# Decoupling Suspension Controller Based on Magnetic Flux Feedback

Authors: Wenqing Zhang; Jie Li; Kun Zhang; Peng Cui
Journal: The Scientific World Journal
 (2013)

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## Abstract

The suspension module control system model has been established based on MIMO (multiple input and multiple output) state feedback linearization. We have completed decoupling between double suspension points, and the new decoupling method has been applied to CMS04 magnetic suspension vehicle in national mid-low-speed maglev experiment field of Tangshan city in China. Double suspension system model is very accurate for investigating stability property of maglev control system. When magnetic flux signal is taken back to the suspension control system, the suspension module’s antijamming capacity for resisting suspension load variety has been proved. Also, the external force interference has been enhanced. As a result, the robustness and stability properties of double-electromagnet suspension control system have been enhanced.


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## Body

## 1. Introduction

Maglev vehicle has minor noise, no pollution safety, and comfort many other advantages, so the maglev traffic has a bright prospect in the future. Maglev vehicle concludes several complex subsystems [1] with coupling relations. The vehicle’s suspension and guidance depend on magnetic force, and its traction relies on linear motion actuator. According to the production method of magnetic force, maglev system can be divided into two types: EDS and EMS. EMS can make vehicle suspend on the guideway keeping a certain gap, but suspension system in itself is not stable, so it needs active control. Maglev control technology is one of crucial techniques in suspension system. Maglev vehicle is a typical nonlinear system, and suspension module concludes two coupled suspension points which are connected by a rigid joint. The coupling problem is not obvious on straight guideway, but when maglev vehicle arrives at the vertical curve and the curved guideway, the coupling problem can make maglev system unstable. So how to work out this problem is an imperative thing for maglev engineers.  Lin et al.  have studied the design of a robust discrete-time sliding mode control (DT-SMC) [2] for a high-precision electrohydraulic actuator (EHA) recently. Ngoc [3] first proved an explicit criterion for positive linear time-varying differential systems with distributed delay. A new approach can keep stabilization of time-varying nonlinear systems with distributed input delay by feedback of plant’s state in paper [4]. The stability bound [5] of the singular perturbation parameter can be obtained by solving a set of matrix inequalities. Control redundancies are proposed [6], for example, the controllable redundancy, observable redundancy, stabilization redundancy, and detectable redundancy. The fuzzy sliding mode control approach [7] can be applied to deal with the output tracking of the uncertain system. Nonlinear value control based on FDM (feedback domination method) is simple and has robustness [8] to some kinds of unknown disturbances. The nonlinear feedback principle is developed [9] using the direct-axis and the quadrature-axis stator voltage as manipulated variables. Roy and Asada have investigated nonlinear feedback control of a gravity assisted under actuated manipulator [10] with application to aircraft assembly. A simple methodology [11] to evaluate harmonic distortion in the frequency domain for circuits and systems made up of a nonlinear high-gain path with a nonlinear feedback network is presented. Think that suspension force is a single function about magnetic flux density, and the relation between suspension force and magnetic density’s square is linear [12]. So we take magnetic flux density back to maglev system for promoting the robustness and stability. CMS04 maglev vehicle designed by NUDT (National University of Defense Technology) is showed in Figure 1.Figure 1
CMS04 mid-low-speed maglev vehicle.


## 2. Foundation of Flux Feedback Control Suspension Model

EMS  middle- and low-speed  maglev vehicle applies modular suspension bogies, and one module concludes two suspension points. Double suspension points’ suspension task is accomplished by one suspension controller.Assume the following:(1)
the leakage flux of magnetic winding is neglected;(2)
the magnetic resistances of the ferrite core and rail are neglected; namely, magnetic potential falls on air gapz(t) evenly;(3)
the inclination angle of magnetic rigid body is minuscule, and active point of magnetic force is considered invariable;(4)
the action line of load forces is superposed with direction of suspension gap measured;(5)
distribution of mass of the bracket is even, and the masses of two magnets are equal, so the action point of gravity is superposed on the geometry centerO.Based on above assumptions, the force analysis and geometrical relationship of maglev system are showed in Figure2.Figure 2
Suspension system’s force analysis map.Signs of Figure2 are illuminated in Table 1.Table 1
Symbols in double suspension points system.
Signs
Signification
N
Number of magnetic coils
R
Magnetic resistance
μ
0
Magnetic permeability of atmosphere4π×10-7 H/m
g
Acceleration of gravitation9.8m/s2
θ
Separation angle between electromagnet axis line and horizon
F
1
Electromagnetic force of suspension pointP1
N
1
Disturbing force of suspension pointP1
L
Total length of electromagnet
i
1
(
t
)
Current of magnetic coil in suspensionP1
u
1
(
t
)
Voltage of magnetic coil in suspension pointP1
z
1
(
t
)
Measured position value in suspension pointP1
d
1
(
t
)
Average gap value between guideway and suspension pointP1
S
Magnetic pole area
B
Suspension gap flux density
M
Total mass of suspension system
I
Rotation inertia of electromagnet forO point
d
Distance from guideway toO point
F
2
Electromagnetic force of suspension pointP2
N
2
Disturbing force of suspension pointP2
l
Disturbing force of arm relativeto O point
i
2
(
t
)
Current of magnetic coil in suspension pointP2
u
2
(
t
)
Voltage of magnetic coil in suspension pointP2
z
2
(
t
)
Measured position value in suspension pointP2
d
2
(
t
)
Average gap value between guideway and suspension pointP2


### 2.1. Mathematical Model

#### 2.1.1. Kinematics Equations

When electromagnet module is in condition of balance, we can obtain the equation∑Fi=0 and ∑Mi=0. The kinematics equations of maglev system can be got as follows:
(1)12M·(z¨1+z¨2)=Mg-F1-F2+f1+f2,IL·(z¨1-z¨2)=f1·12l-f2·12l-14F1·l+14F2·l.Extract acceleration signals from (1):
(2)z¨1=-2L-3l2ML·F1+-2L+3l2ML·F2+L+3lML·f1+L-3lML·f2+g,z¨2=-2L+3l2ML·F1+-2L-3l2ML·F2+L-3lML·f1+L+3lML·f2+g.SetA=(-2L-3l)/2ML, B=(-2L+3l)/2ML, C=(L+3l)/ML, and D=(L-3l)/ML.Simplify (2):
(3)z¨1=A·F1+B·F2+C·f1+D·f2+g,z¨2=B·F1+A·F2+D·f1+C·f2+g.


#### 2.1.2. Electromagnetics Equations

We can get geometrical relationship of parameters in Figure2. The relation between measurement positions z1, z2 and real physical positions d1, d2 is
(4)d1=12(z1+z)=34z1+14z2,d2=12(z2+z)=14z1+34z2.Magnetic force equations are as follows:(5)F1=B12Sμ0,F2=B22Sμ0.


#### 2.1.3. Electricity Equations

Voltage balance equations of electromagnet winding are denoted in (6):
(6)u1=2Rd1μ0NB1+NSB˙1,u2=2Rd2μ0NB2+NSB˙2.Substituting (4) into (6), we get
(7)u1=R(3z1+z2)2μ0N·B1+NSB˙1,u2=R(z1+3z2)2μ0N·B2+NSB˙2.From (7), we obtain
(8)B˙1=φ1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φ2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.On all accounts, the dynamic law of maglev system can be determined by the following equations:(9)z¨1=A·B12Sμ0+B·B22Sμ0+C·f1+D·f2+g,z¨2=B·B12Sμ0+A·B22Sμ0+D·f1+C·f2+g,B˙1=φi1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φi2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.


### 2.2. State-Space Equations

Choosex=[x1,x2,x3,x4,x5,x6]T=[z1,z˙1,z2,z˙2,B1,B2]T as state variable vectors, and the state-space model of maglev system is given as follows:
(10)x˙1=x2,x˙2=A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+g,x˙3=x4,x˙4=B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g,x˙5=-R·(3x1+x3)2μ0SN2x5+1NSu1,x˙6=-R·(x1+3x3)2μ0SN2x6+1NSu2.Simplify (10):
(11)x˙=f(x)+g(x)·u,y=h(x),
where
(12)f(x)=[x2A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+gx4B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g-R·(3x1+x3)2μ0SN2x5-R·(x1+3x3)2μ0SN2x6],g(x)=[g1(x)g2(x)]=[000000001NS001NS],h(x)=[h1(x)h2(x)]=[x1x3],u=[u1u2].Theorem 1.
MIMO affine nonlinear system is described as(13)x˙=f(x)+∑i=1mgi(x)ui,y=h(x).
Set the equilibrium pointx0∈X. The problem of MIMO nonlinear system feedback linearization will have a solution, if and only if a neighborhood U near x0 and m functions h1(x),…,hm(x) exists. The solution makes relative degree (r1,…,rm) of nonlinear system (11) satisfy r1+r2+⋯+rm=n, where n denotes the dimension of system and m stands for input dimension.


### 2.3. Demonstration of Definition 1

Define the equilibrium point of maglev systemx0=[z10,z˙10,z20,z˙20,i10,i20]T, and suppose state variables x1,x2,x5,x6∈R+, according to real maglev system construction. Compute the vector field as follows, by f(x) and g(x):
(14)Lg1Lf0h1(x)=0,Lg2Lf0h1(x)=0,Lg1Lfh1(x)=0,Lg2Lfh1(x)=0,Lg1Lf2h1(x)=2A·x5μ0N≠0,Lg2Lf2h1(x)=2B·x6μ0N≠0,Lg1Lf0h2(x)=0,Lg2Lf0h2(x)=0,Lg1Lfh2(x)=0,Lg2Lfh2(x)=0,Lg1Lf2h2(x)=2B·x5μ0N≠0,Lg2Lf2h2(x)=2A·x6μ0N≠0.Namely, above equations satisfy(15)LgjLfkhi(x)=0,∀x∈V,1≤j≤m,1≤i≤m,pppppppppppppppppppppppppppp0≤k≤ri-2,LgjLfrihi(x)≠0,
where
(16)H(x)=[Lg1Lfr1-1h1(x)Lg2Lfr1-1h1(x)Lg1Lfr2-1h2(x)Lg2Lfr2-1h2(x)]=[2A·x5μ0N2B·x6μ0N2B·x5μ0N2A·x6μ0N].At the moment,detH(x)=4(A2-B2)·x5x6/μ02N2≠0; then E(x) is not singular. Relative degree of maglev system is (r1,r2)=(3,3), and
(17)r=∑i=12ri=6=n.Therefore, Theorem1 has been proved.


### 2.4. MIMO Double Suspension Points Model with Feedback Linearization

Compute the vector field generated byf(x) and h(x) as follows:
(18)Lf3h1(x)=1μ02N2[-AR(3x1+x3)x52-BR(x1+3x3)x62],Lf3h2(x)=1μ02N2[-BR(3x1+x3)x52-AR(x1+3x3)x62].Design feedback control valueu=H-1(x)[-b(x)+v], where the terms u=[u1u2]T, v=[v1v2]T, and
(19)H-1(x)=μ0N2(A2-B2)·[Ax5-Bx6-Bx5Ax6],b(x)=[Lfr1h1(x)Lfr2h2(x)]T=[Lf3h1(x)Lf3h2(x)]T.We can obtain the control value after linearization from (19):
(20)u=H-1(x)[-b(x)+v]={μ0N2(A2-B2)·[-Ax5·Lf3h1(x)+Bx6·Lf3h2(x)μ0N2(A2-B2)·3+Ax5·v1-Bx6·v2]μ0N2(A2-B2)·[Bx5·Lf3h1(x)-Ax6·Lf3h2(x)μ0N2(A2-B2)·3-Bx5·v1+Ax6·v2].The diffeomorphic mapping matrix is(21)Φ(x)=[h1(x)Lfh1(x)Lf2h1(x)h2(x)Lfh2(x)Lf2h2(x)]=[x1x2A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+gx3x4B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g].Choose the coordinates of transformation by matrixΦ(x):
(22)δ=[h1(x)Lfh1(x)Lf2h1(x)h2(x)Lfh2(x)Lf2h2(x)]T.In sum, maglev control system model after linearization is showed as follows:(23)δ˙=Ψδ+Tv,y=Ωδ,
where
(24)Ψ=[010000001000000000000010000001000000],T=[000010000001],Ω=[100000000100].Maglev system after feedback linearization is expressed by two-level integral subsystems:(25)G(s)=[1s3001s3].Double suspension points’ closed control block diagram with magnetic flux feedback is showed in Figure3.Figure 3
Double suspension points’ control construction diagram with feedback linearization.


## 2.1. Mathematical Model

### 2.1.1. Kinematics Equations

When electromagnet module is in condition of balance, we can obtain the equation∑Fi=0 and ∑Mi=0. The kinematics equations of maglev system can be got as follows:
(1)12M·(z¨1+z¨2)=Mg-F1-F2+f1+f2,IL·(z¨1-z¨2)=f1·12l-f2·12l-14F1·l+14F2·l.Extract acceleration signals from (1):
(2)z¨1=-2L-3l2ML·F1+-2L+3l2ML·F2+L+3lML·f1+L-3lML·f2+g,z¨2=-2L+3l2ML·F1+-2L-3l2ML·F2+L-3lML·f1+L+3lML·f2+g.SetA=(-2L-3l)/2ML, B=(-2L+3l)/2ML, C=(L+3l)/ML, and D=(L-3l)/ML.Simplify (2):
(3)z¨1=A·F1+B·F2+C·f1+D·f2+g,z¨2=B·F1+A·F2+D·f1+C·f2+g.


### 2.1.2. Electromagnetics Equations

We can get geometrical relationship of parameters in Figure2. The relation between measurement positions z1, z2 and real physical positions d1, d2 is
(4)d1=12(z1+z)=34z1+14z2,d2=12(z2+z)=14z1+34z2.Magnetic force equations are as follows:(5)F1=B12Sμ0,F2=B22Sμ0.


### 2.1.3. Electricity Equations

Voltage balance equations of electromagnet winding are denoted in (6):
(6)u1=2Rd1μ0NB1+NSB˙1,u2=2Rd2μ0NB2+NSB˙2.Substituting (4) into (6), we get
(7)u1=R(3z1+z2)2μ0N·B1+NSB˙1,u2=R(z1+3z2)2μ0N·B2+NSB˙2.From (7), we obtain
(8)B˙1=φ1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φ2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.On all accounts, the dynamic law of maglev system can be determined by the following equations:(9)z¨1=A·B12Sμ0+B·B22Sμ0+C·f1+D·f2+g,z¨2=B·B12Sμ0+A·B22Sμ0+D·f1+C·f2+g,B˙1=φi1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φi2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.


## 2.1.1. Kinematics Equations

When electromagnet module is in condition of balance, we can obtain the equation∑Fi=0 and ∑Mi=0. The kinematics equations of maglev system can be got as follows:
(1)12M·(z¨1+z¨2)=Mg-F1-F2+f1+f2,IL·(z¨1-z¨2)=f1·12l-f2·12l-14F1·l+14F2·l.Extract acceleration signals from (1):
(2)z¨1=-2L-3l2ML·F1+-2L+3l2ML·F2+L+3lML·f1+L-3lML·f2+g,z¨2=-2L+3l2ML·F1+-2L-3l2ML·F2+L-3lML·f1+L+3lML·f2+g.SetA=(-2L-3l)/2ML, B=(-2L+3l)/2ML, C=(L+3l)/ML, and D=(L-3l)/ML.Simplify (2):
(3)z¨1=A·F1+B·F2+C·f1+D·f2+g,z¨2=B·F1+A·F2+D·f1+C·f2+g.


## 2.1.2. Electromagnetics Equations

We can get geometrical relationship of parameters in Figure2. The relation between measurement positions z1, z2 and real physical positions d1, d2 is
(4)d1=12(z1+z)=34z1+14z2,d2=12(z2+z)=14z1+34z2.Magnetic force equations are as follows:(5)F1=B12Sμ0,F2=B22Sμ0.


## 2.1.3. Electricity Equations

Voltage balance equations of electromagnet winding are denoted in (6):
(6)u1=2Rd1μ0NB1+NSB˙1,u2=2Rd2μ0NB2+NSB˙2.Substituting (4) into (6), we get
(7)u1=R(3z1+z2)2μ0N·B1+NSB˙1,u2=R(z1+3z2)2μ0N·B2+NSB˙2.From (7), we obtain
(8)B˙1=φ1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φ2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.On all accounts, the dynamic law of maglev system can be determined by the following equations:(9)z¨1=A·B12Sμ0+B·B22Sμ0+C·f1+D·f2+g,z¨2=B·B12Sμ0+A·B22Sμ0+D·f1+C·f2+g,B˙1=φi1=-R(3z1+z2)2μ0SN2·B1+1NS·u1,B˙2=φi2=-R(z1+3z2)2μ0SN2·B2+1NS·u2.


## 2.2. State-Space Equations

Choosex=[x1,x2,x3,x4,x5,x6]T=[z1,z˙1,z2,z˙2,B1,B2]T as state variable vectors, and the state-space model of maglev system is given as follows:
(10)x˙1=x2,x˙2=A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+g,x˙3=x4,x˙4=B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g,x˙5=-R·(3x1+x3)2μ0SN2x5+1NSu1,x˙6=-R·(x1+3x3)2μ0SN2x6+1NSu2.Simplify (10):
(11)x˙=f(x)+g(x)·u,y=h(x),
where
(12)f(x)=[x2A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+gx4B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g-R·(3x1+x3)2μ0SN2x5-R·(x1+3x3)2μ0SN2x6],g(x)=[g1(x)g2(x)]=[000000001NS001NS],h(x)=[h1(x)h2(x)]=[x1x3],u=[u1u2].Theorem 1.
MIMO affine nonlinear system is described as(13)x˙=f(x)+∑i=1mgi(x)ui,y=h(x).
Set the equilibrium pointx0∈X. The problem of MIMO nonlinear system feedback linearization will have a solution, if and only if a neighborhood U near x0 and m functions h1(x),…,hm(x) exists. The solution makes relative degree (r1,…,rm) of nonlinear system (11) satisfy r1+r2+⋯+rm=n, where n denotes the dimension of system and m stands for input dimension.


## 2.3. Demonstration of Definition 1

Define the equilibrium point of maglev systemx0=[z10,z˙10,z20,z˙20,i10,i20]T, and suppose state variables x1,x2,x5,x6∈R+, according to real maglev system construction. Compute the vector field as follows, by f(x) and g(x):
(14)Lg1Lf0h1(x)=0,Lg2Lf0h1(x)=0,Lg1Lfh1(x)=0,Lg2Lfh1(x)=0,Lg1Lf2h1(x)=2A·x5μ0N≠0,Lg2Lf2h1(x)=2B·x6μ0N≠0,Lg1Lf0h2(x)=0,Lg2Lf0h2(x)=0,Lg1Lfh2(x)=0,Lg2Lfh2(x)=0,Lg1Lf2h2(x)=2B·x5μ0N≠0,Lg2Lf2h2(x)=2A·x6μ0N≠0.Namely, above equations satisfy(15)LgjLfkhi(x)=0,∀x∈V,1≤j≤m,1≤i≤m,pppppppppppppppppppppppppppp0≤k≤ri-2,LgjLfrihi(x)≠0,
where
(16)H(x)=[Lg1Lfr1-1h1(x)Lg2Lfr1-1h1(x)Lg1Lfr2-1h2(x)Lg2Lfr2-1h2(x)]=[2A·x5μ0N2B·x6μ0N2B·x5μ0N2A·x6μ0N].At the moment,detH(x)=4(A2-B2)·x5x6/μ02N2≠0; then E(x) is not singular. Relative degree of maglev system is (r1,r2)=(3,3), and
(17)r=∑i=12ri=6=n.Therefore, Theorem1 has been proved.


## 2.4. MIMO Double Suspension Points Model with Feedback Linearization

Compute the vector field generated byf(x) and h(x) as follows:
(18)Lf3h1(x)=1μ02N2[-AR(3x1+x3)x52-BR(x1+3x3)x62],Lf3h2(x)=1μ02N2[-BR(3x1+x3)x52-AR(x1+3x3)x62].Design feedback control valueu=H-1(x)[-b(x)+v], where the terms u=[u1u2]T, v=[v1v2]T, and
(19)H-1(x)=μ0N2(A2-B2)·[Ax5-Bx6-Bx5Ax6],b(x)=[Lfr1h1(x)Lfr2h2(x)]T=[Lf3h1(x)Lf3h2(x)]T.We can obtain the control value after linearization from (19):
(20)u=H-1(x)[-b(x)+v]={μ0N2(A2-B2)·[-Ax5·Lf3h1(x)+Bx6·Lf3h2(x)μ0N2(A2-B2)·3+Ax5·v1-Bx6·v2]μ0N2(A2-B2)·[Bx5·Lf3h1(x)-Ax6·Lf3h2(x)μ0N2(A2-B2)·3-Bx5·v1+Ax6·v2].The diffeomorphic mapping matrix is(21)Φ(x)=[h1(x)Lfh1(x)Lf2h1(x)h2(x)Lfh2(x)Lf2h2(x)]=[x1x2A·x52Sμ0+B·x62Sμ0+C·f1+D·f2+gx3x4B·x52Sμ0+A·x62Sμ0+D·f1+C·f2+g].Choose the coordinates of transformation by matrixΦ(x):
(22)δ=[h1(x)Lfh1(x)Lf2h1(x)h2(x)Lfh2(x)Lf2h2(x)]T.In sum, maglev control system model after linearization is showed as follows:(23)δ˙=Ψδ+Tv,y=Ωδ,
where
(24)Ψ=[010000001000000000000010000001000000],T=[000010000001],Ω=[100000000100].Maglev system after feedback linearization is expressed by two-level integral subsystems:(25)G(s)=[1s3001s3].Double suspension points’ closed control block diagram with magnetic flux feedback is showed in Figure3.Figure 3
Double suspension points’ control construction diagram with feedback linearization.


## 3. Design of Suspension Controller

Controlled matrix of system (23) is
(26)Mc=[TΨTΨ2TΨ3TΨ4TΨ5T]=[000010000000001000000000100000000000000001000000000100000000010000000000].Because ofrank(Mc)=6, maglev system after linearization is controlled completely. So we design double suspension controller for regulating control properties of suspension system:
(27)v1=Kp1·(d1-z0)+Kd1·d˙1+Ki1·∫(d1-z10)·dt,v2=Kp2·(d2-z0)+Kd2·d˙2+Ki2·∫(d2-z20)·dt.The geometrical relationship between measured positions and real physical positions in (28) is as follows:
(28)d1=34z1+14z2,d2=14z1+34z2.We can get(29)v1=Kp1·(34z1+14z2-z10)+Kd1·z˙1+Ki1·∫(34z1+14z2-z10)·dt,v2=Kp2·(14z1+34z2-z0)+Kd2·z˙2+Ki2·∫(14z1+34z2-z20)·dt.By now, double suspension points’ controller based on magnetic flux feedback was completed. Construction of the controller is described in Figure4.Figure 4
Block diagram of double suspension points system.


## 4. Experiments

Some experiments have been completed on CMS04 suspension bogie designed by NUDT (National University of Defense Technology), which is showed in Figure5. These experiments conclude experiment S1 and experiment S2. Algorithm S1: traditional position-current double cascade suspension PID control method. Algorithm S2: magnetic flux feedback control algorithm based on MIMO feedback linearization. Initial suspension gap of maglev system is 25 mm, and the set value is 10 mm. Decoupling control experiment has been implemented on CMS04 maglev control experiment platform.Figure 5
CMS04 maglev control experiment platform based on magnetic flux feedback.Standard maglev bogie’s parameters are given in Table2.Table 2
Standard maglev bogie parameters of CMS04 maglev vehicle.
Parameters
Values
m [kg]
653
N [integer]
324
A [m2]
0.0235
R [Ω]
0.5
z
0
/
m
0.008
B
0
/
T
23
g
9.8
μ
0
4
π
×
1
0
-
7Decoupling property test comes true on one suspension point of maglev bogie. Set expected position 10 mm. When maglev system  becomes  stable, we add additional square signal with amplitude 0.5 mm and period 4 s. Observe suspension signals with two control algorithms S1 and S2. Experiment results are showed in Figures6 and 7.Figure 6
Position curves of algorithm S1.Figure 7
Position curves of algorithm S2.Experiment results illustrate that when double suspension control system applies algorithm S2, the dynamic decoupling problem has been worked out. S2 raises the robustness and stability properties of maglev control system, but method S1 has no decoupling effect.


## 5. Conclusions

Double suspension control model has been founded with magnetic flux signal based on MIMO feedback linearization. The feedback linearization algorithm enables  accurate  linearizing model to keep all properties of original nonlinear system which  overcome  the disadvantages of Taylor’s expansion linearization method. In order to work out dynamic coupling problem and external interference problem of EMS mid-low-speed maglev vehicle, we take magnetic flux signal back to maglev control system and design double suspension compensable controller. Some experiments about new algorithm have been done in maglev vehicle CMS04 designed by NUDT. Experiment results demonstrate that double suspension module is precise based on MIMO state feedback linearization theory. With magnetic flux feedback, the maglev control system has better robustness and adaptability than traditional algorithm.



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*Source: 956790-2013-06-11.xml*