CN105511268B - A kind of composite control method for train actuator failures - Google Patents

Abstract

The invention discloses a kind of composite control method for train actuator failures, comprise the following steps：S1, force analysis is carried out to Train's Longitudinal Movement, set up the lengthwise movement kinetic equation of train；S2, according to Train's Longitudinal Movement kinetic equation, set up Train's Longitudinal Movement state space equation；S3, according to actuator failures and Train's Longitudinal Movement state space equation, the Train's Longitudinal Movement state space equation set up in the case of actuator failures；S4, according to the train status space equation in the case of actuator failures, using observer and controller based on disturbance, set up train closed-loop dynamic equation；S5, the observer gain and controller gain obtained by LMI in the composite control method of train actuator failures, and then the actual displacement using observer and controller equation the control train based on disturbance and the desired displacement of speed convergence and speed.The present invention solves slope disturbance, the influence of gust disturbances and actuator failures to train.

Description

A kind of composite control method for train actuator failures

Technical field

The present invention relates to Train Control Technology field.More particularly, to a kind of for the compound of train actuator failures Control method.

Background technology

The performances such as comfortableness, convenience and the validity of train are how improved, is the research side that next ought cause concern To.Further to study train system, scholars set up simple substance point model by Newton's law, and simple substance point model is with the letter of its structure Singly it is widely used.In addition, also there are another train model-many Mass Models.Compared with simple substance point model, many particles The coupler force between adjacent compartment is considered in model, therefore, train model of many Mass Models closer to reality.

Based on above-mentioned simple substance point and many Mass Models, in order to obtain desired performance, a series of control strategy is employed In train system, such as PID control parameter, Self Adaptive Control, fuzzy control, optimal control and PREDICTIVE CONTROL.

Above-mentioned analysis is without simultaneously in view of the influence of frequency conversion fitful wind, actuator failures and slope resistance to train.

Accordingly, it is desirable to provide a kind of composite control method for train actuator failures.

The content of the invention

It is an object of the invention to provide a kind of composite control method for train actuator failures, solve slope and disturb The dynamic, influence of gust disturbances and actuator failures to train.

To reach above-mentioned purpose, the present invention uses following technical proposals：

A kind of composite control method for train actuator failures, the method comprises the following steps：

S1, force analysis is carried out to Train's Longitudinal Movement, set up the lengthwise movement kinetic equation of train；

S2, according to Train's Longitudinal Movement kinetic equation, set up Train's Longitudinal Movement state space equation；

S3, according to actuator failures and Train's Longitudinal Movement state space equation, the row set up in the case of actuator failures Car lengthwise movement state space equation；

S4, according to the train status space equation in the case of actuator failures, using the observer based on disturbance and control Device, sets up train closed-loop dynamic equation；

S5, obtained by LMI observer gain in the composite control method of train actuator failures and Controller gain, and then the actual displacement using observer and controller equation the control train based on disturbance and speed convergence phase The displacement of prestige and speed.

Preferably, the lengthwise movement kinetic equation of train is in step S1：

Wherein, m_iIt is the actual mass in the section of train i-th compartment, i=1,2 ..., n；K is the car for connecting two adjacent sections compartment The coefficient of elasticity of hook；T ∈ [0, T '], T ' are the run times of train；x_iT () is section reality of the compartment from 0 to t of train i-th Border displacement；It is the actual speed of the section compartment t of train i-th,Be train i-th section compartment t reality add Speed；u_iT () is the actual controling power that train i-th saves compartment t；c_o、c_vAnd c_aIt is Davis's coefficient；ψ_i(t)=m_igsin (θ_i(t)) it is slope resistance that train i-th saves compartment t, g represents acceleration of gravity；θ_iT () represents the gradient in the i-th section compartment Angle；Sin () is SIN function；It is fitful wind resistance that t is acted on the i-th section compartment.

Preferably, step S2 further includes following sub-step：

S2.1, the desired displacement in compartment of the setting section of train i-th, speed and acceleration are respectivelyWith Definition With reference to The lengthwise movement kinetic equation of the train, obtains the desired controling power in each compartment of train as follows：

Wherein, m_iIt is the actual mass in the section of train i-th compartment, i=1,2 ..., n；It is desired controling power；c_o、c_v And c_aIt is Davis's coefficient；It is the grade resistance on desired position suffered by the section of train i-th compartment；

S2.2, definitionIgnore higher order termObtain following Train's Longitudinal Movement Linear space equation：

Wherein,

The definition of parameter A and B is as follows respectively：

Represent real matrix.

Preferably, the Train's Longitudinal Movement state space equation in the case of the actuator failures is：

Wherein, parameter B_f=BL_f,Expression actuator failures parameter, and satisfaction 0≤ λ_i≤1。

Preferably, step S4 further includes following sub-step：

S4.1, the state expression formula for setting up following fitful wind model：

Wherein, W is the frequency matrix of fitful wind, andIt is known gust frequency value；L₁And L₄It is battle array The magnitude matrix of wind；Δ W (t) represents the frequency property matrix of fitful wind, and w (t) is the state in the state expression formula of fitful wind model Variable；

S4.2, setting (A, B_f) controllable, (W+ Δs W (t), BL₁) considerable, with reference to fitful wind model, design is following to be based on what is disturbed Observer：

Wherein,WithIt is respectively d₁The estimate of (t) and w (t), parameter L₄, it is known that unknown parameter L₂It is to be based on disturbing Dynamic observer gain；

Define error termWithThen the observer error based on disturbance is：

S4.3, design controller are as follows：

Wherein, unknown parameter N_uRepresent controller gain；

S4.4, basis observer error and controller based on disturbance, set up such as Train closed-loop dynamic equation：

Preferably, step S5 further includes following sub-step：

S5.1, definition system state variablesWith reference to train closed-loop dynamic equation, following augmented system is obtained：

Wherein,

S5.2, the reference output for defining augmented system：

Wherein, coefficient matrix

S5.3, it is defined as follows H_∞Performance index function

Wherein, γ is given normal number；

Obtained with reference to the method for Lyapunov analytic approach and LMI：For γ, there is scalar ε₁＞ 0, square Battle arrayMeet following linear MATRIX INEQUALITIES：

Wherein,

Observer gain based on disturbance is obtained by the LMIController gain

S5.4, actual displacement and the expectation of speed convergence using observer and controller equation the control train based on disturbance Displacement and speed.

Beneficial effects of the present invention are as follows：

Influence and effective attenuation or removal of the technical scheme effective compensation actuator failures of the present invention to train system The influence of slope resistance and unknown fitful wind resistance to train system, makes train system have good position and speed tracing Energy.

Brief description of the drawings

Specific embodiment of the invention is described in further detail below in conjunction with the accompanying drawings；

Fig. 1 shows the flow chart of the composite control method for train actuator failures；

Fig. 2 shows the force analysis schematic diagram of the lengthwise movement of train；

Fig. 3 shows to be directed to the schematic diagram of displacement error response curve in the composite control method of train actuator failures；

Fig. 4 shows the schematic diagram of the composite control method medium velocity error responses curve for train actuator failures；

Fig. 5 shows the single H for train actuator failures_∞The schematic diagram of displacement error response curve in control method；

Fig. 6 shows the single H for train actuator failures_∞The schematic diagram of control method medium velocity error responses curve.

Specific embodiment

In order to illustrate more clearly of the present invention, the present invention is done further with reference to preferred embodiments and drawings It is bright.Similar part is indicated with identical reference in accompanying drawing.It will be appreciated by those skilled in the art that institute is specific below The content of description is illustrative and be not restrictive, and should not be limited the scope of the invention with this.

When the composite control method for train actuator failures that the present embodiment is provided is for train actuator failures In position and speed tracking control, as shown in figure 1, the method comprises the following steps：

S1, force analysis is carried out to Train's Longitudinal Movement, set up the lengthwise movement kinetic equation of train；

S2, according to Train's Longitudinal Movement kinetic equation, set up Train's Longitudinal Movement state space equation；

S3, according to actuator failures and Train's Longitudinal Movement state space equation, the row set up in the case of actuator failures Car lengthwise movement state space equation；

S4, according to the train status space equation in the case of actuator failures, using the observer based on disturbance and control Device, sets up train closed-loop dynamic equation；

S5, obtained by LMI observer gain in the composite control method of train actuator failures and Controller gain, and then the actual displacement using observer and controller equation the control train based on disturbance and speed convergence phase The displacement of prestige and speed.

Wherein,

In step S1, the train N with reference to shown in Fig. 2 saves the force analysis figure of compartment lengthwise movement, in two adjacent sections compartment, Front compartment is to the coupler force φ (ε) of trunk：

φ (ε)=k ε=k (x_i(t)-x_i-1(t)) (1)

Wherein, k is the coefficient of elasticity of the hitch for connecting two adjacent sections compartment, k>0；ε is the relative position in two adjacent sections compartment Move；T ∈ [0, T '], T ' are the run times of train；x_iT () is section actual displacement of the compartment from 0 to t of train i-th, i= 1,2 ..., n.

The kinetic equation of Train's Longitudinal Movement is：

Wherein, m_iIt is the actual mass in the section of train i-th compartment；It is the actual speed of the section compartment t of train i-th,It is the actual acceleration of the section compartment t of train i-th；u_iT () is the actual controling power that train i-th saves compartment t, Controling power includes tractive force or brake force；c_o、c_vAnd c_aIt is Davis's coefficient, and is all higher than 0, Davis's coefficient of different trains Difference, c_o、c_vAnd c_aAccording to actual situation value；ψ_i(t)=m_igsin(θ_i(t)) be train i-th save compartment t slope Resistance, g represents acceleration of gravity；θ_iT () represents the angle of gradient in the i-th section compartment；Sin () is SIN function；It is t Act on the fitful wind resistance on the i-th section compartment.

Step S2 further includes following sub-step：

S2.1, the desired displacement in compartment of the setting section of train i-th, speed and acceleration are respectivelyWith Definition It is actual displacement x of the section compartment 0 of train i-th to t_i(t) and expectation position MoveBetween error, i.e.,It is the actual speed of the section compartment t of train i-thWith Desired speedBetween error, i.e.,It is the actual acceleration of the section compartment t of train i-th DegreeWith expectation accelerationBetween error, i.e.,v₀＞ 0 is the value of desired speed, is root According to the value that different requirements sets；With reference to above-mentioned Train's Longitudinal Movement kinetic equation, the desired controling power in each compartment of train is obtained It is as follows：

Wherein,It is desired controling power；It is the gradient on desired position suffered by the section of train i-th compartment Resistance.

S2.2, definitionIt is the actual controling power u of the section compartment t of train i-th_i(t) with Desired control powerBetween error, substituted into the kinetic equation of Train's Longitudinal Movement, ignore higher order termObtain following Train's Longitudinal Movement linear space equation：

Wherein,

The definition of parameter A and B is as follows respectively：

Represent real matrix.

In step S3, when actuator breaks down, performed as follows according to Train's Longitudinal Movement linear space establishing equation Train's Longitudinal Movement state space equation in the case of device failure：

Wherein, parameter B_f=BL_f,Expression actuator failures parameter, and satisfaction 0≤ λ_i≤ 1, and λ_i=0 represents that i-th actuator of train system is entirely ineffective；0 ＜ λ_i＜ 1 represents i-th execution of train system Device partial failure；λ_i=1 i-th actuator normal work for representing train system.

Step S4 further includes following sub-step：

S4.1, fitful wind expression formula are as follows：

Wherein, A_gRepresent the amplitude of fitful wind, t_stAnd t_endBetween representing respectively at the beginning of fitful wind is acted on train and terminate Time, cos () is cosine function.The form of fitful wind expression formula (6) is written as first form of formula in formula (7), will be remaining String function cos () sets up the state expression formula of following fitful wind model as the w (t) in (7)：

Wherein, W is the frequency matrix of fitful wind, L₁And L₄It is the magnitude matrix of fitful wind, and For known Gust frequency value, Δ W (t) represents the frequency property matrix of fitful wind, and it is known matrix to meet Δ W (t)=E Σ (t) F, E, F, and Unknown matrix Σ (t) meets Σ (t) Σ^TT ()≤I, w (t) are the state variable in the state expression formula of fitful wind model.

S4.2, setting (A, B_f) controllable, (W+ Δs W (t), BL₁) considerable, with reference to fitful wind model, design is following to be based on what is disturbed Observer：

Wherein,WithIt is respectively d₁The estimate of (t) and w (t), parameter L₄, it is known that unknown parameter L₂It is to be based on disturbing Dynamic observer gain.

Define error termWithThen the observer error based on disturbance is：

S4.3, design controller are as follows：

Wherein, unknown parameter N_uRepresent controller gain；

S4.4, basis observer error and controller based on disturbance, set up such as Train closed-loop dynamic equation：

Step S5 further includes following sub-step：

S5.1, one new system state variables of definitionWith reference to closed-loop system dynamical equation, one is obtained New augmented system：

Wherein,

S5.2, the reference output for defining augmented system：

Wherein, coefficient matrix

S5.3, it is defined as follows H_∞Performance index function

Wherein, γ is given normal number；

Obtained with reference to the method for Lyapunov analytic approach and LMI：For γ, there is scalar ε₁＞ 0, square Battle arrayMeet following linear MATRIX INEQUALITIES：

Wherein,

It is based on the observer gain for disturbing by what LMI can obtain train system The controller gain of train system is

S5.4, actual displacement and the expectation of speed convergence using observer and controller equation the control train based on disturbance Displacement and speed.

Below, in order to verify the present embodiment provide the composite control method for train actuator failures validity, Emulation experiment checking is carried out using MATLAB, and is explained in detail：

The many Mass Models of train that the present embodiment is provided, consider actuator failures, slope resistance and unknown fitful wind pair The influence of train position and speed tracing performance, using control (DOBC) method and H of the observer based on disturbance_∞Control method The composite controller being combined, makes closed-loop system Asymptotic Stability, with good position and speed tracing performance, and has to failure There is good robustness.

The Train Parameters of table 1

Pa-rameter symbols	Parameter value	Unit
				69000	kg
	80000	kg
				74000	kg
	83000	kg
				66000	kg
	48000	kg
				54000	kg
	76000	kg
			k	40000	N/m
	0.01176	N/kg
				0.00077616	N s/m kg
	0.000016

By LMI, the observer gain L based on disturbance is tried to achieve₂With controller gain N_uRespectively：

L₂=[0_2×8 L₁₂ L₂₂], N_u=[N₁₁ N₁₂ N₁₃]；

Wherein,

Based on above-mentioned parameter, simulating, verifying is carried out to the composite control method that the present embodiment is provided, obtain Fig. 3, Fig. 4.Wherein, Fig. 3 shows control (DOBC) strategy and H of the observer based on disturbance_∞The displacement in each compartment of control strategy Train system rings Curve, Fig. 4 is answered to show control (DOBC) strategy and H of the observer based on disturbance_∞Each compartment of control strategy Train system Velocity-response curve.

To prove the validity of the observer based on disturbance in the composite control method that the present embodiment is provided, using independent H_∞Control strategy, analogous diagram is as shown in Figure 5, Figure 6.Wherein, Fig. 5 shows single H_∞Each compartment of control strategy Train system Dynamic respond curve, Fig. 6 shows single H_∞The velocity-response curve in each compartment of control strategy Train system.

By above-mentioned analysis, it was demonstrated that composite control method for train actuator failures that the present embodiment is provided has Effect property.

Obviously, the above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not right The restriction of embodiments of the present invention, for those of ordinary skill in the field, may be used also on the basis of the above description To make other changes in different forms, all of implementation method cannot be exhaustive here, it is every to belong to this hair Obvious change that bright technical scheme is extended out changes row still in protection scope of the present invention.

Claims (2)

1. a kind of composite control method for train actuator failures, it is characterised in that the method comprises the following steps：

S1, force analysis is carried out to Train's Longitudinal Movement, sets up the lengthwise movement kinetic equation of train,

Wherein, m_iIt is the actual mass in the section of train i-th compartment, i=1,2 ..., n；K is the hitch for connecting two adjacent sections compartment Coefficient of elasticity；T ∈ [0, T '], T ' are the run times of train；X_iT () is section actual bit of the compartment from 0 to t of train i-th Move；It is the actual speed of the section compartment t of train i-th,It is the actual acceleration of the section compartment t of train i-th；u_i T () is the actual controling power that train i-th saves compartment t；c_o、c_vAnd c_aIt is Davis's coefficient；ψ_i(t)=m_igsin(θ_i(t)) It is the slope resistance of the section compartment t of train i-th, g represents acceleration of gravity；θ_iT () represents the angle of gradient in the i-th section compartment；sin () is SIN function；It is fitful wind resistance that t is acted on the i-th section compartment；

S2, according to Train's Longitudinal Movement kinetic equation, set up Train's Longitudinal Movement state space equation, S2.1, setting train i-th The section desired displacement in compartment, speed and acceleration are respectivelyWith, definition

$x_1^e\left(t\right)=x_2^e\left(t\right)=\mathrm{...}=x_n^e\left(t\right),{{\stackrel{\·}{x}}^e}_1\left(t\right)={{\stackrel{\·}{x}}^e}_2\left(t\right)=\mathrm{...}={{\stackrel{\·}{x}}^e}_n\left(t\right)=v_0,$

${{\stackrel{\·\·}{x}}^e}_1\left(t\right)={{\stackrel{\·\·}{x}}^e}_2\left(t\right)=\mathrm{...}={{\stackrel{\·\·}{x}}^e}_n\left(t\right)=0,{\tilde{x}}_i\left(t\right)=x_i\left(t\right)-x_i^e\left(t\right),{\stackrel{\·}{\tilde{x}}}_i\left(t\right)={\stackrel{\·}{x}}_i\left(t\right)-{\stackrel{\·}{x}}_i^e\left(t\right);,{\stackrel{\·\·}{\tilde{x}}}_i\left(t\right)={\stackrel{\·\·}{x}}_i\left(t\right)-{\stackrel{\·\·}{x}}_i^e\left(t\right);$

With reference to the lengthwise movement kinetic equation of the train, the desired controling power in each compartment of train is obtained as follows：

$\left\{\begin{array}{c}{u}_1^e\left(t\right)=c_o{m}_1+c_v{v}_0{m}_1+c_a{v}_0^2\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i\right)+{\mathrm{\ψ}}_1^e\left(t\right)\\ u_i^e\left(t\right)=c_o{m}_i+c_v{v}_0{m}_i+{\mathrm{\ψ}}_i^e\left(t\right),i=2,\mathrm{...},n\end{array}\right.$

Wherein, m_iIt is the actual mass in the section of train i-th compartment, i=1,2 ..., n；It is desired controling power；c_o、c_vWith c_aIt is Davis's coefficient；It is the grade resistance on desired position suffered by the section of train i-th compartment；

S2.2, definitionIgnore higher order termObtain as Train is vertical To the linear space equation of motion：

$\stackrel{\·}{\mathrm{\ξ}}\left(t\right)=A\mathrm{\ξ}\left(t\right)+Bu\left(t\right)+{\mathrm{Bd}}_1\left(t\right)-{\mathrm{Bd}}_2\left(t\right)$

Wherein,

$\mathrm{\ξ}\left(t\right)={\left[\begin{array}{cccccc}{\tilde{x}}_1\left(t\right)& \mathrm{...}& {\tilde{x}}_n\left(t\right)& {\stackrel{\·}{\tilde{x}}}_1\left(t\right)& \mathrm{...}& {\stackrel{\·}{\tilde{x}}}_n\left(t\right)\end{array}\right]}^T,$

$d_2\left(t\right)={\[{\widetilde{\mathrm{\ψ}}}_1\left(t\right)\mathrm{...}{\widetilde{\mathrm{\ψ}}}_n\left(t\right)\]}^T,$

$u\left(t\right)={\[{\tilde{u}}_1\left(t\right)\mathrm{...}{\tilde{u}}_n\left(t\right)\]}^T;$

The definition of parameter A and B is as follows respectively：

Represent real matrix；

S3, according to actuator failures and Train's Longitudinal Movement state space equation, the train set up in the case of actuator failures is indulged To motion state space equation, the Train's Longitudinal Movement state space equation in the case of the actuator failures is：

$\stackrel{\·}{\mathrm{\ξ}}\left(t\right)=A\mathrm{\ξ}\left(t\right)+B_{f}u\left(t\right)+{\mathrm{Bd}}_1\left(t\right)-{\mathrm{Bd}}_2\left(t\right)$

Wherein, parameter B_f=BL_f,Represent actuator failures ginseng Number, and meet 0≤λ_i≤1；

S4, according to the train status space equation in the case of actuator failures, using observer and controller based on disturbance, build Vertical train closed-loop dynamic equation, S4.1, sets up the state expression formula of following fitful wind model：

$\left\{\begin{array}{c}{d}_1\left(t\right)=L_{1}w\left(t\right)+L_4\\ \stackrel{\·}{w}\left(t\right)=(W+\mathrm{\Δ}W(t\left)\right)w\left(t\right)\end{array}\right.$

Wherein, W is the frequency matrix of fitful wind, and It is known gust frequency value；L₁And L₄It is fitful wind Magnitude matrix；Δ W (t) represents the frequency property matrix of fitful wind, and w (t) is the state variable in the state expression formula of fitful wind model；

S4.2, setting (A, B_f) controllable, (W+ Δs W (t), BL₁) considerable, with reference to fitful wind model, the following observation based on disturbance of design Device：

$\left\{\begin{array}{c}{\hat{d}}_1\left(t\right)=L_1\hat{w}\left(t\right)+L_4\\ \tilde{w}\left(t\right)=v\left(t\right)-L_2\mathrm{\ξ}\left(t\right)\\ \stackrel{\·}{v}\left(t\right)=(W+\mathrm{\Δ}W(t)+L_2{\mathrm{BL}}_1)\hat{w}\left(t\right)+L_2{\mathrm{BL}}_4+L_2\left(A\mathrm{\ξ}\right(t)+B_{f}u(t\left)\right)\end{array}\right.$

Wherein,WithIt is respectively d₁The estimate of (t) and w (t), parameter L₄, it is known that unknown parameter L₂It is to be based on disturbing Dynamic observer gain；

Define error termWithWith based on disturbance Observer error be：

$\left\{\begin{array}{c}{d}_1\left(t\right)=L_1\hat{w}\left(t\right)\\ \stackrel{\·}{\tilde{w}}\left(t\right)=(W+\mathrm{\Δ}W(t)+L_2{\mathrm{BL}}_1)\hat{w}\left(t\right)-L_2{\mathrm{Bd}}_2\left(t\right)\end{array}\right.$

S4.3, design controller are as follows：

$u\left(t\right)=N_u\mathrm{\ξ}\left(t\right)-L_f^{-1}{\hat{d}}_1\left(t\right))$

Wherein, unknown parameter N_uRepresent controller gain；

S4.4, basis observer error and controller based on disturbance, set up such as Train closed-loop dynamic equation：

$\stackrel{\·}{\mathrm{\ξ}}\left(t\right)=(A+B_f{N}_u)\mathrm{\ξ}\left(t\right)+{\mathrm{BL}}_1\tilde{w}\left(t\right)-{\mathrm{Bd}}_2\left(t\right);$

S5, the observer gain in the composite control method of train actuator failures and control are obtained by LMI Device gain, so it is desired using the actual displacement and speed convergence of observer and controller equation the control train based on disturbance Displacement and speed.

2. the composite control method for train actuator failures according to claim 1, it is characterised in that step S5 enters One step includes following sub-step：

S5.1, definition system state variablesWith reference to train closed-loop dynamic equation, following augmented system is obtained：

$\stackrel{\·}{\mathrm{\η}}\left(t\right)=\stackrel{\‾}{A}\left(t\right)\mathrm{\η}\left(t\right)+\stackrel{\‾}{M}{d}_2\left(t\right)$

Wherein,

S5.2, the reference output for defining augmented system：

$z\left(t\right)=C_1\mathrm{\ξ}\left(t\right)+C_2\tilde{w}\left(t\right)=\stackrel{\‾}{C}\mathrm{\η}\left(t\right)$

Wherein, coefficient matrix

S5.3, it is defined as follows H_∞Performance index function

$J={\∫}_0^{T_1}\left(z^T\right(t\left)z\right(t)-{{\mathrm{\γd}}_2}^T(t\left)d_2\right(t\left)\right)dt$

Wherein, γ is given normal number；

Obtained with reference to the method for Lyapunov analytic approach and LMI：For γ, there is scalar ε₁＞ 0, matrixMeet following linear MATRIX INEQUALITIES：

$\left[\begin{array}{ccccc}{\widehat{\mathrm{\&Phi;}}}_1+{\widehat{\mathrm{\&Phi;}}}_2& {\mathrm{BL}}_1& -B& 0& {\hat{A}}_1{C}_1^T\\ {\left({\mathrm{BL}}_1\right)}^T& {\widehat{\mathrm{\&Phi;}}}_3+{\widehat{\mathrm{\&Phi;}}}_4+{\mathrm{\&epsiv;}}_1{F}^{T}F& -{\hat{A}}_{4}B& {\hat{A}}_{2}E& C_2^T\\ -B^T& -{\left({\hat{A}}_{4}B\right)}^T& -\mathrm{\&gamma;}I& 0& 0\\ 0& {\left({\hat{A}}_{2}E\right)}^T& 0& -{\mathrm{\&epsiv;}}_{1}I& 0\\ C_1{\hat{A}}_1^T& C^T& 0& 0& -I\end{array}\right]<0$

Wherein,

${\widehat{\mathrm{\&Phi;}}}_1=A{\hat{A}}_1+{\hat{A}}_1^T{A}^T,{\widehat{\mathrm{\&Phi;}}}_2=B_f{\hat{A}}_3+{\hat{A}}_3^T{B}_f^T,{\widehat{\mathrm{\&Phi;}}}_3={\hat{A}}_{2}W+W^T{\hat{A}}_2^T,{\widehat{\mathrm{\&Phi;}}}_4={\hat{A}}_4{\mathrm{BL}}_1+L_1^T{B}^T{\hat{A}}_4^T;$

Observer gain based on disturbance is obtained by the LMIController gain

S5.4, the actual displacement using observer and controller equation the control train based on disturbance and the desired position of speed convergence Move and speed.