixthly, the third step, the fourth step and the fifth step are repeatedly executed according to an iterative method, and the final position information and the final speed information of the vibrating parts of the micro-gyroscope are obtained. By means of the method, the reference trajectory tracking performance of the micro-gyroscope system can be improved.

Description

The adaptive iterative learning control method of gyroscope

Technical field

The present invention relates to the control system of oscillating micro gyroscope instrument and method, more particularly to oscillating micro gyroscope instrument from Adapt to iterative learning control systems and method.

Background technology

Oscillating micro gyroscope instrument (mems vibratory gyroscopes, hereinafter referred to as gyroscope) is using micro- electricity The senser element for sensing angular velocity that sub- technology and micro-processing technology process.It is by a vibration being made up of silicon Micromechanical component detecting angular velocity, therefore gyroscope is very easy to miniaturization and batch production, has low cost and body Long-pending little the features such as, thus be widely used in Aeronautics and Astronautics, navigation, the navigation of land vehicle and positioning, consumer electronics field and In the military affairs such as In Oil Field Exploration And Development, civil area.But, due to mismachining tolerance inevitable during manufacturing and ring The impact of border temperature, can cause original paper characteristic and design between difference, lead to gyroscope to there is parameter uncertainty it is difficult to Set up accurate mathematical model.Along with the track so that gyroscope is can not ignore in the external disturbance effect in working environment Tracing Control is difficult to, and robustness is relatively low.

At present, both at home and abroad structure design and manufacturing technology aspect are concentrated mainly at present for the research of gyroscope, with And above-mentioned mechanical compensation technology and drive circuit research, and the research of the tracing control aspect for gyroscope oscillation trajectory Little, realize the research of track following aspect in particular with modern intelligent control method and achievement extremely lacks.

The existing control method being applied to gyroscope has the methods such as Self Adaptive Control and sliding formwork control, but these designs Method is complex, computationally intensive it is difficult to application, and the robustness of disturbance to external world is very low, easily makes system become unstable.

As can be seen here, above-mentioned existing gyroscope, it is clear that having still suffered from inconvenience and defect on using, and is urgently entered One step is improved.In order to solve existing gyroscope in problem present on use, relevant manufactures there's no one who doesn't or isn't painstakingly to be sought to solve Jue Zhi road, but have no that applicable design is developed completing for a long time always.

Content of the invention

It is an object of the invention to, the defect overcoming existing gyroscope control method to exist, particularly there is mould Shape parameter do not know and outside noise disturbed condition under, for improve gyroscope system the tracking performance of reference locus is carried A kind of adaptive iterative learning control system and method for gyroscope.

The object of the invention to solve the technical problems employs the following technical solutions to realize, gyroscope adaptive Answer iterative learning control systems, comprising:

Reference locus module (101), for exporting the reference locus of gyroscope x and y-axis vibration, including position, speed Signal；

Adaptive law module (102), for receiving the output of reference locus and gyroscope system, is estimated using adaptive law Count out the increment of parameter；

Controller module (103), for receiving new parameter estimation, and with track following error, speed Tracking error altogether Same-action produces the control signal output of self adaptation iterative learning control method；

Gyroscope system (104), the mathematical model of controlled device, it is contemplated that the impact of mechanical noise, receives controller The output signal of module, the position of output gyroscope vibrating mass and velocity information；

Memory module (105), for preserving parameter estimation information during current iteration, for parameter during next iteration Estimate.

The adaptive iterative learning control method of gyroscope is it is characterised in that comprise the following steps:

1) set up the dimensionless kinetic model of gyroscope；

2) reference locus module exports gyroscope x and the reference locus of y-axis vibration, including position, rate signal；

3) adaptive law module receives the output of reference locus and gyroscope system, estimates parameter using adaptive law Increment；

4) controller module receives new parameter estimation, and produces with track following error, speed Tracking error collective effect It is conigenous the control signal output adapting to iterative learning control method；

5) output signal of controller module, the position of output gyroscope vibrating mass and velocity information are received；

6) utilize alternative manner repeat step 3)-step 5), obtain the final position of gyroscope vibrating mass and speed Degree information.

In described step 1) in, the dimensionless kinetic model of gyroscope is:

When considering external interference, oscillating micro gyroscope instrument model is expressed with formula (6):

Wherein: d represents external interference；

$q=\left[\begin{array}{c}x\\ y\end{array}\right],d=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],k=\left[\begin{array}{cc}{\mathrm{\ω}}_x^2& {\mathrm{\ω}}_{\mathrm{xy}}\\ {\mathrm{\ω}}_{\mathrm{xy}}& {\mathrm{\ω}}_y^2\end{array}\right],u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],\mathrm{\ω}=\left[\begin{array}{cc}0& -{\mathrm{\ω}}_z\\ {\mathrm{\ω}}_z& 0\end{array}\right];$ u_x、u_y Represent the driving force along x-axis, y-axis direction；And d_xx、d_yy、d_xyRepresent respectively x-axis, y-axis, x-axis and y-axis it Between spring constant and damped coefficient；M is quality；ω_zRepresent angular velocity along the z-axis direction；ω₀Resonant frequency for two axles；It is velocity vector and vector acceleration respectively；

In iterative control process, formula (6) is expressed as:

${\stackrel{\·\·}{q}}_k+(d+2\mathrm{\ω}){\stackrel{\·}{q}}_k+k{q}_k=u_k+d_k---\left(7\right)$

In formula, k is iterationses, and k is positive integer,q_k、u_k、d_kIt is respectivelyThe kth time of q, u, d Acceleration signal vector, rate signal vector, position signalling vector, input dominant vector, interference vector.

In described step 3) in, adaptive parameter estimation is carried out according to the dimensionless kinetic model of gyroscope, adaptive The parameter estimation algorithm is answered to be:

${\widehat{\mathrm{\θ}}}_k\left(t\right)={\stackrel{\&overbar;}{\mathrm{\θ}}}_k+{\widehat{\mathrm{\θ}}}_{k-1}\left(t\right)---\left(9\right)$

Wherein θ is the vector being made up of system unknown parameter,Estimated value for θ,Estimate for θ The initial value of value,Increment for the estimated value of θ during kth time iteration；Matrixγ is positive definite symmetric matrices, γ= diag(90,90,90,90,90,90,90,90)；

$\mathrm{\θ}=\left(\begin{array}{c}{d}_{\mathrm{xx}}\\ d_{\mathrm{xy}}\\ d_{\mathrm{yy}}\\ {\mathrm{\ω}}_z\\ {\mathrm{\ω}}_x^2\\ {\mathrm{\ω}}_{\mathrm{xy}}\end{array}\right),$ β is arithmetic number；

${\stackrel{\·}{e}}_k\left(t\right)={\stackrel{\·}{q}}_d\left(t\right)-{\stackrel{\·}{q}}_k\left(t\right);$ For desired rate signal.

In described step 4) in, the dimensionless kinetic model according to gyroscope and adaptive parameter estimation algorithm, enter Row adaptive iterative learning control, control signal u_kT () is defined as:

Wherein matrixk_p、k_dIt is all positive definite symmetric matrices, $k_p=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],$ $k_d=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],$ Then when meeting iterated conditional unknown errors initial signal e_k(0)=0 and velocity error initial signalWhen, unknown errors signal e_k(t) and velocity error initial signalBounded, and Time t is in iteration cycle [0, t].

The beneficial effect that the present invention is reached: the present invention is directed to unknown parameters and the oscillating micro gyroscope that there is external interference Instrument system, it is proposed that adaptive iterative learning control scheme to realize gyroscope system on the basis of its mathematical model of deriving The Trajectory Tracking Control of system.The iteration item that this control program is made up of traditional pd feedback control, unknown parameter and tracking error Composition, control law illustrates its stability by class lyapunov Theory of Stability it is ensured that the global stability of control system Asymptotic Behavior For Some with tracking error.The present invention is that the extension of gyroscope range of application provides the micro- of the good basis present invention Gyroscope control method, exist model parameter do not know and outside noise disturbed condition under, gyroscope system can be improved The tracking performance to reference locus for the system.

Brief description

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

Fig. 2 is the tracking curves of the gyroscope x-axis based on the present invention；

Fig. 3 is the tracking curves of the gyroscope y-axis based on the present invention；

Fig. 4 is the speed Tracking curve of the x-axis of gyroscope in the present invention；

Fig. 5 is the speed Tracking curve of the y-axis of gyroscope in the present invention.

Specific embodiment

The adaptive iterative learning control method of the gyroscope of the present invention, comprises the following steps:

1) set up the dimensionless kinetic model of gyroscope；

2) reference locus module exports gyroscope x and the reference locus of y-axis vibration, including position, rate signal；

3) adaptive law module receives the output of reference locus and gyroscope system, estimates parameter using adaptive law Increment；

4) controller module receives new parameter estimation, and produces with track following error, speed Tracking error collective effect It is conigenous the control signal output adapting to iterative learning control method；

5) output signal of controller module, the position of output gyroscope vibrating mass and velocity information are received；

6) utilize alternative manner repeat step 3)-step 5), obtain the final position of gyroscope vibrating mass and speed Degree information.

In described step 1) in, set up the dimensionless kinetic model of gyroscope, particularly as follows:

When gyroscope rotates along the z-axis direction, gyroscope can be subject to using the Newton's law in rotation system Power is analyzed:

f_r=f_phy+f_centri+f_colis+f_eular=ma_r(1)

Wherein f_rWhat expression mass was subject in rotation system makes a concerted effort, f_phyRepresent that mass is subject under inertial reference system Make a concerted effort, f_centriIt is centrifugal force, f_colisIt is Coriolis force, f_eulerIt is Euler force, a_rIt is that mass rotates against the acceleration being Degree, m is quality.

It is assumed that gyroscope input angular velocity ω keeps constant within the sufficiently long time, that is, input angular velocity ω is normal Amount, and it is believed that mass is limited in x-y plane motion it is impossible to move along z-axis for z-axis gyroscope, therefore edge X-axis and the angular velocity omega in y-axis direction_x=ω_y=0.

In formula (1), Euler force is represented byWherein r_rIt is the position that mass is with respect to rotation system Move.Because input angular velocity ω is constant, f_eular=0, t are the time.

Centrifugal force f_centri=-m ω × (ω × r_r), due to ω_x=ω_y=0, centrifugal force therefore along the x-axis direction can table It is shown as f_centri-x=-m ω_z ²X, wherein x represent mass displacement along the x-axis direction, and centrifugal force along the x-axis direction is represented by f_centri-y=-m ω_z ²Y, wherein y represent mass displacement along the y-axis direction.Due to f_centri-xAnd f_centri-yValue very little, It is typically not greater than the one thousandth of other active forces, be therefore negligible.

Coriolis force f_colis=-2m ω × v_r, wherein v_rRepresent that mass rotates against the speed being.According to Ke Liao Sharp power action principle, Coriolis force along the x-axis direction is represented byIn formulaRepresent along the y-axis direction Movement velocity, Coriolis force along the y-axis direction is represented byIn formulaRepresent along the x-axis direction Movement velocity.ω_zRepresent angular velocity along the z-axis direction.

The f with joint efforts that mass is subject under inertial reference system_phyMainly it is made up of driving force, spring force and damping force.Point Do not use u_x、u_yRepresent the driving force along x-axis, y-axis direction.Use k_xx、k_yy、k_xyAnd d_xx、d_yy、d_xyRespectively represent x-axis, y-axis, x-axis and Spring constant between y-axis and damped coefficient, wherein k_xy、d_xyThe structure that causes mainly due to foozle is asymmetric to be caused Two axles coupling.In inertial reference system along the x-axis direction make a concerted effort be $f_{\mathrm{phy}-x}=u_x-k_{\mathrm{xx}}x-k_{\mathrm{xy}}y-d_{\mathrm{xx}}\stackrel{\·}{x}-d_{\mathrm{xy}}\stackrel{\·}{y},$ Along the y-axis direction make a concerted effort be $f_{\mathrm{phy}-y}=u_y-k_{\mathrm{yy}}y-k_{\mathrm{xy}}x-d_{\mathrm{yy}}\stackrel{\·}{y}-d_{\mathrm{xy}}\stackrel{\·}{x}.$

Analyzed according to above, formula (1) is deployable to be:

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

It is respectively the acceleration signal of x-axis and y-axis.Below non-dimensionalized is carried out to the model that formula (2) is described Process.Take nondimensional time t^*=ω₀T, wherein ω₀For the resonant frequency of two axles, value in 1khz, then:

$\stackrel{\·}{x}={\mathrm{\ω}}_0{\stackrel{\·}{x}}^{*},\stackrel{\·\·}{x}={{\mathrm{\ω}}_0}^2{\stackrel{\·\·}{x}}^{*},\stackrel{\·}{y}={\mathrm{\ω}}_0{\stackrel{\·}{y}}^{*},\stackrel{\·\·}{y}={{\mathrm{\ω}}_0}^2{\stackrel{\·\·}{y}}^{*}---\left(3\right)$

Say that above formula brings (2) formula into, and in equation the right and left with divided by quality m, ω₀ ²With reference length q₀Can obtain:

$\begin{array}{c}\frac{{\stackrel{\·\·}{x}}^{*}}{q_0}+\frac{d_{\mathrm{xx}}}{m{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{x}}^{*}}{q_0}+\frac{d_{\mathrm{xy}}}{m{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{y}}^{*}}{q_0}+\frac{k_{\mathrm{xx}}}{m{{\mathrm{\ω}}_0}^2}\frac{x^{*}}{q_0}+\frac{k_{\mathrm{xy}}}{m{{\mathrm{\ω}}_0}^2}\frac{y^{*}}{q_0}=\frac{u_x}{m{{\mathrm{\ω}}_0}^2{q}_0}+2\frac{{\mathrm{\ω}}_z}{{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{y}}^{*}}{q_0}\\ \frac{{\stackrel{\·\·}{y}}^{*}}{q_0}+\frac{d_{\mathrm{xy}}}{m{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{x}}^{*}}{q_0}+\frac{d_{\mathrm{yy}}}{m{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{y}}^{*}}{q_0}+\frac{k_{\mathrm{xy}}}{m{{\mathrm{\ω}}_0}^2}\frac{x^{*}}{q_0}+\frac{k_{\mathrm{yy}}}{m{{\mathrm{\ω}}_0}^2}\frac{y^{*}}{q_0}=\frac{u_y}{m{{\mathrm{\ω}}_0}^2{q}_0}-2\frac{{\mathrm{\ω}}_z}{{\mathrm{\ω}}_0}\frac{{\stackrel{\·}{x}}^{*}}{q_0}\end{array}---\left(4\right)$

x^*、y^*、Represent position signalling, rate signal and the acceleration of nondimensional x-axis and y-axis respectively Degree signal.

Rewrite above formula in the form of vectors can obtain:

$\stackrel{\·\·}{q}+d\stackrel{\·}{q}+\mathrm{kq}=u-2\mathrm{\ω}\stackrel{\·}{q}---\left(5\right)$

In formula, $q=\left[\begin{array}{c}\frac{x^{*}}{q_0}\\ \frac{y^{*}}{q_0}\end{array}\right],d=\left[\begin{array}{cc}\frac{d_{\mathrm{xx}}}{m{\mathrm{\ω}}_0}& \frac{d_{\mathrm{xy}}}{m{\mathrm{\ω}}_0}\\ \frac{d_{\mathrm{xy}}}{m{\mathrm{\ω}}_0}& \frac{d_{\mathrm{yy}}}{m{\mathrm{\ω}}_0}\end{array}\right],k=\left[\begin{array}{cc}\frac{k_{\mathrm{xx}}}{m{{\mathrm{\ω}}_0}^2}& \frac{k_{\mathrm{xy}}}{m{{\mathrm{\ω}}_0}^2}\\ \frac{k_{\mathrm{xy}}}{m{{\mathrm{\ω}}_0}^2}& \frac{k_{\mathrm{yy}}}{m{{\mathrm{\ω}}_0}^2}\end{array}\right],u=\left[\begin{array}{c}\frac{u_x}{m{{\mathrm{\ω}}_0}^2{q}_0}\\ \frac{u_y}{m{{\mathrm{\ω}}_0}^2{q}_0}\end{array}\right],\mathrm{\ω}=\left[\begin{array}{cc}0& -\frac{{\mathrm{\ω}}_z}{{\mathrm{\ω}}_0}\\ \frac{{\mathrm{\ω}}_z}{{\mathrm{\ω}}_0}& 0\end{array}\right],$ First derivative and the second dervative of position signalling vector q respectively, i.e. rate signal vector sum acceleration signal vector. Succinct for writing, order Then $q=\left[\begin{array}{c}x\\ y\end{array}\right],$ $d=\left[\begin{array}{cc}{d}_{\mathrm{xx}}& d_{\mathrm{xy}}\\ d_{\mathrm{xy}}& d_{\mathrm{yy}}\end{array}\right],k=\left[\begin{array}{cc}{\mathrm{\ω}}_x^2& {\mathrm{\ω}}_{\mathrm{xy}}\\ {\mathrm{\ω}}_{\mathrm{xy}}& {\mathrm{\ω}}_y^2\end{array}\right],u=\left[\begin{array}{c}{u}_x\\ u_y\end{array}\right],\mathrm{\ω}=\left[\begin{array}{cc}0& -{\mathrm{\ω}}_z\\ {\mathrm{\ω}}_z& 0\end{array}\right].$

When considering external interference, oscillating micro gyroscope instrument model can be expressed with following formula:

$\stackrel{\·\·}{q}+(d+2\mathrm{\ω})\stackrel{\·}{q}+kq=u+d---\left(6\right)$

In formula, d represents external interference；

In iterative learning control, system dynamics equation is expressed as:

${\stackrel{\·\·}{q}}_k+(d+2\mathrm{\ω}){\stackrel{\·}{q}}_k+k{q}_k=u_k+d_k---\left(7\right)$

In formula, k is iterationses, and k is positive integer,q_k、u_k、d_kIt is respectivelyThe kth time of q, u, d Acceleration signal vector, rate signal vector, position signalling vector, input dominant vector, interference vector.

Aforesaid step 3), the method that adaptive parameter estimation is carried out according to the dimensionless kinetic model of gyroscope, Concretely comprise the following steps:

From analysis, system model also meets following characteristic:

(1)Due to q_kWithFor detectable mass displacement and speed Degree, soFor known matrix, ξ unknown vector, it is made up of system structure parameter, its concrete form is shown below:

${\left(\begin{array}{ccccccc}{\stackrel{\·}{q}}_1& {\stackrel{\·}{q}}_2& 0& -2{\stackrel{\·}{q}}_2& q_1& q_2& 0\\ 0& {\stackrel{\·}{q}}_1& {\stackrel{\·}{q}}_2& -2{\stackrel{\·}{q}}_1& 0& q_1& q_2\end{array}\right)}_k=\mathrm{\ψ}(q_k,{\stackrel{\·}{q}}_k)$

$\left(\begin{array}{c}{d}_{\mathrm{xx}}\\ d_{\mathrm{xy}}\\ d_{\mathrm{yy}}\\ {\mathrm{\ω}}_z\\ {\mathrm{\ω}}_x^2\\ {\mathrm{\ω}}_{\mathrm{xy}}\\ {\mathrm{\ω}}_y^2\end{array}\right)=\mathrm{\ξ}$

$k{q}_k\left(t\right)+(d+2\mathrm{\ω}){\stackrel{\·}{q}}_k\left(t\right)={\left(\begin{array}{ccccccc}{\stackrel{\·}{q}}_1& {\stackrel{\·}{q}}_2& 0& -2{\stackrel{\·}{q}}_2& q_1& q_2& 0\\ 0& \stackrel{\·}{q_1}& {\stackrel{\·}{q}}_2& -2{\stackrel{\·}{q}}_1& 0& q_1& q_2\end{array}\right)}_k\left(\begin{array}{c}{d}_{\mathrm{xx}}\\ d_{\mathrm{xy}}\\ d_{\mathrm{yy}}\\ {\mathrm{\ω}}_z\\ {\mathrm{\ω}}_x^2\\ {\mathrm{\ω}}_{\mathrm{xy}}\\ {\mathrm{\ω}}_y^2\end{array}\right)=\mathrm{\ψ}(q_k,{\stackrel{\·}{q}}_k)\mathrm{\ξ}$

(2)β is arithmetic number,For expectation signal for faster vector；

(3) θ (t)=[ξ^t(t)β]^t, θ is made up of system structure parameter and β, that is, $\mathrm{\θ}=\left(\begin{array}{c}{d}_{\mathrm{xx}}\\ d_{\mathrm{xy}}\\ d_{\mathrm{yy}}\\ {\mathrm{\ω}}_z\\ {\mathrm{\ω}}_x^2\\ {\mathrm{\ω}}_{\mathrm{xy}}\\ {\mathrm{\ω}}_x^2\\ \mathrm{\β}\end{array}\right).$

(4)Sgn () is sign function,R is real Number, position error signal vector e_k(t)=q_d(t)-q_k(t), speed error signal vectorConcrete shape Formula is shown below:

According to system above characteristic it is proposed that adaptive parameter estimation algorithm:

${\stackrel{\&overbar;}{\mathrm{\θ}}}_k\left(t\right)={\stackrel{\&overbar;}{\mathrm{\θ}}}_k+{\widehat{\mathrm{\θ}}}_{k-1}\left(t\right)---\left(9\right)$

WhereinEstimated value for θ, Increment for the estimated value of θ during kth time iteration.Matrixγ is positive definite symmetric matrices, γ=diag (90,90,90,90,90,90,90,90).

Aforesaid step 4), the dimensionless kinetic model according to gyroscope and adaptive parameter estimation algorithm, adaptive Answer iterative learning control method control signal u_kT () is defined as:

Wherein matrixk_p、k_dIt is all positive definite symmetric matrices, $k_p=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],$ $k_d=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],$ Then when meeting iterated conditional unknown errors initial signal e_k(0)=0 and velocity error initial signalWhen, unknown errors signal e_k(t) and velocity error initial signalBounded, and $\underset{k\→0}{\lim }{e}_k\left(t\right)=\underset{k\→0}{\lim }{\stackrel{\·}{e}}_k\left(t\right)=0,$ T is in iteration cycle [0, t].

When iterationses tend to infinite, the track following error of gyroscope and speed Tracking error level off to zero, real It is only necessary to 5 iteration just can be implemented in unknown parameters and realize track following in the case of there is external interference in the application of border Error and speed Tracking error level off to zero, have actual application value.

For further illustrating that the present invention is to reach technological means and effect that predetermined goal of the invention is taken, below in conjunction with Accompanying drawing and preferred embodiment, are carried out to the adaptive iterative learning control system and method according to gyroscope proposed by the present invention After describing in detail such as.

Adaptive iterative learning control method in order to gyroscope proposed by the present invention is described controls system to gyroscope The stability of system and effectiveness, are now illustrated by class lyapunov theory.

Lyapunov function is designed as:

$w_k(e_k\left(t\right),{\stackrel{\·}{e}}_k\left(t\right),{\widetilde{\mathrm{\θ}}}_k\left(t\right))=v_k(e_k\left(t\right),{\stackrel{\·}{e}}_k\left(t\right))+\frac{1}{2}{\&integral;}_0^t{\widetilde{\mathrm{\θ}}}_k^t\left(t\right){\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_k\left(t\right)\mathrm{d\τ}---\left(4\right)$

Wherein $v_k(e_k\left(t\right),{\stackrel{\·}{e}}_k\left(t\right))=\frac{1}{2}(e_k^t{k}_p{e}_k+{\stackrel{\·}{e}}_k^t{\stackrel{\·}{e}}_k),{\widetilde{\mathrm{\θ}}}_k\left(t\right)=\mathrm{\θ}\left(t\right)-{\widehat{\mathrm{\θ}}}_k\left(t\right),{\widehat{\mathrm{\θ}}}_k\left(t\right)={\left[\begin{array}{cc}{\widehat{\mathrm{\ξ}}}_k^t\left(t\right)& {\widehat{\mathrm{\β}}}_k\end{array},\left(t\right)\right]}^t$ Estimated value for θ (t).

(1)w_kFor nonincreasing sequence

$\mathrm{\δ}{w}_k=w_k-w_{k-1}=v_k-v_{k-1}+\frac{1}{2}{\&integral;}_0^t({\widetilde{\mathrm{\θ}}}_k^t\left(t\right){\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_k\left(t\right)-{\widetilde{\mathrm{\θ}}}_{k-1}^t\left(t\right){\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_{k-1}\left(t\right))\mathrm{d\τ}---\left(5\right)$

Take ${\stackrel{\&overbar;}{\mathrm{\θ}}}_k={\widehat{\mathrm{\θ}}}_k\left(t\right)-{\widehat{\mathrm{\θ}}}_{k-1}\left(t\right),$ Then ${\stackrel{\&overbar;}{\mathrm{\θ}}}_k=\mathrm{\θ}-{\widetilde{\mathrm{\θ}}}_k\left(t\right)-\mathrm{\θ}+{\widetilde{\mathrm{\θ}}}_{k-1}\left(t\right)=-{\widetilde{\mathrm{\θ}}}_k\left(t\right)+{\widetilde{\mathrm{\θ}}}_{k-1}\left(t\right),$ And

${\widetilde{\mathrm{\θ}}}_k^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_k-{\widetilde{\mathrm{\θ}}}_{k-1}^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_{k-1}=-{\stackrel{\&overbar;}{\mathrm{\θ}}}_k^t{\mathrm{\γ}}^{-1}{\stackrel{\&overbar;}{\mathrm{\θ}}}_k-2{\stackrel{\&overbar;}{\mathrm{\θ}}}_k^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_k$

This formula is brought into formula (11) obtain:

$\mathrm{\δ}{w}_k=w_k-w_{k-1}=v_k-v_{k-1}-\frac{1}{2}{\&integral;}_0^t({\stackrel{\&overbar;}{\mathrm{\θ}}}_k^t{\mathrm{\γ}}^{-1}{\stackrel{\&overbar;}{\mathrm{\θ}}}_k+2{\stackrel{\&overbar;}{\mathrm{\θ}}}_k^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_k)\mathrm{d\τ}---\left(6\right)$

Due to ${\&integral;}_0^t{\stackrel{\·}{v}}_k\left(t\right)\mathrm{d\τ}=v_k\left(t\right)-v_k\left(0\right),$ I.e. $v_k\left(t\right)=v_k\left(0\right)+{\&integral;}_0^t{\stackrel{\·}{v}}_k\left(t\right)\mathrm{d\τ}.$ And due to

Then

In formula (13),This formula is brought into formula (14) can get:

By iterated conditional e_k(0)=0, ${\stackrel{\·}{e}}_k\left(0\right)=0,$ So $v_k({\stackrel{\·}{e}}_k\left(0\right),\left(0\right))=0,$ Then

From adaptive lawAccording to this formula, can there is following knot Really:

Formula (13) is brought in formula (16)～(18) obtain

Therefore w_kFor nonincreasing sequence.

(2)w₀The boundedness of (t)

W is understood by formula (11)₀T the first derivative of () is

${\stackrel{\·}{w}}_0({\stackrel{\·}{e}}_0\left(t\right),e_0\left(t\right),{\widetilde{\mathrm{\θ}}}_0\left(t\right))={\stackrel{\·}{v}}_0(e_0\left(t\right),{\stackrel{\·}{e}}_0\left(t\right))+\frac{1}{2}{\widetilde{\mathrm{\θ}}}_0^t\left(t\right){\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0\left(t\right)---\left(13\right)$

As k=0, formula (16) both sides derivation is obtainedBring formula (19) into obtain

Due to ${\widehat{\mathrm{\θ}}}_{-1}\left(t\right)=0,$ SoThenSubstitute into formula again (20)

${\stackrel{\·}{w}}_0\≤-{\stackrel{\·}{e}}_0^t{k}_d{\stackrel{\·}{e}}_0+({\widehat{\mathrm{\θ}}}_0^t+\frac{1}{2}{\widetilde{\mathrm{\θ}}}_0^t){\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0=-{\stackrel{\·}{e}}_0^t{k}_d{\stackrel{\·}{e}}_0-\frac{1}{2}{\widetilde{\mathrm{\θ}}}_0^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0+{\mathrm{\θ}}_0^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0---\left(15\right)$

Again by young ' s inequality (a²+b²>=2ab), thenWherein k₁> 0.Because k_dFor positively definite matrix, two eigenvalue λ_d2≥λ_d1>=0, soHave in the same manner $-\frac{1}{2}{\widetilde{\mathrm{\θ}}}_0^t{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0\≤-\frac{1}{2}{\mathrm{\λ}}_1{\left|\right|{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2,k_1{\left|\right|{\mathrm{\γ}}^{-1}{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2\≤k_1{\mathrm{\λ}}_2^2{\left|\right|{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2,$ Wherein λ₁、λ₂It is respectively positive definite matrix γ^-1Minimum, Big eigenvalue.

$\begin{array}{c}{\stackrel{\·}{w}}_0\≤-{\mathrm{\λ}}_{d1}{\left|\right|{\stackrel{\·}{e}}_0\left|\right|}^2-\frac{1}{2}{\mathrm{\λ}}_1{\left|\right|{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2+k_1{\mathrm{\λ}}_2^2{\left|\right|{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2+\frac{1}{{4k}_1}{\left|\right|\mathrm{\θ}\left|\right|}^2\\ =-{\mathrm{\λ}}_{d1}{\left|\right|{\stackrel{\·}{e}}_0\left|\right|}^2-(\frac{1}{2}{\mathrm{\λ}}_1-k_1{\mathrm{\λ}}_2^2){\left|\right|{\widetilde{\mathrm{\θ}}}_0\left|\right|}^2+\frac{1}{{4k}_1}{\left|\right|\mathrm{\θ}\left|\right|}^2\end{array}---\left(16\right)$

TakeThenFormula (23) can obtain furtherI.e. w₀T () is in t ∈ [0, t] bounded.

(3)w_kThe boundedness of (t)

Because w_kT () is lypunov energy function and is nonincreasing sequence on iteration axle, so having 0≤w for k >=1_k (t)≤w₀(t).Again because w₀T () is in t ∈ [0, t] bounded, so w_kT () is in t ∈ [0, t] bounded.

According to the explanation of above three parts, can deriveHaveProcess is such as Under.

w_kT () can be written asFormula (19) and formula (11) are brought into and can be obtained

$w_k\≤w_0-\underset{j=1}{\overset{k}{\mathrm{\σ}}}{v}_{j-1}\≤w_0-\frac{1}{2}\underset{j=1}{\overset{k}{\mathrm{\σ}}}({\stackrel{\·}{e}}_{j-1}^t{\stackrel{\·}{e}}_{j-1}+e_{j-1}^t{k}_p{e}_{j-1})$

Then

$\underset{j=1}{\overset{k}{\mathrm{\σ}}}({\stackrel{\·}{e}}_{j-1}^t{\stackrel{\·}{e}}_{j-1}+e_{j-1}^t{k}_p{e}_{j-1})\≤2(w_0-w_k)\≤{2w}_0---\left(17\right)$

Formula (24) containsThe system energy when iterationses tend to infinite Reference locus on perfect tracking.

Finally, carry out Computer Simulation

In the present embodiment, carry out computer simulation experiment using mathematical software matlab/simulink, choose gyroscope Parameter be:

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^{- 6}N s/m, d_yy=1.8 × 10^-6N s/m, d_xy=3.6 × 10^-7n·s/m

Unknown input angular velocity is assumed to ω_z=100rad/s.Reference length is chosen for q₀=1 μm, reference frequency ω₀ =1000hz, after non-dimensionalized, each gyroscope parameter is as follows:

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

Reference locus are chosen $q_d=\left[\begin{array}{c}{x}_d\\ y_d\end{array}\right]=\left[\begin{array}{c}\sin \left(6.17t\right)\\ 1.2\sin \left(5.11t\right)\end{array}\right],d_k=\left[\begin{array}{c}\mathrm{rand}\left(1\right)\sin \left(t\right)\\ \mathrm{rand}\left(1\right)\sin \left(t\right)\end{array}\right]$ The initial shape of controlled device State is q_k(0)=q_d(0), ${\stackrel{\·}{q}}_k\left(0\right)={\stackrel{\·}{q}}_d\left(0\right).$ Controller parameter is set to $k_p=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],k_d=\left[\begin{array}{cc}70& 0\\ 0& 70\end{array}\right],$ Adaptive Parameter γ=diag (90,90,90,90,90,90,90,90) should be restrained.

Simulation result is as shown in Figure 2-5.

Fig. 2 shows the position tracing figure in x-axis and y-axis direction the 5th iteration cycle.In figure solid line represents x-axis and y-axis The reference locus in direction, dotted line represents x-axis and the actual path in y-axis direction.Can be it is clear to see that when the 5th changes from figure Dai Shi, using the position curve almost reference curve on perfect tracking of adaptive iterative learning control scheme.

Fig. 3 shows the maximum value situation of change of each iterative position tracking error in 5 iterative process, in figure position Put error maximum value be defined as e1=max (| q1_d(t)-q1_k(t) |), e2=max (| q2_d(t)-q2_k(t) |), t ∈ [0, t].In figure can clearly find out that x-axis and y-axis site error maximum value initial value are little, and declines quickly, in the 5th iteration When nearly close to zero.

Fig. 4 and Fig. 5 reflects velocity tracking scenario and speed Tracking error maximum value situation of change respectively.Can from figure To be visually observed that very much the speed Tracking better performances using adaptive iterative learning control scheme.

Can be seen that control method proposed by the present invention from above analogous diagram has to the track following of gyroscope very well Control effect, substantially increase tracking performance and the robustness of gyroscope system, to gyroscope two shaft vibration track High accuracy control provides theoretical foundation and Math, and algorithm is simple, it is easy to accomplish, there is preferable practical value.

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, be only presently preferred embodiments of the present invention, but be not limited to the present invention, any is familiar with basis Technical professional, in the range of without departing from technical solution of the present invention, when the technology contents of available the disclosure above are made Being permitted to change or be modified to the Equivalent embodiments of equivalent variations, as long as being the content without departing from technical solution of the present invention, all being still fallen within The protection domain of the bright technical scheme of we.

Claims (2)

1. the adaptive iterative learning control method of gyroscope is it is characterised in that comprise the following steps:

1) set up the dimensionless kinetic model of gyroscope；

2) reference locus module exports gyroscope x and the reference locus of y-axis vibration, including position, rate signal；

3) adaptive law module receives the output of reference locus and gyroscope system, estimates the increasing of parameter using adaptive law Amount；

4) controller module receives new parameter estimation, and is produced from track following error, speed Tracking error collective effect Adapt to the control signal output of iterative learning control method；

5) output signal of controller module, the position of output gyroscope vibrating mass and velocity information are received；

6) utilize alternative manner repeat step 3)-step 5), obtain the final position of gyroscope vibrating mass and speed letter Breath；

In described step 1) in, the dimensionless kinetic model of gyroscope is:

When considering external interference, oscillating micro gyroscope instrument model is expressed with formula (6):

$\stackrel{\·\·}{q}+(d+2\mathrm{\ω})\stackrel{\·}{q}+kq=u+d---\left(6\right)$

Wherein: d represents external interference；

u_x、u_yRepresent edge X-axis, the driving force in y-axis direction；ω_xy、And d_xx、d_yy、d_xyRepresent the spring system between x-axis, y-axis, x-axis and y-axis respectively Number and damped coefficient；M is quality；ω_zRepresent angular velocity along the z-axis direction；ω₀Resonant frequency for two axles；It is respectively Velocity vector and vector acceleration；

In iterative control process, formula (6) is expressed as:

${\stackrel{\·\·}{q}}_k+(d+2\mathrm{\ω}){\stackrel{\·}{q}}_k+{\mathrm{kq}}_k=u_k+d_k---\left(7\right)$

In formula, k is iterationses, and k is positive integer,q_k、u_k、d_kIt is respectivelyThe acceleration of the kth time of q, u, d Signal vector, rate signal vector, position signalling vector, input dominant vector, interference vector；

In described step 3) in, adaptive parameter estimation is carried out according to the dimensionless kinetic model of gyroscope, self adaptation is joined Number algorithm for estimating is:

${\widehat{\mathrm{\θ}}}_k\left(t\right)={\stackrel{\&overbar;}{\mathrm{\θ}}}_k+{\widehat{\mathrm{\θ}}}_{k-1}\left(t\right)---\left(9\right)$

Wherein θ is the vector being made up of system unknown parameter,Estimated value for θ, First for θ estimated value Initial value,Increment for the estimated value of θ during kth time iteration；Matrix γ ∈ r^8×8, γ is positive definite symmetric matrices, γ=diag (90, 90,90,90,90,90,90,90)；

β is arithmetic number；

For desired rate signal.

2. the adaptive iterative learning control method of gyroscope according to claim 1 is it is characterised in that in described step In rapid 4), the dimensionless kinetic model according to gyroscope and adaptive parameter estimation algorithm, carry out adaptive iteration study Control, control signal u_kT () is defined as:

Wherein matrix k_p∈r^2×2, k_d∈r^2×2, k_p、k_dIt is all positive definite symmetric matrices, Then when meeting iterated conditional unknown errors initial signal e_k(0)=0 and velocity error initial signalWhen, unknown errors Signal e_k(t) and velocity error initial signalBounded, andTime t be in iteration cycle [0, T] in.