CN104360679A - Train suspension system fault diagnosis and fault-tolerant control method based on dynamic actuator - Google Patents

Abstract

The invention discloses a train active suspension system fault diagnosis and fault-tolerant control device and a train active suspension system fault diagnosis and fault-tolerant control method based on a dynamic actuator, and belongs to the technical field of automatic control. The train active suspension system fault diagnosis and fault-tolerant control device based on the dynamic actuator comprises a dynamic actuator fault injection module, a platform control module, a fault diagnosis module, a real-time monitoring module and a data acquiring module; and the dynamic actuator adopts an electromagnetic actuator. By the online parameter estimation and adaptive robust fault-tolerant control method based on the dynamic actuator, limitation of the traditional fault diagnosis device under the condition that outside disturbance exists and faults of a plurality of actuators occur synchronously is avoided. The train active suspension system fault diagnosis and fault-tolerant control device and the train active suspension system fault diagnosis and fault-tolerant control method based on the dynamic actuator are easy to operate and high in implementability, and can be used for verifying feasibility on fault diagnosis and state monitoring of a train active suspension system actuating mechanism.

Description

Based on the train suspension system fault diagnosis and fault-tolerant control method of dynamicer

Technical field

The present invention relates to automatic control technology field, particularly a kind of train active suspension fault diagnosis and fault-tolerant control device and method based on dynamicer.

Background technology

Train suspension system is for the car body and the bogie that support train, and isolating the power be applied on wheel produced by track irregularity has important function and significance with the control vehicle body attitude relevant with raceway surface to provide comfortable riding quality.

According to the difference of control form, suspension is divided into three classes substantially: passive suspension system (fixing spring, damping structure), semi-active suspension system (spring, variable damper structure) and active suspension (spring, damping, actuator structure).Passive suspension structure is simple, design difficulty is low, cheap, reliability is high, but belongs to opened loop control due to it, and do not carry out error correction by signal feedback, therefore damping property is limited, can not adapt to multiple rail conditions; Semi-active suspension is damping adjustable vibration damper by replacing damping element, system capacity is consumed little, and structure is simple, and has certain adaptive faculty to the track condition of change; Active Suspensions reaches best performance by the riding comfort that increases active power generating means and appropriate control law and make train under different driving conditions and control stability compromise, and active suppression track irregularity brings the impact of car body, therefore its damping property is obviously better than passive suspension and semi-active suspension.

Train active suspension is inevitably subject to the interference of external disturbance and actuator failures etc. in train travelling process.Fault refers to that at least one characteristic of system or parameter occur larger deviation and beyond acceptable scope, cause the performance of system be starkly lower than its normal level and be difficult to the function of expection.The position that the classification of fault can occur according to fault is divided into sensor fault, actuator failures and components and parts fault, is divided into mutation failure and soft fault, is divided into multiplicative fault and additivity fault according to modeling angle according to nature of trouble.Actuator failures generally includes three kinds of operation conditionss: normally work, now do not consider fault; Actuator partial failure due to the reason such as part aging, external interference; And actuator complete failure.

In order to ensure ride comfort security in train travelling process and control stability, system needs disturbance to external world or the situations such as actuator failures occurs to have Ability of emergency management, so carry out fault detect to system and identification is very necessary.

Summary of the invention

Technical matters solved by the invention is to provide a kind of train active suspension fault diagnosis and fault-tolerant control device and method based on dynamicer, improve system reliability, ensure the ride comfort security in train travelling process and control stability, when effectively estimating time and size that fault occurs in system when some signal or component failure and giving the alarm.

The technical solution realizing the object of the invention is: a kind of train active suspension fault diagnosis and fault-tolerant control device based on dynamicer, comprise dynamicer direct fault location module, platform control module, fault diagnosis module, real-time monitoring module and data acquisition module, described dynamicer is electromagnetic actuator, wherein dynamicer direct fault location module is connected with platform control module, the failure message of simulation is supplied to platform control module, and show fault characteristic by platform control module, the displacement information that platform control module will be recorded by data acquisition module, velocity information and acceleration information are transferred to fault diagnosis module, fault diagnosis module is connected with real-time monitoring module, the malfunction of detection is shown, described fault diagnosis module is connected with platform control module simultaneously, namely carry out, after detection identifies, faults-tolerant control is restrained information transmission to platform control module to fault-signal.

Further, described platform control module comprises computing machine, power amplifier, signal compiling and conversion equipment, with the train suspension system analog platform of electromagnetic actuator control system, wherein electromagnetic actuator control system comprises non-brush permanent-magnet DC motor, electric machine control system and ball-screw transmission mechanism, described non-brush permanent-magnet DC motor is dynamicer, dynamicer is divided into the second order dynamicer of first-order dynamic actuator and popularization, train suspension system analog platform comprises bogie, bogie integration test cabinet and sensor, described computing machine is connected with train suspension system analog platform by power amplifier, described train suspension system analog platform is compiled by signal simultaneously and conversion equipment is connected with computing machine.

Further, described fault diagnosis module comprises the fault detect of distribution and identification module and ADAPTIVE ROBUST fault-tolerant controller, and the fault detect of described distribution and identification module comprise and be distributed in observer on each dynamicer and synergistic residual signals generation module with it.

The present invention also provide a kind of based on described in claim 1 based on the fault diagnosis and fault-tolerant control method of the fault diagnosis and fault-tolerant control device of dynamicer, comprise the following steps:

Step 1, train suspension system analog platform with many bodies dynamic model of train active suspension for research object, described model is made up of two motor-cars and a trailer, two motor-cars are respectively car body 1 and car body 3, a trailer is car body 2, the passive power of the secondary suspender between the car body of three cars and bogie depends primarily on the relative displacement of car body and bogie, joint joining place is simulated with spring, the active controlling force of active suspension is produced by the electromagnetic actuator control system be added on passive suspension spring and damping shock absorber basis, additional interference is the irregular input of track, regard the car body of three cars and bogie as barycenter respectively and force analysis is carried out to it, consider the vertical and luffing of car body and the catenary motion of bogie, using car body working direction as lateral shaft, using suffered gravity direction as vertical axle, vertical deviation is car body and the displacement of bogie on vertical axle, the angle of pitch is the angle that car body luffing departs from lateral shaft, according to dynamic balance and the equalising torque of each barycenter, the kinetics equation obtaining train active suspension many bodies dynamic model is:

$m_p{\stackrel{\·\·}{y}}_1+c_1{\stackrel{\·}{y}}_1-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1-c_1{\stackrel{\·}{y}}_4+(k_1+k)y_1-{\mathrm{ky}}_2+({\mathrm{kd}}_2-k_1{d}_1){\mathrm{\θ}}_1+{\mathrm{kd}}_3{\mathrm{\θ}}_2-k_1{y}_4=f_1$

$m_t{\stackrel{\·\·}{y}}_2+c_2{\stackrel{\·}{y}}_2-c_2{\stackrel{\·}{y}}_5-{\mathrm{ky}}_1+(k_2+2k)y_2-{\mathrm{ky}}_3-{\mathrm{kd}}_2{\mathrm{\θ}}_1+{\mathrm{kd}}_2{\mathrm{\θ}}_3-k_2{y}_5=f_2$

$m_p{\stackrel{\·\·}{y}}_3+c_1{\stackrel{\·}{y}}_3+c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{\stackrel{\·}{y}}_6-{\mathrm{ky}}_2+(k_1+k)y_3-{\mathrm{kd}}_3{\mathrm{\θ}}_2+(k_1{d}_1-{\mathrm{kd}}_2){\mathrm{\θ}}_3-k_1{y}_6=f_3$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_1-c_1{d}_1{\stackrel{\·}{y}}_1+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_1+c_1{d}_1{\stackrel{\·}{y}}_4+({\mathrm{kd}}_2-k_1{d}_1)y_1-{\mathrm{kd}}_2{y}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_1+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+k_1{d}_1{y}_4=-d_1{f}_1$

$I_t{\stackrel{\·\·}{\mathrm{\θ}}}_2+{\mathrm{kd}}_3{y}_1-{\mathrm{kd}}_3{y}_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_1+2{{\mathrm{kd}}_3}^2{\mathrm{\θ}}_2+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_3=0$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_3+c_1{d}_1{\stackrel{\·}{y}}_3+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{d}_1{\stackrel{\·}{y}}_6+{\mathrm{kd}}_2{y}_2+(k_1{d}_1-{\mathrm{kd}}_2)y_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_3-k_1{d}_1{y}_6=d_1{f}_3$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_4-c_1{\stackrel{\·}{y}}_1+c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1+(c_1+c_3){\stackrel{\·}{y}}_4-k_1{y}_1+k_1{d}_1{\mathrm{\θ}}_1+(k_1+k_3)y_4=k_3{y}_7+c_3{\stackrel{\·}{y}}_7-f_1$

$m_{\mathrm{tb}}{\stackrel{\·\·}{y}}_5-c_2{\stackrel{\·}{y}}_2+(c_2+c_4){\stackrel{\·}{y}}_5-k_2{y}_2+(k_2+k_4)y_5=k_4{y}_8+c_4{\stackrel{\·}{y}}_8-f_2$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_6-c_1{\stackrel{\·}{y}}_3-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3+(c_1+c_3){\stackrel{\·}{y}}_6-k_1{y}_3-k_1{d}_1{\mathrm{\θ}}_3+(k_1+k_3)y_6=k_3{y}_9+c_3{\stackrel{\·}{y}}_9-f_3$

Wherein: m _p, m _t, m _pb, m _tbbe respectively motor-car quality, trailer quality, motor car bogie quality, trailer bogie quality, I _p, I _tbe respectively motor-car pitching inertia, trailer pitching inertia, d ₁, d ₂, d ₃be respectively Edge Distance before and after motor-car center of gravity and hanging position distance, motor-car center of gravity and car back edge distance, trailer center of gravity and car, k, k ₁, k ₂, k ₃, k ₄be respectively the stiffness factor of joint joining place spring, the secondary pendulum spring of motor-car, the secondary pendulum spring of trailer, the secondary pendulum spring of motor car bogie, the secondary pendulum spring of trailer bogie, c ₁, c ₂, c ₃, c ₄be respectively the ratio of damping that motor-car secondary hangs, trailer secondary hangs, motor car bogie secondary hangs, trailer bogie secondary hangs, f ₁, f ₂, f ₃for the active controlling force of car body 1, car body 2, car body 3, y ₁, y ₂, y ₃be respectively the vertical deviation of car body 1, car body 2, car body 3 center of gravity, θ ₁, θ ₂, θ ₃be respectively the angle of pitch of three body gravities, y ₄, y ₅, y ₆be respectively the vertical deviation of three bogie centers of gravity, then the suspender displacement of train and joint are connected displacement and can be expressed as:

y ₁₀＝y ₁-d ₁θ ₁，y ₁₂＝y ₁+d ₂θ ₁，y ₁₃＝y ₂-d ₃θ ₂，

y ₂₄＝y ₂+d ₃θ ₂，y ₂₃＝y ₃-d ₂θ ₃，y ₁₁＝y ₃+d ₁θ ₃；

Wherein: y ₁₀for the suspender displacement of car body 1, y ₁₂for the joint of car body 1 is connected displacement, y ₁₃and y ₂₄for the joint of car body 2 is connected displacement, y ₂₃for the joint of car body 3 is connected displacement, y ₁₁for the suspender displacement of car body 3;

Above-mentioned equation is determined under following hypothesis relation:

1. all train compositions are rigidity;

2. train composition Striking symmetry;

3. the train body center just heart and center of gravity place in the structure;

4. the luffing angle change of car body is less than 5 °;

Step 2, determine the description form of adopted dynamicer model, i.e. first-order dynamic actuator model or second order dynamicer model, then the integrality space equation being obtained train active suspension by the motor characteristic of electromagnetic actuator control system and control characteristic;

When adopting first-order dynamic actuator model, described model is the core component of electromagnetic actuator and the single order simplified model of non-brush permanent-magnet DC motor:

$u=U_s-u_e=L_s\frac{\mathrm{di}}{\mathrm{dt}}+\mathrm{Ri}$

Wherein: u is the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor, and i is electric current, U _sand u _ebe respectively equivalent source voltage and back electromotive force, L _sfor inductance coefficent, R is phase resistance, non-brush permanent-magnet DC motor and electric machine control system and ball-screw transmission mechanism form electromagnetic actuator control system jointly, then by the control characteristic of described electromagnetic actuator control system obtain its actual export to the vertical acting force of suspension be:

Wherein: T _lfor the torque of the actual output of motor, P _hfor ball-screw helical pitch, T _mfor motor output torque, J _rfor the moment of inertia of rotor, J _nfor the nut moment of inertia of ball-screw, ω is rotor rotating speed, K _tfor motor torque constant, i is control electric current, for electromagnetic actuator stretching speed and suspender travel speed;

for constant of the machine, for the equivalenting inertia torque of rotor and feed screw nut;

The integrality space equation then obtaining train active suspension is:

$\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bv}+\mathrm{E\η}=\stackrel{\‾}{A}x+\stackrel{\‾}{B}i+\stackrel{\‾}{E}\mathrm{\η}\\ {\stackrel{.}{i}}_j=-{\mathrm{\λ}}_j({\mathrm{Ri}}_j-u_j),j=\mathrm{1,2,3}\end{array}$

Wherein: x=[x ₁ ^tx ₂ ^t] ^tfor state vector, x ₁=[y ₁ ^tθ ₁ ^ty ₄ ^ty ₂ ^tθ ₂ ^ty ₅ ^ty ₃ ^tθ ₃ ^ty ₆ ^t] ^t, $x_2={\left[\begin{array}{ccccccccc}{{\stackrel{.}{y}}_1}^T& {{\stackrel{.}{\mathrm{\θ}}}_1}^T& {{\stackrel{.}{y}}_4}^T& {{\stackrel{.}{y}}_2}^T& {{\stackrel{.}{\mathrm{\θ}}}_2}^T& {{\stackrel{.}{y}}_5}^T& {{\stackrel{.}{y}}_3}^T& {{\stackrel{.}{\mathrm{\θ}}}_3}^T& {{\stackrel{.}{y}}_6}^T\end{array}\right]}^T,$ I=[i ₁ ^ti ₂ ^ti ₃ ^t] ^tfor controlling electric current, $\mathrm{\η}\left(t\right)={\left[\begin{array}{cccccc}{y_7}^T& {y_8}^T& {y_9}^T& {{\stackrel{\·}{y}}_7}^T& {{\stackrel{\·}{y}}_8}^T& {{\stackrel{\·}{y}}_9}^T\end{array}\right]}^T$ For the interference that the irregular input of track produces, i _jfor dynamicer exports, u _jfor dynamicer input, v be active controlling force and by

Obtain v=(I+JNB) ^-1(Ψ i-JNAx-JNE η), wherein I is the unit matrix of suitable dimension, and O is the null matrix of suitable dimension, J=diag{ [J _dj _dj _d], Ψ=diag{ [Φ Φ Φ] }, $A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ A ₁₁＝O ₉，A ₁₂＝I ₉， $B=\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right],$ B ₁＝O _9×3， $\stackrel{\‾}{B}=B{(I+\mathrm{JNB})}^{-1}\mathrm{\Ψ},$ $\stackrel{\‾}{E}=E-B{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},E=\left[\begin{array}{c}{E}_1\\ E_2\end{array}\right],E_1=O_{9\×6},$

$N=\left[\begin{array}{cccccccccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 1& -d_1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& d_1& -1\end{array}\right],$

$A_{21}=\left[\begin{array}{ccccccccc}-\frac{k_1+k}{m_p}& \frac{k_1{d}_1-{\mathrm{kd}}_2}{m_p}& \frac{k_1}{m_p}& \frac{k}{m_p}& -\frac{{\mathrm{kd}}_3}{m_p}& 0& 0& 0& 0\\ \frac{k_1{d}_1-{\mathrm{kd}}_2}{I_p}& -\frac{k_1{d_1}^2+{{\mathrm{kd}}_2}^2}{I_p}& -\frac{k_1{d}_1}{I_p}& \frac{{\mathrm{kd}}_2}{I_p}& -\frac{{\mathrm{kd}}_2{d}_3}{I_p}& 0& 0& 0& 0\\ \frac{k_1}{m_{\mathrm{pb}}}& -\frac{k_1{d}_1}{m_{\mathrm{pb}}}& -\frac{k_1+k_3}{m_{\mathrm{pb}}}& 0& 0& 0& 0& 0& 0\\ \frac{k}{m_t}& \frac{{\mathrm{kd}}_2}{m_t}& 0& -\frac{k_2+2k}{m_t}& 0& \frac{k_2}{m_t}& \frac{k}{m_t}& -\frac{{\mathrm{kd}}_2}{m_t}& 0\\ -\frac{{\mathrm{kd}}_3}{I_t}& -\frac{{\mathrm{kd}}_2{d}_3}{I_t}& 0& 0& -\frac{2{{\mathrm{kd}}_3}^2}{I_t}& 0& \frac{{\mathrm{kd}}_3}{I_t}& -\frac{{\mathrm{kd}}_2{d}_3}{I_t}& 0\\ 0& 0& 0& \frac{k_2}{m_{\mathrm{tb}}}& 0& -\frac{k_2+k_4}{m_{\mathrm{tb}}}& 0& 0& 0\\ 0& 0& 0& \frac{k}{m_p}& \frac{{\mathrm{kd}}_3}{m_p}& 0& -\frac{k_1+k}{m_p}& \frac{{\mathrm{kd}}_2-k_1{d}_1}{m_p}& \frac{k_1}{m_p}\\ 0& 0& 0& -\frac{{\mathrm{kd}}_2}{I_p}& -\frac{{\mathrm{kd}}_2{d}_3}{I_p}& 0& \frac{{\mathrm{kd}}_2-k_1{d}_1}{I_p}& -\frac{k_1{d_1}^2+{{\mathrm{kd}}_2}^2}{I_p}& \frac{k_1{d}_1}{I_p}\\ 0& 0& 0& 0& 0& 0& \frac{k_1}{m_{\mathrm{pb}}}& \frac{k_1{d}_1}{m_{\mathrm{pb}}}& -\frac{k_1+k_3}{m_{\mathrm{pb}}}\end{array}\right],$

$A_{22}=\left[\begin{array}{ccccccccc}-\frac{c_1}{m_p}& \frac{c_1{d}_1}{m_p}& \frac{c_1}{m_p}& 0& 0& 0& 0& 0& 0\\ \frac{c_1{d}_1}{I_p}& -\frac{c_1{d_1}^2}{I_p}& -\frac{c_1{d}_1}{I_p}& 0& 0& 0& 0& 0& 0\\ \frac{c_1}{m_{\mathrm{pb}}}& -\frac{c_1{d}_1}{m_{\mathrm{pb}}}& -\frac{c_1+c_3}{m_{\mathrm{pb}}}& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -\frac{c_2}{m_t}& 0& \frac{c_2}{m_t}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& \frac{c_2}{m_{\mathrm{tb}}}& 0& -\frac{c_2+c_4}{m_{\mathrm{tb}}}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -\frac{c_1}{m_p}& -\frac{c_1{d}_1}{m_p}& \frac{c_1}{m_p}\\ 0& 0& 0& 0& 0& 0& -\frac{c_1{d}_1}{I_p}& -\frac{c_1{d_1}^2}{I_p}& \frac{c_1{d}_1}{I_p}\\ 0& 0& 0& 0& 0& 0& \frac{c_1}{m_{\mathrm{pb}}}& \frac{c_1{d}_1}{m_{\mathrm{pb}}}& -\frac{c_1+c_3}{m_{\mathrm{pb}}}\end{array}\right],B_2=\left[\begin{array}{ccc}\frac{1}{m_p}& 0& 0\\ -\frac{d_1}{I_p}& 0& 0\\ -\frac{1}{m_{\mathrm{pb}}}& 0& 0\\ 0& \frac{1}{m_t}& 0\\ 0& 0& 0\\ 0& -\frac{1}{m_{\mathrm{tb}}}& 0\\ 0& 0& \frac{1}{m_p}\\ 0& 0& \frac{d_1}{I_p}\\ 0& 0& -\frac{1}{m_{\mathrm{pb}}}\end{array}\right],$

$E_2=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& \frac{k_4}{m_{\mathrm{tb}}}& 0& 0& \frac{c_4}{m_{\mathrm{tb}}}& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}\end{array}\right];$

When being generalized to second order dynamicer model, by the transport function of described first-order dynamic actuator model $G\left(s\right)=\frac{1}{L_{s}s+R}=\frac{{\mathrm{\λ}}_j}{s+{\mathrm{\λ}}_{j}R}$ Obtaining second-order model is:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{1j}{i}_{1j}-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}\frac{u_j}{R}\end{array}$

Wherein i _1jfor electric current, u _jfor voltage, R is resistance, and its proper polynomial is s ²+ λ _2js+ λ _1j=(s+ μ) (s+ λ _jr), make parameter μ > > 1, and then obtain λ _1j> > 1, λ _1j> > λ _2j;

Above-mentioned equation is determined under following hypothesis relation:

1. armature winding full symmetric, magnetic circuit is unsaturated, ignores the impact of teeth groove, commutation and armature reaction;

2. the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor is only considered;

3. the electromagnetic consumable of non-brush permanent-magnet DC motor is not considered;

4. winding inductance coefficient L _s≤ 0.005;

Step 3, set up dynamicer fault model according to the fault type of electromagnetic actuator;

Described first-order dynamic actuator failures model is:

${\stackrel{\·}{i}}_j=-{\mathrm{\α}}_j{\mathrm{\λ}}_j(R{i}_j-{\mathrm{\β}}_j{u}_j)$

Wherein α _jfor consider actuator generation motor overload even stall fault time fault parameter, when actuator motor runs well, α _j(t)=1; When motor overload even stall time, α _j(t)=0; Now due to the effect of current controller in electric machine control system, for time of failure; β _jfor considering fault parameter during actuator generation importation failure of removal, when actuator input is normal, β _j(t)=1, when actuator fractionated gain decays, wherein

In like manner setting up second order dynamicer fault model is:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})\end{array}$

Wherein i _1jcan be obtained by current sensor measurement;

The fault detect and the recognition system that step 4, the basis of dynamicer fault model determined in step 3 construct distribution carry out on-line parameter estimation for the fault of each actuator;

First-order dynamic actuator is adopted then to be constructed as follows observer:

${\stackrel{\stackrel{\·}{^}}{i}}_j=-{\mathrm{\λ}}_j({\hat{i}}_j-i_j)+{\mathrm{\λ}}_j{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j{u}_j-R{i}_j)$

Wherein be respectively i _j, α _j, β _jobserved reading, for making parameter estimation in known span, adopt projection operator design adaptive law, following adaptive law is provided to ensure error e to the parameter in described single order fault model _1j∈ L ^∞∩ L ²:

$\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}=\mathrm{Pr}{\mathrm{oj}}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_j{e}_{1j}{\mathrm{\δ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1$

$\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}=\mathrm{Pr}{\mathrm{oj}}_{[9,1]}\{-{\mathrm{\γ}}_{{\mathrm{\β}}_j}{\mathrm{\λ}}_j{e}_{1j}{\mathrm{\δ}}_{\mathrm{\βj}}\},\widehat{\mathrm{\β}}\left(0\right)=1$

Wherein: for adaptive gain, $e_{1j}={\hat{i}}_j-i_j$ For observational error, ${\mathrm{\δ}}_{{\mathrm{\α}}_j}={\widehat{\mathrm{\β}}}_j{u}_j-{\mathrm{Ri}}_j,$ ${\mathrm{\δ}}_{{\mathrm{\β}}_j}=u_j,$ Then according to Lyapunov stable theory, e _1j∈ L ^∞∩ L ²;

Second order dynamicer is adopted then to construct observer as follows:

${\stackrel{\stackrel{\·}{^}}{i}}_{1j}=-{\mathrm{\τ}}_j({\hat{i}}_{1j}-i_{1j})+({\mathrm{\λ}}_{\mathrm{Fj}}-{\mathrm{\λ}}_{2j}){i_{2j}}^F+{\mathrm{\λ}}_{1j}{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j$

Wherein: for i _1jobserved reading, ${i_{1j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{1j},{i_{2j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{2j},{u_j}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{u}_j$ For filtering variable, λ _fj> 0 is filter time constant, τ _jand ε _jfor the parameter to be designed for ensureing system stability, for making parameter estimation in known span, the same projection operator that adopts designs adaptive law, provides following adaptive law to ensure error e to parameter each in second order fault model and observer _2j∈ L ^∞∩ L ²:

$\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}=\mathrm{Pr}{\mathrm{oj}}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1$

$\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}=\mathrm{Pr}{\mathrm{oj}}_{[\mathrm{\η},1]}\{-{\mathrm{\γ}}_{{\mathrm{\β}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\βj}}\},\widehat{\mathrm{\β}}\left(0\right)=1$

${\stackrel{\·}{\mathrm{\ϵ}}}_j=-{\mathrm{\λ}}_{2j}{\mathrm{\ϵ}}_j-{\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}}_j{{\mathrm{\κ}}_{\mathrm{\αj}}}^F-{\mathrm{\α}}_j{\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}}_j\frac{{{\mathrm{\κ}}_{\mathrm{\βj}}}^F}{R},{\mathrm{\ϵ}}_j\left(0\right)=0$

Wherein: for adaptive gain, $e_{2j}={\hat{i}}_{1j}-i_{1j}$ For observational error, ${{\mathrm{\κ}}_{\mathrm{\αj}}}^F={{\widehat{\mathrm{\β}}}_j}^F\frac{{u_j}^F}{R}-{i_{1j}}^F,$ κ _{β j} ^f=u _j ^f, κ _{β j}=u _j, then according to Lyapunov stable theory, e _2j∈ L ^∞∩ L ²;

Step 5, the actuator failures parameter determination ADAPTIVE ROBUST faults-tolerant control rule estimated by step 4, making system have fault-tolerant ability to fault and robustness when there is external disturbance, completing the fault diagnosis based on dynamicer and faults-tolerant control; Be specially:

(1) obtained by first-order dynamic actuator failures model described in step 3 obtained further by singular perturbation theory or obtained by second order dynamicer fault model by singular perturbation theory and λ _1j> > 1, λ _1j> > λ _2jobtain further $i_{1j}\≅{\mathrm{\α}}_j{\mathrm{\β}}_j\frac{u_j}{R}+(1-{\mathrm{\α}}_j)i\left(t_{F_j}\right),$ Wherein $i\left(t_{F_j}\right)=i_r$ For $t\≥t_{F_j}$ Time motor transship the actuator after even stall fault and export;

(2) constitution realization jamproof LQG controller u _r=Gx, wherein for the feedback gain matrix of controller, P is following Riccati non trivial solution ${M=\stackrel{\‾}{C}}^T\stackrel{\‾}{Q}\stackrel{\‾}{D},$ $\stackrel{\‾}{C}=C-D{(I+\mathrm{JNB})}^{-1}\mathrm{JNA},\stackrel{\‾}{D}=D{(I+\mathrm{JNB})}^{-1}\mathrm{\ψ},$ $\stackrel{\‾}{F}=F-D{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},$ $F=\left[\begin{array}{cc}{O}_{12\×3}& O_{12\×3}\\ -I_3& O_3\end{array}\right],$ Wherein O is the null matrix of suitable dimension, and I is the unit matrix of suitable dimension, $\stackrel{\‾}{Q}=\mathrm{diag}\left\{\begin{array}{ccccccccccccccc}{q}_1& q_2& q_3& q_4& q_5& q_6& q_7& q_8& q_9& q_{10}& q_{11}& q_{12}& q_{13}& q_{14}& q_{15}\end{array}\right\},$ $\stackrel{\‾}{R}=\mathrm{diag}\left\{\begin{array}{ccc}{q}_{16}& q_{17}& q_{18}\end{array}\right\},$ Q ₁~ q ₁₈for quadratic performance function J _lthe performance weighting coefficient of middle property indices, $\begin{array}{c}{J}_l=\underset{T\→\∞}{\lim }\frac{1}{T}\underset{0}{\overset{T}{\∫}}[q_1{{\stackrel{..}{y}}_{10}}^2+q_2{{\stackrel{..}{y}}_1}^2+q_3{{\stackrel{..}{y}}_{12}}^2+q_4{{\stackrel{..}{y}}_{13}}^2+q_5{{\stackrel{..}{y}}_2}^2+q_6{{\stackrel{..}{y}}_{24}}^2+q_7{{\stackrel{..}{y}}_{23}}^2+q_8{{\stackrel{..}{y}}_3}^2+q_9{{\stackrel{..}{y}}_{11}}^2+q_{10}{(y_{10}-y_4)}^2\\ +q_{11}{(y_2-y_5)}^2+q_{12}{(y_{11}-y_6)}^2+q_{13}{(y_4-y_7)}^2+q_{14}{(y_5-y_8)}^2+q_{15}{(y_6-y_9)}^2+q_{16}{i_1}^2+q_{17}{i_2}^2\\ +q_{18}{i_3}^2]\mathrm{dt},\end{array}$

(3) adaptive controller of constitution realization faults-tolerant control $u_s=-S\widehat{\mathrm{\Σ}}{\widehat{\mathrm{\Λ}}}^T{\left(\widehat{\mathrm{\Λ}}\widehat{\mathrm{\Σ}}S\widehat{\mathrm{\Σ}}{\widehat{\mathrm{\Λ}}}^T\right)}^{-1}\left[\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{\stackrel{\‾}{B}}_j(1-{\widehat{\mathrm{\α}}}_{j}R)i_r\right],$ Wherein $\stackrel{\‾}{B}=\left[\begin{array}{ccc}{\stackrel{\‾}{B}}_1& {\stackrel{\‾}{B}}_2& {\stackrel{\‾}{B}}_3\end{array}\right],\widehat{\mathrm{\Λ}}=\left[\begin{array}{ccc}{\widehat{\mathrm{\α}}}_1{\stackrel{\‾}{B}}_1& {\widehat{\mathrm{\α}}}_2{\stackrel{\‾}{B}}_2& {\widehat{\mathrm{\α}}}_3{\stackrel{\‾}{B}}_3\end{array}\right],\widehat{\mathrm{\Σ}}=\mathrm{diag}\left(\left[\begin{array}{ccc}{\widehat{\mathrm{\β}}}_1& {\widehat{\mathrm{\β}}}_2& {\widehat{\mathrm{\β}}}_3\end{array}\right]\right),$ S > 0 is symmetric positive definite diagonal weight matrix;

(4) designing ADAPTIVE ROBUST fault-tolerant controller is u=u _r+ u _s.

Further, because second order dynamicer model is for observation i _2jthere is inconvenience in dynamic Design of Observer, therefore when actuator motor overload even stall time, set up following second order fault model:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-[{\mathrm{\λ}}_{2j}+(1-{\mathrm{\α}}_j){\mathrm{\ρ}}_j]i_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}(\frac{1}{R}{u}_j-i_{1j})\end{array}$

Wherein λ _2j+ ρ _j> > 1; When motor runs well, α _j(t)=1, when motor overload even stall time, α _j(t)=0, i _1j(t _fj)=i _r, and i _2jwill with λ _2j+ ρ _jspeed asymptotic convergence in zero, by select ρ _jvalue, make fault occur after i _1jand i _2jall can rapidly converge to zero with arbitrary speed; And when losing efficacy in actuator importation, set up following second order fault model:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})\end{array}$

And hypothesis is under fault existence condition, λ _2jenough large to ensure i _2jcan zero be rapidly converged to, then make ρ _j=0, obtain second order dynamicer fault block mold.

The present invention compared with prior art, its remarkable advantage is: (1) adopts software fault injection method, do not destroy the integrality of train active suspension and electromagnetic actuator control system, and can the position of unrestricted choice direct fault location and size, without the need to extra hardware device, to direct fault location, topworks does not cause physical damage; (2) utilize electromagnetic actuator control technology to suppress vibration, Conversion of Energy mode is simple, and efficiency is higher, and has low-friction coefficient and linear mechanical characteristic, also can synchronization implementation energy regenerating; (3) fault detect distributed and recognition system, to each dynamicer independent operating observer, only use local message and do not need the status information of the overall situation to realize the on-line tuning estimated fault parameter; (4) dynamicer can adapt to the situation that multiple dissimilar actuator failures synchronously occurs under the immesurable condition of speed only having actuator output to survey; (5) the ADAPTIVE ROBUST fault-tolerant controller designed by can be deposited in case in external disturbance, parameter estimation result is utilized to make system have fault-tolerant ability to fault, ensure the robustness of system state and parameter estimation, thus ensure ride comfort security and control stability; (6) real-time faults injection condition, current topworks duty and system performance index change in human-computer interaction interface, realizes fault pre-alarming and Real-Time Monitoring; (7) for fault diagnosis observer and the ADAPTIVE ROBUST fault-tolerant controller of the train active suspension design distribution based on dynamicer, both achieved and the on-line tuning of multiple dissimilar actuator failures parameter had been estimated, restrained effectively again the adverse effect of external disturbance to system, make system have fault-tolerant ability to fault and robustness simultaneously; (8) the present invention may be used for actuator failure analysis and the systems reliability analysis in train active suspension semi-physical simulation stage.

Accompanying drawing explanation

Fig. 1 is the train active suspension trouble-shooter schematic diagram based on dynamicer of the present invention.

Fig. 2 is train many bodies dynamic model.

Fig. 3 is electric machine control system.

Fig. 4 is the current estimation error of dynamicer when breaking down and parameter estimation result, wherein (a) is current estimation error time inefficacy in actuator importation, b () is β parameter estimation time inefficacy in actuator importation, (c) for motor overload even stall time current estimation error, (d) for motor overload even stall time alpha parameter estimate.

Fig. 5 be 15 performance index of car body 1 under the effect of electromagnetic actuator Active Suspensions with the Contrast on effect of passive suspension, wherein (a) is the contrast of car precursor vertical acceleration, b () is the contrast of center of gravity vertical acceleration, c () is body vertical acceleration contrast after car, d () is that bogie 1 hangs the contrast of dynamic stroke, (e) takes turns movement of the foetus displacement comparison for bogie 1.

The performance index of car body when Fig. 6 is actuator fault, the performance index when electromagnetic actuator that wherein (a) and (b) is car body 1 breaks down, the performance index when electromagnetic actuator that (c) and (d) is car body 3 breaks down.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further illustrated.

As shown in Figure 1, a kind of train active suspension fault diagnosis and fault-tolerant control device based on dynamicer, comprise dynamicer direct fault location module 1, platform control module, fault diagnosis module, real-time monitoring module 10 and data acquisition module 9, described dynamicer is electromagnetic actuator, wherein dynamicer direct fault location module is connected with platform control module, the failure message of simulation is supplied to platform control module, and show fault characteristic by platform control module, the displacement information that platform control module will be recorded by data acquisition module, velocity information and acceleration information are transferred to fault diagnosis module, fault diagnosis module is connected with real-time monitoring module, the malfunction of detection is shown, described fault diagnosis module is connected with platform control module simultaneously, namely carry out, after detection identifies, faults-tolerant control is restrained information transmission to platform control module to fault-signal.

Described platform control module comprises computing machine 2, power amplifier 3, signal compiling and conversion equipment 5, with the train suspension system analog platform 4 of electromagnetic actuator control system, wherein electromagnetic actuator control system comprises non-brush permanent-magnet DC motor, electric machine control system and ball-screw transmission mechanism, described non-brush permanent-magnet DC motor is dynamicer, dynamicer is divided into the second order dynamicer of first-order dynamic actuator and popularization, train suspension system analog platform comprises bogie, bogie integration test cabinet and sensor, described computing machine 2 is connected with train suspension system analog platform 4 by power amplifier 3, described train suspension system analog platform 4 is compiled by signal simultaneously and conversion equipment 5 is connected with computing machine 2.

Described fault diagnosis module comprises the fault detect of distribution and identification module 7 and ADAPTIVE ROBUST fault-tolerant controller 8, and the fault detect of described distribution and identification module 7 comprise and be distributed in observer on each dynamicer and synergistic residual signals generation module with it.

More detailed description, device of the present invention consists of the following components:

1. electromagnetic actuator control system, comprises non-brush permanent-magnet DC motor, electric machine control system and ball-screw transmission mechanism;

2. train suspension system analog platform, comprise bogie, bogie integration test cabinet and sensor, wherein data that sensor is surveyed by bus transfer to switch board, the bus form that switch board is connected with bogie is RS232 serial bus, and Programmable Logic Controller chip is housed in switch board, language used is PLC, can change controling parameters as requested;

3. computing machine requires to be provided with MATLAB, LabVIEW, real-time control software QuaRC etc.;

4. fault diagnosis module, comprise software fault injection, method for diagnosing faults design, here the injection of fault can cause the loss of actuator voltage, the fault detect and the recognition system that build distribution carry out online fault parameter estimation to train active suspension, design fault-tolerant controller when the loss of voltage, make the runnability that system keeps certain;

5. machine Interaction Interface Design, realizes fault pre-alarming and monitoring, and QuaRC software can be connected with MATLAB/SIMULINK/RTW or LabVIEW here, and the interface fault state of detection being presented at design is preserved.

Be connected on bogie integration test cabinet and power amplifier with white wire and black line respectively by the encoder port on the data acquisition card in data acquisition module and analog output port, corresponding power supply black line is connected on train suspension system analog platform.The instruction that computing machine sends is changed by signal acquiring board D/A, amplify drive motor by power amplifier to run, detect train displacement, speed and acceleration signal by the scrambler on data acquisition card, the signal of collection is changed by signal acquiring board A/D and is exported to computing machine.

By start-up simulation machine, power up to power amplifier and drive electromagnetic actuator and bogie integration test cabinet; Then set the characteristic information of the contingent specific fault of motor, comprise fault type, start end time, fault parameter, the failure message according to setting carries out signal transacting to control signal, outputs to motor, simulated implementation dynamicer fault; By distribution fault detect and identification module in multiple observer and designed adaptive law, realize the On-line Estimation to fault parameter, and estimated result fed back in electromagnetic actuator control system by adaptive fusion device; Finally, with data acquisition card, signal is gathered, the displacement of analytic system, speed, acceleration signal and voltage signal the Performance Evaluating Indexes of observing system.

The fault diagnosis and fault-tolerant control method of described fault diagnosis and fault-tolerant control device, comprises the following steps:

Step 1, train suspension system analog platform with many bodies dynamic model of train active suspension for research object, described model is made up of two motor-cars and a trailer, two motor-cars are respectively car body 1 and car body 3, a trailer is car body 2, the passive power of the secondary suspender between car body and bogie depends primarily on the relative displacement of car body and bogie, joint joining place is simulated with spring, the active controlling force of active suspension is produced by the electromagnetic actuator control system be added on passive suspension spring and damping shock absorber basis, additional interference is the irregular input of track, regard the car body of three cars and bogie as barycenter respectively and force analysis is carried out to it, for simplicity, only consider the catenary motion of the vertical of car body and luffing and bogie, therefore using car body working direction as lateral shaft, using suffered gravity direction as vertical axle, vertical deviation is car body and the displacement of bogie on vertical axle, the angle of pitch is the angle that car body luffing departs from lateral shaft, according to dynamic balance and the equalising torque of each barycenter, obtain the kinetics equation of train active suspension many bodies dynamic model, as Fig. 2,

The kinetics equation of described train active suspension many bodies dynamic model is:

$m_p{\stackrel{\·\·}{y}}_1+c_1{\stackrel{\·}{y}}_1-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1-c_1{\stackrel{\·}{y}}_4+(k_1+k)y_1-{\mathrm{ky}}_2+({\mathrm{kd}}_2-k_1{d}_1){\mathrm{\θ}}_1+{\mathrm{kd}}_3{\mathrm{\θ}}_2-k_1{y}_4=f_1$

$m_t{\stackrel{\·\·}{y}}_2+c_2{\stackrel{\·}{y}}_2-c_2{\stackrel{\·}{y}}_5-{\mathrm{ky}}_1+(k_2+2k)y_2-{\mathrm{ky}}_3-{\mathrm{kd}}_2{\mathrm{\θ}}_1+{\mathrm{kd}}_2{\mathrm{\θ}}_3-k_2{y}_5=f_2$

$m_p{\stackrel{\·\·}{y}}_3+c_1{\stackrel{\·}{y}}_3+c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{\stackrel{\·}{y}}_6-{\mathrm{ky}}_2+(k_1+k)y_3-{\mathrm{kd}}_3{\mathrm{\θ}}_2+(k_1{d}_1-{\mathrm{kd}}_2){\mathrm{\θ}}_3-k_1{y}_6=f_3$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_1-c_1{d}_1{\stackrel{\·}{y}}_1+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_1+c_1{d}_1{\stackrel{\·}{y}}_4+({\mathrm{kd}}_2-k_1{d}_1)y_1-{\mathrm{kd}}_2{y}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_1+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+k_1{d}_1{y}_4=-d_1{f}_1$

$I_t{\stackrel{\·\·}{\mathrm{\θ}}}_2+{\mathrm{kd}}_3{y}_1-{\mathrm{kd}}_3{y}_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_1+2{{\mathrm{kd}}_3}^2{\mathrm{\θ}}_2+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_3=0$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_3+c_1{d}_1{\stackrel{\·}{y}}_3+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{d}_1{\stackrel{\·}{y}}_6+{\mathrm{kd}}_2{y}_2+(k_1{d}_1-{\mathrm{kd}}_2)y_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_3-k_1{d}_1{y}_6=d_1{f}_3$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_4-c_1{\stackrel{\·}{y}}_1+c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1+(c_1+c_3){\stackrel{\·}{y}}_4-k_1{y}_1+k_1{d}_1{\mathrm{\θ}}_1+(k_1+k_3)y_4=k_3{y}_7+c_3{\stackrel{\·}{y}}_7-f_1$

$m_{\mathrm{tb}}{\stackrel{\·\·}{y}}_5-c_2{\stackrel{\·}{y}}_2+(c_2+c_4){\stackrel{\·}{y}}_5-k_2{y}_2+(k_2+k_4)y_5=k_4{y}_8+c_4{\stackrel{\·}{y}}_8-f_2$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_6-c_1{\stackrel{\·}{y}}_3-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3+(c_1+c_3){\stackrel{\·}{y}}_6-k_1{y}_3-k_1{d}_1{\mathrm{\θ}}_3+(k_1+k_3)y_6=k_3{y}_9+c_3{\stackrel{\·}{y}}_9-f_3$

Wherein m _p, m _t, m _pb, m _tbbe respectively motor-car quality, trailer quality, motor car bogie quality, trailer bogie quality, I _p, I _tbe respectively motor-car pitching inertia, trailer pitching inertia, d ₁, d ₂, d ₃be respectively Edge Distance before and after motor-car center of gravity and hanging position distance, motor-car center of gravity and car back edge distance, trailer center of gravity and car, k, k ₁, k ₂, k ₃, k ₄be respectively the stiffness factor of joint joining place spring, the secondary pendulum spring of motor-car, the secondary pendulum spring of trailer, the secondary pendulum spring of motor car bogie, the secondary pendulum spring of trailer bogie, c ₁, c ₂, c ₃, c ₄be respectively the ratio of damping that motor-car secondary hangs, trailer secondary hangs, motor car bogie secondary hangs, trailer bogie secondary hangs, f ₁, f ₂, f ₃for the active controlling force of car body 1, car body 2, car body 3, y ₁, y ₂, y ₃be respectively the vertical deviation of car body 1, car body 2, car body 3 center of gravity, θ ₁, θ ₂, θ ₃be respectively the angle of pitch of three body gravities, y ₄, y ₅, y ₆be respectively the vertical deviation of three bogie centers of gravity, then the suspender displacement of train and joint are connected displacement and can be expressed as:

y ₁₀＝y ₁-d ₁θ ₁，y ₁₂＝y ₁+d ₂θ ₁，y ₁₃＝y ₂-d ₃θ ₂(1)

y ₂₄＝y ₂+d ₃θ ₂，y ₂₃＝y ₃-d ₂θ ₃，y ₁₁＝y ₃+d ₁θ ₃(2)

Wherein: y ₁₀for the suspender displacement of car body 1, y ₁₂for the joint of car body 1 is connected displacement, y ₁₃and y ₂₄for the joint of car body 2 is connected displacement, y ₂₃for the joint of car body 3 is connected displacement, y ₁₁for the suspender displacement of car body 3.

Above-mentioned equation is determined under following hypothesis relation:

1. all train compositions are rigidity;

2. train composition Striking symmetry;

3. the train body center just heart and center of gravity place in the structure;

4. the luffing angle change of car body is very little, is namely less than 5 °.

Step 2, determine the description form of adopted dynamicer model, when adopting first-order dynamic actuator model, described model is the core component of electromagnetic actuator and the single order simplified model of non-brush permanent-magnet DC motor:

$u=U_s-u_e=L_s\frac{\mathrm{di}}{\mathrm{dt}}+\mathrm{Ri}$

Wherein u is the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor, and i is electric current, U _sand u _ebe respectively equivalent source voltage and back electromotive force, L _sfor inductance coefficent, R is phase resistance, non-brush permanent-magnet DC motor and electric machine control system and ball-screw transmission mechanism form electromagnetic actuator control system jointly, then by the control characteristic of described electromagnetic actuator control system obtain its actual export to the vertical acting force of suspension be:

Wherein T _lfor the torque of the actual output of motor, P _hfor ball-screw helical pitch, T _mfor motor output torque, J _rfor the moment of inertia of rotor, J _nfor the nut moment of inertia of ball-screw, ω is rotor rotating speed, K _tfor motor torque constant, i is control electric current, for electromagnetic actuator stretching speed and suspender travel speed, for constant of the machine, for the equivalenting inertia torque of rotor and feed screw nut, then the integrality space equation obtaining train active suspension is:

$\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bv}+\mathrm{E\η}=\stackrel{\‾}{A}x+\stackrel{\‾}{B}i+\stackrel{\‾}{E}\mathrm{\η}\\ {\stackrel{.}{i}}_j=-{\mathrm{\λ}}_j({\mathrm{Ri}}_j-u_j),j=\mathrm{1,2,3}\end{array}---\left(5\right)$

Wherein x=[x ₁ ^tx ₂ ^t] ^tfor state vector, x ₁=[y ₁ ^tθ ₁ ^ty ₄ ^ty ₂ ^tθ ₂ ^ty ₅ ^ty ₃ ^tθ ₃ ^ty ₆ ^t] ^t, $x_2={\left[\begin{array}{ccccccccc}{{\stackrel{.}{y}}_1}^T& {{\stackrel{.}{\mathrm{\θ}}}_1}^T& {{\stackrel{.}{y}}_4}^T& {{\stackrel{.}{y}}_2}^T& {{\stackrel{.}{\mathrm{\θ}}}_2}^T& {{\stackrel{.}{y}}_5}^T& {{\stackrel{.}{y}}_3}^T& {{\stackrel{.}{\mathrm{\θ}}}_3}^T& {{\stackrel{.}{y}}_6}^T\end{array}\right]}^T,$ I=[i ₁ ^ti ₂ ^ti ₃ ^t] ^tfor controlling electric current, $\mathrm{\η}\left(t\right)={\left[\begin{array}{cccccc}{y_7}^T& {y_8}^T& {y_9}^T& {{\stackrel{\·}{y}}_7}^T& {{\stackrel{\·}{y}}_8}^T& {{\stackrel{\·}{y}}_9}^T\end{array}\right]}^T$ For the interference that the irregular input of track produces, i _jfor dynamicer exports, u _jfor input, v be active controlling force and by

Obtain v=(I+JNB) ^-1(Ψ i-JNAx-JNE η), wherein I is the unit matrix of suitable dimension, and O is the null matrix of suitable dimension, J=diag{ [J _dj _dj _d], Ψ=diag{ [Φ Φ Φ] }, $A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ A ₁₁＝O ₉，A ₁₂＝I ₉， $B=\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right],$ B ₁＝O _9×3， $\stackrel{\‾}{B}=B{(I+\mathrm{JNB})}^{-1}\mathrm{\Ψ},$ $\stackrel{\‾}{E}=E-B{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},E=\left[\begin{array}{c}{E}_1\\ E_2\end{array}\right],E_1=O_{9\×6},$

$N=\left[\begin{array}{cccccccccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 1& -d_1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& d_1& -1\end{array}\right],$

$A_{21}=\left[\begin{array}{ccccccccc}-\frac{k_1+k}{m_p}& \frac{k_1{d}_1-{\mathrm{kd}}_2}{m_p}& \frac{k_1}{m_p}& \frac{k}{m_p}& -\frac{{\mathrm{kd}}_3}{m_p}& 0& 0& 0& 0\\ \frac{k_1{d}_1-{\mathrm{kd}}_2}{I_p}& -\frac{k_1{d_1}^2+{{\mathrm{kd}}_2}^2}{I_p}& -\frac{k_1{d}_1}{I_p}& \frac{{\mathrm{kd}}_2}{I_p}& -\frac{{\mathrm{kd}}_2{d}_3}{I_p}& 0& 0& 0& 0\\ \frac{k_1}{m_{\mathrm{pb}}}& -\frac{k_1{d}_1}{m_{\mathrm{pb}}}& -\frac{k_1+k_3}{m_{\mathrm{pb}}}& 0& 0& 0& 0& 0& 0\\ \frac{k}{m_t}& \frac{{\mathrm{kd}}_2}{m_t}& 0& -\frac{k_2+2k}{m_t}& 0& \frac{k_2}{m_t}& \frac{k}{m_t}& -\frac{{\mathrm{kd}}_2}{m_t}& 0\\ -\frac{{\mathrm{kd}}_3}{I_t}& -\frac{{\mathrm{kd}}_2{d}_3}{I_t}& 0& 0& -\frac{2{{\mathrm{kd}}_3}^2}{I_t}& 0& \frac{{\mathrm{kd}}_3}{I_t}& -\frac{{\mathrm{kd}}_2{d}_3}{I_t}& 0\\ 0& 0& 0& \frac{k_2}{m_{\mathrm{tb}}}& 0& -\frac{k_2+k_4}{m_{\mathrm{tb}}}& 0& 0& 0\\ 0& 0& 0& \frac{k}{m_p}& \frac{{\mathrm{kd}}_3}{m_p}& 0& -\frac{k_1+k}{m_p}& \frac{{\mathrm{kd}}_2-k_1{d}_1}{m_p}& \frac{k_1}{m_p}\\ 0& 0& 0& -\frac{{\mathrm{kd}}_2}{I_p}& -\frac{{\mathrm{kd}}_2{d}_3}{I_p}& 0& \frac{{\mathrm{kd}}_2-k_1{d}_1}{I_p}& -\frac{k_1{d_1}^2+{{\mathrm{kd}}_2}^2}{I_p}& \frac{k_1{d}_1}{I_p}\\ 0& 0& 0& 0& 0& 0& \frac{k_1}{m_{\mathrm{pb}}}& \frac{k_1{d}_1}{m_{\mathrm{pb}}}& -\frac{k_1+k_3}{m_{\mathrm{pb}}}\end{array}\right],$

$A_{22}=\left[\begin{array}{ccccccccc}-\frac{c_1}{m_p}& \frac{c_1{d}_1}{m_p}& \frac{c_1}{m_p}& 0& 0& 0& 0& 0& 0\\ \frac{c_1{d}_1}{I_p}& -\frac{c_1{d_1}^2}{I_p}& -\frac{c_1{d}_1}{I_p}& 0& 0& 0& 0& 0& 0\\ \frac{c_1}{m_{\mathrm{pb}}}& -\frac{c_1{d}_1}{m_{\mathrm{pb}}}& -\frac{c_1+c_3}{m_{\mathrm{pb}}}& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -\frac{c_2}{m_t}& 0& \frac{c_2}{m_t}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& \frac{c_2}{m_{\mathrm{tb}}}& 0& -\frac{c_2+c_4}{m_{\mathrm{tb}}}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& -\frac{c_1}{m_p}& -\frac{c_1{d}_1}{m_p}& \frac{c_1}{m_p}\\ 0& 0& 0& 0& 0& 0& -\frac{c_1{d}_1}{I_p}& -\frac{c_1{d_1}^2}{I_p}& \frac{c_1{d}_1}{I_p}\\ 0& 0& 0& 0& 0& 0& \frac{c_1}{m_{\mathrm{pb}}}& \frac{c_1{d}_1}{m_{\mathrm{pb}}}& -\frac{c_1+c_3}{m_{\mathrm{pb}}}\end{array}\right],B_2=\left[\begin{array}{ccc}\frac{1}{m_p}& 0& 0\\ -\frac{d_1}{I_p}& 0& 0\\ -\frac{1}{m_{\mathrm{pb}}}& 0& 0\\ 0& \frac{1}{m_t}& 0\\ 0& 0& 0\\ 0& -\frac{1}{m_{\mathrm{tb}}}& 0\\ 0& 0& \frac{1}{m_p}\\ 0& 0& \frac{d_1}{I_p}\\ 0& 0& -\frac{1}{m_{\mathrm{pb}}}\end{array}\right],$

$E_2=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& \frac{k_4}{m_{\mathrm{tb}}}& 0& 0& \frac{c_4}{m_{\mathrm{tb}}}& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}\end{array}\right];$

When being generalized to second order dynamicer model, by the transport function of described first-order dynamic actuator model $G\left(s\right)=\frac{1}{L_{s}s+R}=\frac{{\mathrm{\λ}}_j}{s+{\mathrm{\λ}}_{j}R}$ Obtaining second-order model is:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{1j}{i}_{1j}-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}\frac{u_j}{R}\end{array}---\left(7\right)$

Wherein i _1jfor electric current, u _jfor voltage, R is resistance, and its proper polynomial is s ²+ λ _2js+ λ _1j=(s+ μ) (s+ λ _jr), make parameter μ > > 1, and then obtain λ _1j> > 1, λ _1j> > λ _2j;

Above-mentioned equation is determined under following hypothesis relation:

1. armature winding full symmetric, magnetic circuit is unsaturated, ignores the impact of teeth groove, commutation and armature reaction;

2. the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor is only considered;

3. the electromagnetic consumable of non-brush permanent-magnet DC motor is not considered;

4. winding inductance coefficient is very little, i.e. L _s≤ 0.005;

Being described as follows here about electromagnetic actuator control system:

Utilize electromagnetic actuator control technology to suppress vibration, Conversion of Energy mode is simple, and efficiency is higher, and has low-friction coefficient and linear mechanical characteristic, can synchronization implementation energy regenerating under certain condition.Electromagnetic actuator control system is made up of non-brush permanent-magnet DC motor, electric machine control system and ball-screw transmission mechanism, the Main Function of non-brush permanent-magnet DC motor is output torque and performs ACTIVE CONTROL, armature winding adopts the Y-connection of three-phase six state, obtains following motor three-phase voltage equation:

$\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right]=\left[\begin{array}{ccc}R& 0& 0\\ 0& R& 0\\ 0& 0& R\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{ccc}{L}_s& 0& 0\\ 0& L_s& 0\\ 0& 0& L_s\end{array}\right]\left[\begin{array}{c}{\mathrm{di}}_a/\mathrm{dt}\\ {\mathrm{di}}_b/\mathrm{dt}\\ {\mathrm{di}}_c/\mathrm{dt}\end{array}\right]+\left[\begin{array}{c}{e}_a\\ e_b\\ e_c\end{array}\right]---\left(8\right)$

Wherein u _a, u _b, u _c, i _a, i _b, i _c, e _a, e _b, e _cbe respectively the end electromotive force of motor three-phase windings, electric current and back electromotive force, R is phase resistance, L _s=L-M, L are winding coefficient of self-induction, and M is coefficient of mutual inductance between winding.Electric machine control system comprises three-phase inverter, rotor-position sensor, current controller and direct supply, as shown in Figure 3.Do not consider the electromagnetic consumable of non-brush permanent-magnet DC motor, motor output torque T can be obtained _mas follows with the relation controlling current i:

T _m＝K _Ti (9)

Wherein K _tfor motor torque constant.Motor output torque T can be obtained by formula (9) _mbe directly proportional to control current i, then motor output torque can change axial force f into by ball-screw transmission mechanism _m:

$f_m=\frac{2\mathrm{\π}}{P_h}{T}_m---\left(10\right)$

Wherein P _hfor ball-screw helical pitch, the kinetic model expression formula of electromagnetic actuator is:

$(J_r+J_n)\stackrel{\·}{\mathrm{\ω}}=T_m-T_L---\left(11\right)$

Wherein J _rfor the moment of inertia of rotor, J _nfor the nut moment of inertia of ball-screw, ω is rotor rotating speed, T _lfor the torque of the actual output of motor, rotor rotational speed omega and electromagnetic actuator stretching speed and suspender travel speed pass be:

Then the actual output of electromagnetic actuator control system to the vertical acting force of suspension is:

Wherein for constant of the machine, for the equivalenting inertia torque of rotor and feed screw nut.

Step 3, set up fault model according to the contingent two kinds of fault types of electromagnetic actuator, namely when losing efficacy in actuator importation, setting up single order fault model is:

${\stackrel{\·}{i}}_j=-{\mathrm{\λ}}_j(R{i}_j-{\mathrm{\β}}_j{u}_j)---\left(14\right)$

Wherein β _jt ()=1 is value when actuator inputs normal, for value during actuator section gain reduction.When actuator motor overload even stall time, setting up single order fault model is:

${\stackrel{\·}{i}}_j=-{\mathrm{\α}}_j{\mathrm{\λ}}_j(R{i}_j-u_j)---\left(15\right)$

Wherein α _jt ()=1 is value when actuator motor runs well, α _j(t)=0 be motor overload even stall time value, now due to the effect of current controller in electric machine control system, for time of failure.Then can obtain first-order dynamic actuator failures block mold is:

${\stackrel{\·}{i}}_j=-{\mathrm{\α}}_j{\mathrm{\λ}}_j(R{i}_j-{\mathrm{\β}}_j{u}_j)---\left(16\right)$

In like manner setting up second order dynamicer fault block mold is:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})\end{array}---\left(17\right)$

Wherein only has i _1jbe measurable and can be obtained by current sensor measurement, be described as follows here:

Second order dynamicer model (7) is for observation i _2jthere is inconvenience in dynamic Design of Observer, therefore when actuator motor overload even stall time, set up the second order fault model with lower aprons:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-[{\mathrm{\λ}}_{2j}+(1-{\mathrm{\α}}_j){\mathrm{\ρ}}_j]i_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}(\frac{1}{R}{u}_j-i_{1j})\end{array}---\left(18\right)$

Wherein λ _2j+ ρ _j> > 1.When motor runs well, α _j(t)=1, when motor overload even stall time, α _j(t)=0, i _1j(t _fj)=i _r, and i _2jwill with λ _2j+ ρ _jspeed asymptotic convergence in zero, by suitably selecting ρ _jvalue, can make fault occur after i _1jand i _2jall can rapidly converge to zero with arbitrary speed.And when losing efficacy in actuator importation, set up following second order fault model:

$\begin{array}{c}{\stackrel{\·}{i}}_{1j}=i_{2j}\\ {\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})\end{array}---\left(19\right)$

And hypothesis is under fault existence condition, λ _2jenough large to ensure i _2jcan zero be rapidly converged to, then can make ρ _j=0, thus obtain second order dynamicer fault block mold (17).

Step 4, the basis of dynamicer fault model determined in step 3 construct fault detect and the recognition system of distribution, to each dynamicer independent operating observer, only use local message and do not need the status information of the overall situation to realize the on-line tuning estimated fault parameter, as adopted first-order dynamic actuator, then design following distributive observation device:

${\stackrel{\·}{\hat{i}}}_j=-{\mathrm{\λ}}_j({\hat{i}}_j-i_j)+{\mathrm{\λ}}_j{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j{u}_j-R{i}_j)---\left(20\right)$

Wherein be respectively i _j, α _j, β _jobserved reading, and can to obtain:

$\begin{array}{c}{\stackrel{\·}{e}}_{1j}={\stackrel{\·}{\hat{i}}}_j-{\stackrel{\·}{i}}_j\\ =-{\mathrm{\λ}}_j({\stackrel{\·}{\hat{i}}}_j-{\stackrel{\·}{i}}_j)+{\mathrm{\λ}}_j{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j{u}_j-R{i}_j)+{\mathrm{\λ}}_j{\mathrm{\α}}_j(R{i}_j-{\mathrm{\β}}_j{u}_j)\\ =-{\mathrm{\λ}}_j{e}_{1j}+{\mathrm{\λ}}_j({\widehat{\mathrm{\α}}}_j-{\mathrm{\α}}_j)({\widehat{\mathrm{\β}}}_j{u}_j-R{i}_j)+{\mathrm{\λ}}_j{\mathrm{\α}}_j({\widehat{\mathrm{\β}}}_j-{\mathrm{\β}}_j)u_j\end{array}$

If ${\widetilde{\mathrm{\α}}}_j={\widehat{\mathrm{\α}}}_j-{\mathrm{\α}}_j,{\widetilde{\mathrm{\β}}}_j={\widehat{\mathrm{\β}}}_j-{\mathrm{\β}}_j,{\mathrm{\δ}}_{{\mathrm{\α}}_j}={\widehat{\mathrm{\β}}}_j{u}_j-R{i}_j,{\mathrm{\δ}}_{{\mathrm{\β}}_j}=u_j,$ Then:

$\begin{array}{c}{\stackrel{\·}{e}}_{1j}=-{\mathrm{\λ}}_j{e}_{1j}+{\mathrm{\λ}}_j{\widetilde{\mathrm{\α}}}_j{\mathrm{\δ}}_{{\mathrm{\α}}_j}+{\mathrm{\λ}}_j{\mathrm{\α}}_j{\widetilde{\mathrm{\β}}}_j{\mathrm{\δ}}_{{\mathrm{\β}}_j}\\ =-{\mathrm{\λ}}_j(e_{1j}-{\widetilde{\mathrm{\α}}}_j{\mathrm{\δ}}_{{\mathrm{\α}}_j}-{\mathrm{\α}}_j{\widetilde{\mathrm{\β}}}_j{\mathrm{\δ}}_{{\mathrm{\β}}_j})\\ =-{\mathrm{\λ}}_j(e_{1j}-{{\mathrm{\Γ}}_j}^T{\mathrm{\δ}}_j)\end{array}$

Wherein ${\mathrm{\Γ}}_j={\left[\begin{array}{cc}{\widetilde{\mathrm{\α}}}_j& {\widetilde{\mathrm{\β}}}_j\end{array}\right]}^T,$ ${\mathrm{\δ}}_j={\left[\begin{array}{cc}{\mathrm{\δ}}_{{\mathrm{\α}}_j}& {\mathrm{\α}}_j{\mathrm{\δ}}_{{\mathrm{\β}}_j}\end{array}\right]}^T.$ Can obtain according to singular perturbation theory:

e _1j≌Γ _j ^Tδ _j(21)

For making parameter estimation in known span, adopting projection operator design adaptive law, following adaptive law is provided to ensure error e to the parameter in system single order fault model _1j∈ L ^∞∩ L ²:

$\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}=\mathrm{Pr}{\mathrm{oj}}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_j{e}_{1j}{\mathrm{\δ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1---\left(22\right)$

$\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}=\mathrm{Pr}{\mathrm{oj}}_{[\mathrm{\θ},1]}\{-{\mathrm{\γ}}_{{\mathrm{\β}}_j}{\mathrm{\λ}}_j{e}_{1j}{\mathrm{\δ}}_{\mathrm{\βj}}\},\widehat{\mathrm{\β}}\left(0\right)=1---\left(23\right)$

Wherein for adaptive gain, then according to Lyapunov stable theory, e _1j∈ L ^∞∩ L ².As adopted second order dynamicer, due to i _2jimmeasurability, in order to estimated parameter α better _jand β _j, introduce following filtering variable:

${i_{1j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{1j},{i_{2j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{2j},{u_j}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{u}_j---\left(24\right)$

Wherein λ _fj> 0 is filter time constant, then i _2jcan with being expressed as by measuring-signal:

$i_{2j}=({\mathrm{\λ}}_{\mathrm{Fj}}-{\mathrm{\λ}}_{2j}){i_{2j}}^F+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)$

${i_{2j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{2j}=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{\mathrm{si}}_{1j}=i_{1j}-{\mathrm{\λ}}_{\mathrm{Fj}}{i_{1j}}^F$

Following observer is designed according to (17) and (24):

${\stackrel{\stackrel{\·}{^}}{i}}_{1j}=-{\mathrm{\τ}}_j({\hat{i}}_{1j}-i_{1j})+({\mathrm{\λ}}_{\mathrm{Fj}}-{\mathrm{\λ}}_{2j}){i_{2j}}^F+{\mathrm{\λ}}_{1j}{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j---\left(25\right)$

Wherein for i _1jobserved reading, τ _jand ε _jfor the parameter to be designed for ensureing system stability, and obtain error model:

$\begin{array}{c}{\stackrel{\·}{e}}_{2j}={\stackrel{\stackrel{\·}{^}}{i}}_{1j}-{\stackrel{\·}{i}}_{1j}\\ =-{\mathrm{\τ}}_j{e}_{2j}+({\mathrm{\λ}}_{\mathrm{Fj}}-{\mathrm{\λ}}_{2j}){i_{2j}}^F+{\mathrm{\λ}}_{1j}{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j-{\stackrel{\·}{i}}_{1j}\\ =-{\mathrm{\τ}}_j{e}_{2j}+{\mathrm{\λ}}_{1j}{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)-{\mathrm{\λ}}_{1j}{\mathrm{\α}}_j({\mathrm{\β}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j\\ =-{\mathrm{\τ}}_j{e}_{2j}+{\mathrm{\λ}}_{1j}{\widetilde{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}-{i_{1j}}^F)+{\mathrm{\λ}}_{1j}{\mathrm{\α}}_j{\widetilde{\mathrm{\β}}}_j\frac{{u_j}^F}{R}+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j\end{array}$

Choose τ respectively _j=λ _1j/ λ _2j, λ _fj=λ _2j, obtain according to singular perturbation theory:

$e_{2j}\≅{\mathrm{\λ}}_{2j}({\widetilde{\mathrm{\α}}}_j{{\mathrm{\κ}}_{\mathrm{\αj}}}^F+{\mathrm{\α}}_j{\widetilde{\mathrm{\β}}}_j\frac{{{\mathrm{\κ}}_{{\mathrm{\β}}_j}}^F}{R}+{\mathrm{\ϵ}}_j)---\left(26\right)$

Wherein ${{\mathrm{\κ}}_{\mathrm{\αj}}}^F={{\widehat{\mathrm{\β}}}_j}^F\frac{{u_j}^F}{R}-{i_{1j}}^F,{{\mathrm{\κ}}_{\mathrm{\βj}}}^F={u_j}^F$ Then have ${\mathrm{\κ}}_{\mathrm{\αj}}={\widehat{\mathrm{\β}}}_j\frac{u_j}{R}-i_{1j},$ κ _βj＝u _j。For making parameter estimation in known span, the same projection operator that adopts designs adaptive law, provides following adaptive law to ensure error e to parameter each in system failure model _2j∈ L ^∞∩ L ²:

$\stackrel{\·}{\widehat{\mathrm{\α}}}=\mathrm{Pr\; o}{j}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1---\left(27\right)$

$\stackrel{\·}{\widehat{\mathrm{\β}}}=\mathrm{Pr\; o}{j}_{[\mathrm{\η},1]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\β}}\left(0\right)=1---\left(28\right)$

${\stackrel{\·}{\mathrm{\ϵ}}}_j=-{\mathrm{\λ}}_{2j}{\mathrm{\ϵ}}_j-{\stackrel{\·}{\widehat{\mathrm{\α}}}}_j{{\mathrm{\κ}}_{\mathrm{\αj}}}^F-{\mathrm{\α}}_j{\stackrel{\·}{\widehat{\mathrm{\β}}}}_j\frac{{{\mathrm{\κ}}_{\mathrm{\βj}}}^F}{R},{\mathrm{\ϵ}}_j\left(0\right)=0---\left(29\right)$

Wherein for adaptive gain, then according to Lyapunov stable theory, e _2j∈ L ^∞∩ L ².

Step 5, the actuator failures parameter determination ADAPTIVE ROBUST faults-tolerant control rule estimated by step 4, make system when there is external disturbance, there is the fault-tolerant ability to fault, ensure that the robustness of system state and parameter estimation, thus ensure that ride comfort security and control stability, complete the fault diagnosis based on dynamicer and faults-tolerant control, be specially:

(1) obtained by first-order dynamic actuator failures model described in step 3 obtained further by singular perturbation theory or obtained by second order dynamicer fault model by singular perturbation theory and λ _1j> > 1, λ _1j> > λ _2jobtain further wherein for time motor transship the actuator after even stall fault and export;

(2) constitution realization jamproof LQG controller u _r=Gx, wherein for the feedback gain matrix of controller, P is following Riccati non trivial solution

Being described as follows here to LQG controller gain matrix:

In suspension design process, need to consider to be hung by the irregular riding quality problem that causes of track and irregular and track grade causes jointly by track one-level and the deviation of secondary suspension simultaneously.In order to reach optimum ride quality, the vertical acceleration reducing car body 1,2,3 is our main target, consider Ride safety and control stability simultaneously, therefore to pick up the car respectively the car precursor of body 1,2,3, body vertical acceleration after center of gravity and car, the suspension of bogie 1,2,3 moves stroke, wheel movement of the foetus displacement and control inputs as Performance Evaluating Indexes, and obtaining quadratic performance function is:

$\begin{array}{c}{J}_l=\underset{T\→\∞}{\lim }\frac{1}{T}\underset{0}{\overset{T}{\∫}}[q_1{{\stackrel{\·\·}{y}}_{10}}^2+q_2{{\stackrel{\·\·}{y}}_1}^2+q_3{{\stackrel{\·\·}{y}}_{12}}^2+q_4{{\stackrel{\·\·}{y}}_{13}}^2+q_5{{\stackrel{\·\·}{y}}_2}^2+q_6{{\stackrel{\·\·}{y}}_{24}}^2+q_7{{\stackrel{\·\·}{y}}_{23}}^2+q_8{{\stackrel{\·\·}{y}}_3}^2+q_9{{\stackrel{\·\·}{y}}_{11}}^2+\\ q_{10}{(y_{10}-y_4)}^2+q_{11}{(y_2-y_5)}^2+q_{12}{(y_{11}-y_6)}^2+q_{13}{(y_4-y_7)}^2+q_{14}{(y_5-y_8)}^2+\\ q_{15}{(y_6-y_9)}^2+q_{16}{i_1}^2+q_{17}{i_2}^2+q_{18}{i_3}^2]\mathrm{dt}\end{array}$

Wherein q ₁~ q ₁₈for the performance weighting coefficient of property indices.

Choose to measure and export $z=\left[\begin{array}{cccccccccccc}{\stackrel{\·\·}{y}}_{10}& {\stackrel{\·\·}{y}}_1& {\stackrel{\·\·}{y}}_{12}& {\stackrel{\·\·}{y}}_{13}& {\stackrel{\·\·}{y}}_2& {\stackrel{\·\·}{y}}_{24}& {\stackrel{\·\·}{y}}_{23}& {\stackrel{\·\·}{y}}_3& {\stackrel{\·\·}{y}}_{11}& y_{10}-y_4& y_2-y_5& y_{11}-y_6\end{array}\right.$ ${\left.\begin{array}{ccc}{y}_4-y_7& y_5-y_8& y_6-y_9\end{array}\right]}^T,$ Then can obtain:

$\begin{array}{c}z=\mathrm{Cx}+\mathrm{Dv}+\mathrm{F\η}\\ =\stackrel{\‾}{C}x+\stackrel{\‾}{D}i+\stackrel{\‾}{F}\mathrm{\η}\end{array}---\left(30\right)$

Wherein $\stackrel{\‾}{C}=C-D{(I+\mathrm{JNB})}^{-1}\mathrm{JNA},\stackrel{\‾}{D}=D{(I+\mathrm{JNB})}^{-1}\mathrm{\ψ},\stackrel{\‾}{F}=F-D{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},$

$F=\left[\begin{array}{cc}{O}_{12\×3}& O_{12\×3}\\ -I_3& O_3\end{array}\right],$ Wherein O is the null matrix of suitable dimension, and I is the unit matrix of suitable dimension,

Consider the object suppressing interference, ignore the distracter in performance function, and according to the output quantity selected and the theory of optimal control, quadratic performance function is expressed as following quadratic standard forms form:

Wherein: $\stackrel{\‾}{Q}=\mathrm{diag}\left\{\begin{array}{ccccccccccccccc}{q}_1& q_2& q_3& q_4& q_5& q_6& q_7& q_8& q_9& q_{10}& q_{11}& q_{12}& q_{13}& q_{14}& q_{15}\end{array}\right\},$ Then obtain the feedback gain matrix of controller.

(3) make $\stackrel{\‾}{B}=\left[\begin{array}{ccc}{\stackrel{\‾}{B}}_1& {\stackrel{\‾}{B}}_2& {\stackrel{\‾}{B}}_3\end{array}\right],$ If $\mathrm{\Λ}=\left[\begin{array}{ccc}{\mathrm{\α}}_1{\stackrel{\‾}{B}}_1& {\mathrm{\α}}_2{\stackrel{\‾}{B}}_2& {\mathrm{\α}}_3{\stackrel{\‾}{B}}_3\end{array}\right]),$ Σ=diag ([β ₁β ₂β ₃]), then at α _j, β _junder known condition, design ideal fault-tolerant controller is as follows:

$u_s=-S\mathrm{\Σ}{\mathrm{\Λ}}^T{\left(\mathrm{\Λ}\mathrm{\Σ}S\mathrm{\Σ}{\mathrm{\Λ}}^T\right)}^{-1}\left[\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{\stackrel{\‾}{B}}_j(1-{\mathrm{\α}}_{j}R)i_r\right]---\left(31\right)$

Wherein S > 0 is symmetric positive definite diagonal weight matrix, then can obtain each state variable asymptotic convergence of closed-loop control system (5) in zero.But when time of failure and type are all unknown, then must design adaptive fusion device by α _jand β _jvalue use with substitute, first establish $\widehat{\mathrm{\Λ}}=\left[\begin{array}{ccc}{\widehat{\mathrm{\α}}}_1{\stackrel{\‾}{B}}_1& {\widehat{\mathrm{\α}}}_2{\stackrel{\‾}{B}}_2& {\widehat{\mathrm{\α}}}_3{\stackrel{\‾}{B}}_3\end{array}\right],\widehat{\mathrm{\Σ}}=\mathrm{diag}\left(\left[\begin{array}{ccc}{\widehat{\mathrm{\β}}}_1& {\widehat{\mathrm{\β}}}_2& {\widehat{\mathrm{\β}}}_3\end{array}\right]\right),$ Then can design adaptive fusion device is:

$u_s=-S\widehat{\mathrm{\Σ}}{\widehat{\mathrm{\Λ}}}^T{\left(\widehat{\mathrm{\Λ}}\widehat{\mathrm{\Σ}}S\widehat{\mathrm{\Σ}}{\widehat{\mathrm{\Λ}}}^T\right)}^{-1}\left[\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{\stackrel{\‾}{B}}_j(1-{\widehat{\mathrm{\α}}}_{j}R)i_r\right]---\left(32\right)$

Also the state variable asymptotic convergence of closed-loop control system can be obtained in zero.

(4) designing ADAPTIVE ROBUST fault-tolerant controller is u=u _r+ u _s.

Here, by fault diagnosis observer and the separately design of ADAPTIVE ROBUST fault-tolerant controller, consider respective performance again simultaneously, optimize design process.

Simulating, verifying is carried out to method of the present invention below.

Power taking magnetic actuator's parameters is respectively resistance R=1, inductance L _s=L-M=0.002, assumed fault time of origin is t _fj=10s, when actuator input inefficacy 30%, gets γ _{α j}=γ _{β j}=0.05, current estimation error as shown in Fig. 4 (a), the estimated value of correlation parameter β as shown in Fig. 4 (b), when actuator motor overload even stall time, input inefficacy 100%, get γ _{α j}=50, γ _{β j}=0.1, current estimation error is as shown in Fig. 4 (c), and the estimated value of correlation parameter α is as Fig. 4 (d).

Get train suspension system model parameter as table 1, electromagnetic actuator parameter is respectively K _t=0.1518, P _h=0.02, J _r=0.15, J _n=0.1, performance weighting coefficient is respectively q ₁=q ₂=q ₃=q ₄=q ₅=q ₆=q ₇=q ₈=q ₉=1000, q ₁₀=q ₁₁=q ₁₂=q ₁₃=q ₁₄=q ₁₅=10, q ₁₆=q ₁₇=q ₁₈=1, when dynamicer is in unfaulty conditions, obtain LQG controller gain by MATLAB simulation calculation

$\begin{array}{c}\left[G=,\begin{array}{ccccccccc}-1263& -34.914& 232.62& -541.31& -1583.5& 6.1302& 394.97& -2402& 561.71\\ 364.63& -136.82& 18.287& -3312& 0.0000& 5388.7& 364.63& 136.82& 18.287\\ 394.97& 2402& 561.71& -541.71& 1583.5& 6.1302& -1263& 34.914& 232.62\end{array}\right.\\ \left.\begin{array}{ccccccccc}-33.277& -1477.1& 89.692& 41.698& -634.42& 1.8417& 134.99& -900.4& -21\\ 20.379& -245.76& 11.059& 170.95& -0.0002& 247.34& 20.378& 215.76& 11.059\\ 134.99& 900.4& -21& 41.698& 634.42& 1.8417& -33.278& 1477.1& 89.692\end{array}\right]\end{array}$

Then under this controller action, obtain respectively 15 performance index under the effect of electromagnetic actuator Active Suspensions with the Contrast on effect of passive suspension, if Fig. 5 (a) ~ (e) is for the performance index of car body 1, the inhibiting effect of this controller to the interference that the irregular input of track produces is described.

Table 1 light rail suspension system model parameter

When the electromagnetic actuator of car body 1 is at 1s, overload or stall fault occur, crash rate is 100%, and the electromagnetic actuator of car body 3, when 1s, importation failure of removal synchronously occurs, and when crash rate is 70%, gets S=I, γ _{α j}=γ _{β j}=0.05, then control effects is as shown in Fig. 6 (a) He (b) under the effect of ADAPTIVE ROBUST fault-tolerant controller for each performance index of car body 1, and each performance index of car body 3 are as shown in Fig. 6 (c) He (d).

The Fault Estimation of dynamicer effectively can be realized by the known method of the present invention of above-mentioned accompanying drawing, and can carry out fault-tolerant to the fault occurred, make train active suspension still keep good ride comfort security and control stability in case of a fault, this early warning for the system failure and in real time monitoring have great importance.

Claims (5)

1. the train active suspension fault diagnosis and fault-tolerant control device based on dynamicer, it is characterized in that: comprise dynamicer direct fault location module, platform control module, fault diagnosis module, real-time monitoring module and data acquisition module, described dynamicer is electromagnetic actuator, wherein dynamicer direct fault location module is connected with platform control module, the failure message of simulation is supplied to platform control module, and show fault characteristic by platform control module, the displacement information that platform control module will be recorded by data acquisition module, velocity information and acceleration information are transferred to fault diagnosis module, fault diagnosis module is connected with real-time monitoring module, the malfunction of detection is shown, described fault diagnosis module is connected with platform control module simultaneously, namely carry out, after detection identifies, faults-tolerant control is restrained information transmission to platform control module to fault-signal.

2. the train active suspension fault diagnosis and fault-tolerant control device based on dynamicer according to claim 1, it is characterized in that: described platform control module comprises computing machine, power amplifier, signal compiling and conversion equipment, with the train suspension system analog platform of electromagnetic actuator control system, wherein electromagnetic actuator control system comprises non-brush permanent-magnet DC motor, electric machine control system and ball-screw transmission mechanism, described non-brush permanent-magnet DC motor is dynamicer, dynamicer is divided into the second order dynamicer of first-order dynamic actuator and popularization, train suspension system analog platform comprises bogie, bogie integration test cabinet and sensor, described computing machine is connected with train suspension system analog platform by power amplifier, described train suspension system analog platform is compiled by signal simultaneously and conversion equipment is connected with computing machine.

3. the train active suspension fault diagnosis and fault-tolerant control device based on dynamicer according to claim 1, it is characterized in that: described fault diagnosis module comprises the fault detect of distribution and identification module and ADAPTIVE ROBUST fault-tolerant controller, the fault detect of described distribution and identification module comprise and are distributed in observer on each dynamicer and synergistic residual signals generation module with it.

4. based on described in claim 1 based on a fault diagnosis and fault-tolerant control method for the train active suspension fault diagnosis and fault-tolerant control device of dynamicer, it is characterized in that: comprise the following steps:

Step 1, train suspension system analog platform with many bodies dynamic model of train active suspension for research object, described model is made up of two motor-cars and a trailer, two motor-cars are respectively car body 1 and car body 3, a trailer is car body 2, the passive power of the secondary suspender between the car body of three cars and bogie depends primarily on the relative displacement of car body and bogie, joint joining place is simulated with spring, the active controlling force of active suspension is produced by the electromagnetic actuator control system be added on passive suspension spring and damping shock absorber basis, additional interference is the irregular input of track, regard the car body of three cars and bogie as barycenter respectively and force analysis is carried out to it, consider the vertical and luffing of car body and the catenary motion of bogie, using car body working direction as lateral shaft, using suffered gravity direction as vertical axle, vertical deviation is car body and the displacement of bogie on vertical axle, the angle of pitch is the angle that car body luffing departs from lateral shaft, according to dynamic balance and the equalising torque of each barycenter, the kinetics equation obtaining train active suspension many bodies dynamic model is:

$m_p{\stackrel{\·\·}{y}}_1+c_1{\stackrel{\·}{y}}_1-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1-c_1{\stackrel{\·}{y}}_4+(k_1+k)y_1-{\mathrm{ky}}_2+({\mathrm{kd}}_2-k_1{d}_1){\mathrm{\θ}}_1+{\mathrm{kd}}_3{\mathrm{\θ}}_2-k_1{y}_4=f_1$

$m_t{\stackrel{\·\·}{y}}_2+c_2{\stackrel{\·}{y}}_2-c_2{\stackrel{\·}{y}}_5-{\mathrm{ky}}_1+(k_2+2k)y_2-{\mathrm{ky}}_3-{\mathrm{kd}}_2{\mathrm{\θ}}_1+{\mathrm{kd}}_2{\mathrm{\θ}}_3-k_2{y}_5=f_2$

$m_p{\stackrel{\·\·}{y}}_3+c_1{\stackrel{\·}{y}}_3-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{\stackrel{\·}{y}}_6-{\mathrm{ky}}_2+(k_1+k)y_3-{\mathrm{kd}}_3{\mathrm{\θ}}_2+(k_1{d}_1-{\mathrm{kd}}_2){\mathrm{\θ}}_3-k_1{y}_6=f_3$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_1-c_1{d}_1{\stackrel{\·}{y}}_1+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_1+c_1{d}_1{\stackrel{\·}{y}}_4+({\mathrm{kd}}_2-k_1{d}_1)y_1-{\mathrm{kd}}_2{y}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_1+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+k_1{d}_1{y}_4=-d_1{f}_1$

$I_t{\stackrel{\·\·}{\mathrm{\θ}}}_2+{\mathrm{kd}}_3{y}_1-{\mathrm{kd}}_3{y}_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_1+2k{d_3}^2{\mathrm{\θ}}_2+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_3=0$

$I_p{\stackrel{\·\·}{\mathrm{\θ}}}_3+c_1{d}_1{\stackrel{\·}{y}}_3+c_1{d_1}^2{\stackrel{\·}{\mathrm{\θ}}}_3-c_1{d}_1{\stackrel{\·}{y}}_6+{\mathrm{kd}}_2{y}_2+(k_1{d}_1-{\mathrm{kd}}_2)y_3+{\mathrm{kd}}_2{d}_3{\mathrm{\θ}}_2+(k_1{d_1}^2+{{\mathrm{kd}}_2}^2){\mathrm{\θ}}_3-k_1{d}_1{y}_6=d_1{f}_3$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_4-c_1{\stackrel{\·}{y}}_1+c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_1+(c_1+c_3){\stackrel{\·}{y}}_4-k_1{y}_1+k_1{d}_1{\mathrm{\θ}}_1+(k_1+k_3)y_4=k_3{y}_7+c_3{\stackrel{\·}{y}}_7-f_1$

$m_{\mathrm{tb}}{\stackrel{\·\·}{y}}_5-c_2{\stackrel{\·}{y}}_2+(c_2+c_4){\stackrel{\·}{y}}_5-k_2{y}_2+(k_2+k_4)y_5=k_4{y}_8+c_4{\stackrel{\·}{y}}_8-f_2$

$m_{\mathrm{pb}}{\stackrel{\·\·}{y}}_6-c_1{\stackrel{\·}{y}}_3-c_1{d}_1{\stackrel{\·}{\mathrm{\θ}}}_3+(c_1+c_3){\stackrel{\·}{y}}_6-k_1{y}_3-k_1{d}_1{\mathrm{\θ}}_3+(k_1+k_3)y_6=k_3{y}_9+c_3{\stackrel{\·}{y}}_9-f_3$

Wherein: m _p, m _t, m _pb, m _tbbe respectively motor-car quality, trailer quality, motor car bogie quality, trailer bogie quality, I _p, I _tbe respectively motor-car pitching inertia, trailer pitching inertia, d ₁, d ₂, d ₃be respectively Edge Distance before and after motor-car center of gravity and hanging position distance, motor-car center of gravity and car back edge distance, trailer center of gravity and car, k, k ₁, k ₂, k ₃, k ₄be respectively the stiffness factor of joint joining place spring, the secondary pendulum spring of motor-car, the secondary pendulum spring of trailer, the secondary pendulum spring of motor car bogie, the secondary pendulum spring of trailer bogie, c ₁, c ₂, c ₃, c ₄be respectively the ratio of damping that motor-car secondary hangs, trailer secondary hangs, motor car bogie secondary hangs, trailer bogie secondary hangs, f ₁, f ₂, f ₃for the active controlling force of car body 1, car body 2, car body 3, y ₁, y ₂, y ₃be respectively the vertical deviation of car body 1, car body 2, car body 3 center of gravity, θ ₁, θ ₂, θ ₃be respectively the angle of pitch of three body gravities, y ₄, y ₅, y ₆be respectively the vertical deviation of three bogie centers of gravity, then the suspender displacement of train and joint are connected displacement and can be expressed as:

y ₁₀＝y ₁-d ₁θ ₁，y ₁₂＝y ₁+d ₂θ ₁，y ₁₃＝y ₂-d ₃θ ₂，

y ₂₄＝y ₂+d ₃θ ₂，y ₂₃＝y ₃-d ₂θ ₃，y ₁₁＝y ₃+d ₁θ ₃；

Wherein: y ₁₀for the suspender displacement of car body 1, y ₁₂for the joint of car body 1 is connected displacement, y ₁₃and y ₂₄for the joint of car body 2 is connected displacement, y ₂₃for the joint of car body 3 is connected displacement, y ₁₁for the suspender displacement of car body 3;

Above-mentioned equation is determined under following hypothesis relation:

1. all train compositions are rigidity;

2. train composition Striking symmetry;

3. the train body center just heart and center of gravity place in the structure;

4. the luffing angle change of car body is less than 5 °;

Step 2, determine the description form of adopted dynamicer model, i.e. first-order dynamic actuator model or second order dynamicer model, then the integrality space equation being obtained train active suspension by the motor characteristic of electromagnetic actuator control system and control characteristic;

When adopting first-order dynamic actuator model, described model is the core component of electromagnetic actuator and the single order simplified model of non-brush permanent-magnet DC motor:

$u=U_s-u_e=L_s\frac{\mathrm{di}}{\mathrm{dt}}+\mathrm{Ri}$

Wherein: u is the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor, and i is electric current, U _sand u _ebe respectively equivalent source voltage and back electromotive force, L _sfor inductance coefficent, R is phase resistance, non-brush permanent-magnet DC motor and electric machine control system and ball-screw transmission mechanism form electromagnetic actuator control system jointly, then by the control characteristic of described electromagnetic actuator control system obtain its actual export to the vertical acting force of suspension be:

Wherein: T _lfor the torque of the actual output of motor, P _hfor ball-screw helical pitch, T _mfor motor output torque, J _rfor the moment of inertia of rotor, J _nfor the nut moment of inertia of ball-screw, ω is rotor rotating speed, K _tfor motor torque constant, i is control electric current, for electromagnetic actuator stretching speed and suspender travel speed;

for constant of the machine, for the equivalenting inertia torque of rotor and feed screw nut;

The integrality space equation then obtaining train active suspension is:

$\stackrel{\·}{x}=\mathrm{Ax}+\mathrm{Bv}+\mathrm{E\η}=\stackrel{\‾}{A}x+\stackrel{\‾}{B}i+\stackrel{\‾}{E}\mathrm{\η}$

${\stackrel{\·}{i}}_j={-\mathrm{\λ}}_j({\mathrm{Ri}}_j-u_j),j=\mathrm{1,2,3}$

Wherein: x=[x ₁ ^tx ₂ ^t] ^tfor state vector, x ₁=[y ₁ ^tθ ₁ ^ty ₄ ^ty ₂ ^tθ ₂ ^ty ₅ ^ty ₃ ^tθ ₃ ^ty ₆ ^t] ^t, $x_2={\left[\begin{array}{ccccccccc}{{\stackrel{\·}{y}}_1}^T& {{\stackrel{\·}{\mathrm{\θ}}}_1}^T& {{\stackrel{\·}{y}}_4}^T& {{\stackrel{\·}{y}}_2}^T& {{\stackrel{\·}{\mathrm{\θ}}}_2}^T& {{\stackrel{\·}{y}}_5}^T& {{\stackrel{\·}{y}}_3}^T& {{\stackrel{\·}{\mathrm{\θ}}}_3}^T& {{\stackrel{\·}{y}}_6}^T\end{array}\right]}^T,$ I=[i ₁ ^ti ₂ ^ti ₃ ^t] ^tfor controlling electric current, $\mathrm{\η}\left(t\right)={\left[\begin{array}{cccccc}{y_7}^T& {y_8}^T& {y_9}^T& {{\stackrel{\·}{y}}_7}^T& {{\stackrel{\·}{y}}_8}^T& {{\stackrel{\·}{y}}_9}^T\end{array}\right]}^T$ For the interference that the irregular input of track produces, i _jfor dynamicer exports, u _jfor dynamicer input, v be active controlling force and by

Obtain v=(I+JNB) ^-1(Ψ i-JNAx-JNE η), wherein I is the unit matrix of suitable dimension, and O is the null matrix of suitable dimension, J=diag{ [J _dj _dj _d], Ψ=diag{ [Φ Φ Φ] }, $A=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right],$ A ₁₁＝O ₉，A ₁₂＝I ₉， $B=\left[\begin{array}{c}{B}_1\\ B_2\end{array}\right],$ B ₁＝O _9×3， $\stackrel{\‾}{B}=B{(I+\mathrm{JNB})}^{-1}\mathrm{\Ψ},$

$\stackrel{\‾}{E}=E-B{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},E=\left[\begin{array}{c}{E}_1\\ E_2\end{array}\right],$ E ₁＝O _9×6，

$N=\left[\begin{array}{cccccccccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 1& -d_1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& d_1& -1\end{array}\right],$

$E_2=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& \frac{k_4}{m_{\mathrm{tb}}}& 0& 0& \frac{c_4}{m_{\mathrm{tb}}}& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& \frac{k_3}{m_{\mathrm{pb}}}& 0& 0& \frac{c_3}{m_{\mathrm{pb}}}\end{array}\right];$

When being generalized to second order dynamicer model, by the transport function of described first-order dynamic actuator model $G\left(s\right)=\frac{1}{L_{s}s+R}=\frac{{\mathrm{\λ}}_j}{s+{\mathrm{\λ}}_{j}R}$ Obtaining second-order model is:

${\stackrel{\·}{i}}_{1j}=i_{2j}$

${\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{1j}{i}_{1j}-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}\frac{u_j}{R}$

Wherein i _1jfor electric current, u _jfor voltage, R is resistance, and its proper polynomial is s ²+ λ _2js+ λ _1j=(s+ μ) (s+ λ _jr), make parameter μ > > 1, and then obtain λ _1j> > 1, λ _1j> > λ _2j;

Above-mentioned equation is determined under following hypothesis relation:

1. armature winding full symmetric, magnetic circuit is unsaturated, ignores the impact of teeth groove, commutation and armature reaction;

2. the two-phase armature terminal voltage worked in the three-phase of per moment non-brush permanent-magnet DC motor is only considered;

3. the electromagnetic consumable of non-brush permanent-magnet DC motor is not considered;

4. winding inductance coefficient L _s≤ 0.005;

Step 3, set up dynamicer fault model according to the fault type of electromagnetic actuator;

Described first-order dynamic actuator failures model is:

${\stackrel{\·}{i}}_j=-{\mathrm{\α}}_j{\mathrm{\λ}}_j({\mathrm{Ri}}_j-{\mathrm{\β}}_j{u}_j)$

Wherein α _jfor consider actuator generation motor overload even stall fault time fault parameter, when actuator motor runs well, α _j(t)=1; When motor overload even stall time, α _j(t)=0; Now due to the effect of current controller in electric machine control system, for time of failure; β _jfor considering fault parameter during actuator generation importation failure of removal, when actuator input is normal, β _j(t)=1, when actuator fractionated gain decays, wherein

In like manner setting up second order dynamicer fault model is:

${\stackrel{\·}{i}}_{1j}=i_{2j}$

${\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})$

Wherein i _1jcan be obtained by current sensor measurement;

The fault detect and the identification module that step 4, the basis of dynamicer fault model determined in step 3 construct distribution carry out on-line parameter estimation for the fault of each actuator;

First-order dynamic actuator is adopted then to be constructed as follows observer:

${\stackrel{\stackrel{\·}{^}}{i}}_j={-\mathrm{\λ}}_j({\hat{i}}_j-i_j)+{\mathrm{\λ}}_j{\widehat{\mathrm{\α}}}_j({\widehat{\mathrm{\β}}}_j{u}_j-{\mathrm{Ri}}_j)$

Wherein be respectively i _j, α _j, β _jobserved reading, for making parameter estimation in known span, adopt projection operator design adaptive law, following adaptive law is provided to ensure error e to the parameter in described single order fault model _1j∈ L ^∞∩ L ²:

$\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}=\mathrm{Pr}{\mathrm{oj}}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_j{e}_{1j}{\mathrm{\δ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1$

Wherein: for adaptive gain, $e_{1j}={\hat{i}}_j-i_j$ For observational error, ${\mathrm{\δ}}_{{\mathrm{\α}}_j}={\widehat{\mathrm{\β}}}_j{u}_j-{\mathrm{Ri}}_j,{\mathrm{\δ}}_{{\mathrm{\β}}_j}=u_j,$ Then according to Lyapunov stable theory, e _1j∈ L ^∞∩ L ²;

Second order dynamicer is adopted then to construct observer as follows:

${\stackrel{\stackrel{\·}{^}}{i}}_{1j}={-\mathrm{\τ}}_j({\hat{i}}_{1j}-i_{1j})+({\mathrm{\λ}}_{\mathrm{Fj}}-{\mathrm{\λ}}_{2j}){i_{2j}}^F+{\mathrm{\λ}}_{1j}{\widehat{\mathrm{\α}}}_j\left({\widehat{\mathrm{\β}}}_j\frac{{u_j}^F}{R}{{-i}_{1j}}^F\right)+{\mathrm{\λ}}_{1j}{\mathrm{\ϵ}}_j$

Wherein: for i _1jobserved reading, ${i_{1j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{1j},{i_{2j}}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{i}_{2j},{u_j}^F=\frac{1}{s+{\mathrm{\λ}}_{\mathrm{Fj}}}{u}_j$ For filtering variable, λ _fj> 0 is filter time constant, τ _jand ε _jfor the parameter to be designed for ensureing system stability, for making parameter estimation in known span, the same projection operator that adopts designs adaptive law, provides following adaptive law to ensure error e to parameter each in second order fault model and observer _2j∈ L ^∞∩ L ²:

$\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}=\mathrm{Pr}{\mathrm{oj}}_{\left[\mathrm{0,1}\right]}\{-{\mathrm{\γ}}_{{\mathrm{\α}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\αj}}\},\widehat{\mathrm{\α}}\left(0\right)=1$

$\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}=\mathrm{Pr}{\mathrm{oj}}_{[\mathrm{\η},1]}\{-{\mathrm{\γ}}_{{\mathrm{\β}}_j}{\mathrm{\λ}}_{2j}{e}_{2j}{\mathrm{\κ}}_{\mathrm{\βj}}\},\widehat{\mathrm{\β}}\left(0\right)=1$

${\stackrel{\·}{\mathrm{\ϵ}}}_j=-{\mathrm{\λ}}_{2j}{\mathrm{\ϵ}}_j-{\stackrel{\stackrel{\·}{^}}{\mathrm{\α}}}_j{{\mathrm{\κ}}_{\mathrm{\αj}}}^F-{\mathrm{\α}}_j{\stackrel{\stackrel{\·}{^}}{\mathrm{\β}}}_j\frac{{{\mathrm{\κ}}_{\mathrm{\βj}}}^F}{R},{\mathrm{\ϵ}}_j\left(0\right)=0$

Wherein: for adaptive gain, $e_{2j}={\hat{i}}_{1j}-i_{1j}$ For observational error, ${{\mathrm{\κ}}_{\mathrm{\αj}}}^F={{\widehat{\mathrm{\β}}}_j}^F\frac{{u_j}^F}{R}-{i_{1j}}^F,{{\mathrm{\κ}}_{\mathrm{\βj}}}^F={u_j}^F,$ κ _{β j}=u _j, then according to Lyapunov stable theory, e _2j∈ L ^∞∩ L ²;

Step 5, the actuator failures parameter determination ADAPTIVE ROBUST faults-tolerant control rule estimated by step 4, making system have fault-tolerant ability to fault and robustness when there is external disturbance, completing the fault diagnosis based on dynamicer and faults-tolerant control; Be specially:

(1) obtained by first-order dynamic actuator failures model described in step 3 obtained further by singular perturbation theory or obtained by second order dynamicer fault model by singular perturbation theory and λ _1j> > 1, λ _1j> > λ _2jobtain further wherein for time motor transship the actuator after even stall fault and export;

(2) constitution realization jamproof LQG controller u _r=Gx, wherein for the feedback gain matrix of controller, P is following Riccati non trivial solution $\stackrel{\‾}{F}=F-D{(I+\mathrm{JNB})}^{-1}\mathrm{JNE},F=\left[\begin{array}{cc}{O}_{12\×3}& O_{12\×3}\\ -I_3& O_3\end{array}\right],$ Wherein O is the null matrix of suitable dimension, and I is the unit matrix of suitable dimension, $\stackrel{\‾}{Q}=\mathrm{diag}\left\{\begin{array}{ccccccccccccccc}{q}_1& q_2& q_3& q_4& q_5& q_6& q_7& q_8& q_9& q_{10}& q_{11}& q_{12}& q_{13}& q_{14}& q_{15}\end{array}\right\},$ $\stackrel{\‾}{R}=\mathrm{diag}\left\{\begin{array}{ccc}{q}_{16}& q_{17}& q_{18}\end{array}\right\},$ Q ₁~ q ₁₈for quadratic performance function J _lthe performance weighting coefficient of middle property indices,

$\begin{array}{c}{J}_l=\underset{T\→\∞}{\lim }\frac{1}{T}\underset{0}{\overset{T}{\∫}}[q_1{{\stackrel{\·\·}{y}}_{10}}^2+q_2{{\stackrel{\·\·}{y}}_1}^2+q_3{{\stackrel{\·\·}{y}}_{12}}^2+q_4{{\stackrel{\·\·}{y}}_{13}}^2+q_5{{\stackrel{\·\·}{y}}_2}^2+q_6{{\stackrel{\·\·}{y}}_{24}}^2+q_7{{\stackrel{\·\·}{y}}_{23}}^2+q_8{{\stackrel{\·\·}{y}}_3}^2+q_9{{\stackrel{\·\·}{y}}_{11}}^2+q_{10}{(y_{10}-y_4)}^2\\ +q_{11}{(y_2-y_5)}^2+q_{12}{(y_{11}-y_6)}^2+q_{13}{(y_4-y_7)}^2+q_{14}{(y_5-y_8)}^2+q_{15}{(y_6-y_9)}^2+q_{16}{i_1}^2+q_{17}{i_2}^2\\ +q_{18}{i_3}^2]\mathrm{dt},\end{array}$

(3) adaptive controller of constitution realization faults-tolerant control wherein $\stackrel{\‾}{B}=\left[\begin{array}{ccc}{\stackrel{\‾}{B}}_1& {\stackrel{\‾}{B}}_2& {\stackrel{\‾}{B}}_3\end{array}\right],\widehat{\mathrm{\Λ}}=\left[\begin{array}{ccc}{\widehat{\mathrm{\α}}}_1{\stackrel{\‾}{B}}_1& {\widehat{\mathrm{\α}}}_2{\stackrel{\‾}{B}}_2& {\widehat{\mathrm{\α}}}_3{\stackrel{\‾}{B}}_3\end{array}\right],\widehat{\mathrm{\Σ}}=\mathrm{diag}\left(\begin{array}{c}\left[\begin{array}{ccc}{\widehat{\mathrm{\β}}}_1& {\widehat{\mathrm{\β}}}_2& {\widehat{\mathrm{\β}}}_3\end{array}\right]\end{array}\right),$ S > 0 is symmetric positive definite diagonal weight matrix;

(4) designing ADAPTIVE ROBUST fault-tolerant controller is u=u _r+ u _s.

5. a kind of train active suspension fault diagnosis and fault-tolerant control method based on dynamicer according to claim 4, is characterized in that: because second order dynamicer model is for observation i _2jthere is inconvenience in dynamic Design of Observer, therefore when actuator motor overload even stall time, set up following second order fault model:

${\stackrel{\·}{i}}_{1j}=i_{2j}$

${\stackrel{\·}{i}}_{2j}=-[{\mathrm{\λ}}_{2j}+(1-{\mathrm{\α}}_j){\mathrm{\ρ}}_j]i_{2j}+{\mathrm{\α}}_j{\mathrm{\λ}}_{1j}(\frac{1}{R}{u}_j-i_{1j})$

Wherein λ _2j+ ρ _j> > 1; When motor runs well, α _j(t)=1, when motor overload even stall time, α _j(t)=0, i _1j(t _fj)=i _r, and i _2jwill with λ _2j+ ρ _jspeed asymptotic convergence in zero, by select ρ _jvalue, make fault occur after i _1jand i _2jall can rapidly converge to zero with arbitrary speed; And when losing efficacy in actuator importation, set up following second order fault model:

${\stackrel{\·}{i}}_{1j}=i_{2j}$

${\stackrel{\·}{i}}_{2j}=-{\mathrm{\λ}}_{2j}{i}_{2j}+{\mathrm{\λ}}_{1j}({\mathrm{\β}}_j\frac{u_j}{R}-i_{1j})$

And hypothesis is under fault existence condition, λ _2jenough large to ensure i _2jcan zero be rapidly converged to, then make ρ _j=0, obtain second order dynamicer fault block mold.