Research Journal of Applied Sciences, Engineering and Technology 4(15): 2555-2563, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: March 30, 2012
Accepted: April 17, 2012
Published: August 01, 2012
LMI-Based Method of Robust Fault Detection H4 Filter for Anti-Pinch
of Pure Electric Vehicles
1
Xiaogang Yu, 1Changyun Miao, 2Haijing Yang, 1Hongqiang Li, 1Fangshu Liu,
1
Yongqiang Meng and 2Hong Chen
1
School of Electronics and Information Engineering, Tianjin Polytechnic
University, Tianjin 300387, China
2
Library, Tianjin University of Technology, Tianjin 300384, China
3
China Automotive Technology and Research Center, Tianjin 300162, China
Abstract: In order to effectively solve the risk of safety on power window, this study introduces the LMI-based
method of designing robust fault detection H4 filter for anti-pinch window control system. For detecting the
pinched condition, the pinch torque is considered as a fault to design a residual generator. By comparing the
residual signal with the pre-designed threshold, the occurrence of pinch can be detected. The main contribution
consisted of the formulation of the multi-objective optimization H4 and H- problem as H4 optimization problem
by using the residual error instead of residual. The solution of the optimization problem is solved via LMI
technique. Based on MATLAB, the results show that the algorithm can detect the fault after it occurs 70 ms.
In addition, simulation results show that the proposed algorithm has high sensitivity to fault and strong
robustness to uncertainties.
Keywords: Anti-pinch window, H4 filter, LMI, pure electric vehicle, robust fault detection
INTRODUCTION
In the automotive industry, electronic systems used
to provide the rapid increase in customer comfort with a
variety of vehicles, but also put forward new requirements
for the vehicles, such as power windows (Ma et al.,
2008). Power windows automatically rise and fall brings
convenient operation and security issues. It is often
possible hurt part of the body located in the path of the
window (Lee et al., 2008). Numerous of accidents caused
by power window without safety precaution have been
reported. Therefore, an anti-pinch window control system,
which can effectively solve the security risks and will not
affect the vehicle's comfort and working normal has been
paid much attention.
The conventional methods to detect pinching
conditions are generally divided into two categories: The
differential type pinch estimator based on the assumptions
that the sharp decline of velocity in the pinch condition
and the window move at a constant speed in smooth
operating conditions. However, this algorithm is
inadequate in reality, because the window frames friction
torque through the full range of vehicles closed panel is
usually different characteristics. The amount of
computation required in this pinch estimator is small, but
its performance could be degraded in the presence of
measurement noises. On the other hand, the absolute
pinch estimated response time advantage by changes in
the motor control current to compensate for the pinch
torque and angular velocity (Buja et al., 1995; SyedAhmad and Wells, 1993). However, it cannot guarantee
the robustness of abnormal vibration under real driving
conditions. Furthermore, this approach requires additional
current sensor to avoid false positives (Syed-Ahmad and
Wells, 1993), which cannot be a universal solution,
because the detection of the pinching condition depends
entirely on the engineer's inspired to determine current
restrictions. One type which recognizes a pinched
condition from a detected change in window velocity is
proposed and the other type recognizes a pinched
condition when the applied motor torque exceeds a
predetermined limit which requires an additional current
sensor to avoid false alarm (Zhang and Wang, 2011;
Angelo et al., 2006; Henry and Zolghadri, 2005). It might
not be a general solution because its performance relies on
the validity of a current limit. Using the change of motor
control current to detect the pinched condition
compensate the low response time of the pinch torque as
well as the window velocity (Doh and Ryoo, 2008). All
the changes of the DC motor are detected by sensors like
Hall sensors and current sensors in the above references.
These methods are poor on timeliness. The detection of
current amplitude method is proposed, which describes
the anti-pinch measures without sensors, but often makes
error detection (Yang et al., 2005).
Correspondindg Author: Hongqiang Li, School of Electronics and Information Engineering, Tianjin Polytechnic University,
Tianjin 300387, China
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
Model based fault detection has received much
attention in the last years, especially the design of fault
detection observer. The problem is treated in different
ways, for example, unknown input observer (Isermann,
2005), H4/H2 filter (Adil et al., 2010), multiple-observer
(Niaki and Seyed, 2009) and LMI approaches. The main
methods of model based (MBD)fault detection are as
follows:
The first method: utilize a reference model which will be
used to describe the ideal residual r. The reference model
should achieve both robustness and detection performance
which is as follows:
rf(s) = Trf(s) f(s) + Trd(s) d(s)
Trf, Trd are the transfer functions of fault and
disturbance. rf(s) is the residual, f(s) is the fault and d(s)
is the disturbance. In fact the realistic model is different
from the reference model, so the optimization problem
used here to synthesize the residual generator is
formulated as a robust H4 filtering problem.
The second method: provide some performance index
that will transfer the fault diagnosis to an optimization
question. The frequently-used performance indices are as
follows:
min J /  J /  
L
min J  /  J  /  
L
min J J 
L
Trd ( s)

 x  Ax  Bu  B f f  Bd d

 y  Cx  Du  D f f  Dd d
(1)
where x is the state, u is the control input, y is the
measurement, d is the unknown finite energy disturbance
(including modeling error signal, external signal and noise
signal), f represents the faults input. A, B, C, D, Bd, Dd, Bf,
Df are known matrices with appropriate dimensions
(Zheng and Wu, 2009).
The residual generator (or namely fault detection
observer) takes the form:
 x  Ax  Bu  H ( y  y )

 y  Cx  Du
 r  y  y

(2)
Obviously, the design of a robust fault detection
observer, i.e., determination of the observer gain matrix
H. Using (1) and (2), we can obtain the following form:
 e  ( A  HC)e  ( B f  HD f ) f  ( Bd  HDd )d

 r  Ce  D f f  Dd d
(3)
Note that the dynamics of the residual signal r
depends on not only d and f, but also the state e. We can
express the (3) in the form of transfer function:


Trf ( s)
Trd ( s)
Problem statements: Consider the linear time-invariant
system of the following form:

Trf ( s)
Trd ( s)
METHODOLOGY
i (Trf ( jw))

r(s) = Trd(s) d(s) + Trf(s) f(s)
 w  [0,  )
The ||T||4 is the maximum singular value of the
transfer function matrix, ||T||- is the minimum singular
value of the transfer function matrix; Trf, Trd are the
transfers of fault and disturbance. Fi(Trf(jw)) is the
nonzero singular value of the Trf.
In the second method the H- is not a norm, which is
not easy to optimized. So in this study the formulation of
the multi-objective optimization H4 and H- problem as H4
optimization problem by using the residual error instead
of residual. By optimizing the performance index, the gap
between the reference signal and the fault signal is
reduced. As the result, the residual signal has high
sensitivity to fault and strong robustness to uncertainties.
Next the detail devise of robust fault detection observer
based on first method will be discussed.
(4)
Trd, Trf are the transfer functions from d, f to r
respectively. Generating a residual signal which has best
sensitivity to the fault and robustness to the disturbance is
the purpose of the fault detection. In order to achieve the
best features of the residual, the following condition (5),
(6) are represented:
H  Trd
H  Trf



 sup  (Trd ( j ))   0

 inf  (Trf ( j ))  0
 
(5)
(6)
Condition (5) represents the worse-case criterion for
the effect of disturbances on the residual r, condition (6)
stands for the worse-case criterion for the sensitivity of r
to fault. Clearly, these two criteria capture the most
significant features of fault detection observer.
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
Since in condition (6) H- is not a system norm, for
static fault detection observer, we introduce reference
residual model WF(s) to describe the desired behavior for
the residual vector r and define the rF as the reference
residual:
rf(s) = WF(s) f(s).
Fig. 1: Reference residual model in fault detection
The criterion is:
 f  WF ( S )
r  rf
J w  sup
w
wL2 , w  0
sup
Tzw ( s) w
wL2
w
2
2
 sup
2
wL2 , w  0
 Tzw ( s)
2
re
2
w
2


Trf ( s)
  Trd ( s)WF ( s)  Trf ( s)]
So Trd(s), WF(s)-Trf(s) are as smaller as possible, one gets:

f
By the triangle inequality, the following is obtained:

 WF ( s)
So,

 Trf ( s)


f
(11)

  f , 0d
which meets the request of the index in (5) and (6).
The above process can be depicted by Fig. 1.
So the minimum singular value of the original
maximum problem, namely the H- index, is changed into
a H4 model matching problem. Next the fault detection
observer estimation for anti-pinch window based on
reference residual model will be discussed.
(10)
 d ,  f  (0,  ]
WF ( s)  Trf ( s)
 WF ( s)
0  WF ( s)
(9)
  d WF ( s)  Trf ( s)

In Eq. (10), the left reduces the effect of d to residual,
the later makes the fault approaching the reference signal,
which ensures the sensitivity. So designing the following
formularies:
(8)

J<(



Minimize J is minimizing the infinite norm of Eq. (8),
which meet:
Trd ( s)
 Trf ( s)
From the above equations, the following relation is
obtained:
(7)
where w = [uT fT dT], re = r!rf. The optimization criterion
Jw is the worst-case distance between the residual r and
the ideal residual rf, normed by the size of the inputs. The
Jw is the gain from w to the re:
Tzw ( s)


Analytical model of fault detection algorithm:
Modeling of DC motor for fault detection estimation:
The fault detection is based on analytical model. We
firstly estimate the accurate state-space model for the antipinch control system. As shown in the Fig. 2, the DC
motor system to drive window can be linearized.
The nomenclature of the linearized motor is given:
w(angular velocity speed), u(driving voltage),
Fig. 2: Linearized motor model
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
x  Ax  Bu
I(armature current), Tm(rotational torque), Td(disturbance
torque), Tc(control torque), Lm(armature inductance),
Rm(armature resistance), J(moment inertia), B(viscous
friction coefficient), Ke(back electromotive force
coefficient) and Kt(torque coefficient).
From Fig. 2, the transfer function from the rotational
torque to the angular velocity is given by:
 ( s)
Tm

Tm = Tc-Td = Tc-Tp-Tw-Tv
Since the vibration torque varies along the road
condition, it is difficult to define the velocity as a finite
mathematic model. To solve this problem we classified it
into energy bounded disturbance. The motor angular
velocity speed can be rewritten as:
B
1
1
  Tc  (Tp  Tw )  uv
J
J
J
Because of the electrical dynamics of the motor is
faster than the mechanical one, the control torque can be
approximated as follow:
Tc 



A 


1
Js  B
The disturbance torque is classified into vibration
torque Tv, pinch torque Tp and load torque Tw, so the
rotational torque can be written as follow:

y = Cx+Du

Ke Kt
1
K
  (Tp  Tw )  uv  t u
JRm
J
JRm
The Tp and Tw can be modeled as a single state for the
estimator design:
T = Tp+Tw
C
C

0

1 , B 
0

 Kt 
 JR 
 m
 0  , C  [1 0 0], D  [0]
 0 


Armature resistance test: The test is operated under
motor stall and the result is 0.85 S.
EMF coefficient test: Because of the inductor
presence the voltage of the armature reaches the
stable value after an adjustment time which reflects
the inductor.
We can know the adjustment time is 1.2 ms from the
waveform of the voltage changes, so the inductance is
0.649 mH. The stable value of the angular velocity speed
is 99.7 rad/s and the EMF coefficient can be obtained
from linear approximation between the voltage and the
angular velocity speed. Moreover, Ke is equal to Kt. (3)
Moment inertia test. Put the step voltage signal on the
motor and measure the corresponding speed curve, the Tn
can be obtained as 9.3 × 10G3 s under the 5% deviation of
the adjustment time. Based on the formula J =
Ke*Kt*Tn/Rm, the moment inertia is 1.586× 10G4 kgAm2. The
motor parameters are given in Table 1.
The matrices of the model can be designed as follow:
Since uncertain motor parametric uncertainty causes
the bias error in the model estimate, the previous result
using the torque estimate only is not suitable to the
realistic condition. To solve the problem, the torque rate
is augmented as an additional state and seen as a rank
disturbance:
 893109
  107.530  6305170
.
. 
0




0
0
1 , B   0  , C  [1 0 0], D  [0],
A 



0
0
0
 0 
 893109
 893109
. 
. 




Bd   0  , B f   0  , Dd  [0.05], D f  [1]
 0 
 0 
T  uTD
So we can have the state-space model for the design of
pinch estimator.
1
J
0
0
Design parameters for the model system: The main
uncertain factors of the anti-pinch window control system
are the vibration torque uv, model uncertain uTD and the
disturbance from traction torque when the window lifts,
these factors can be attributed as the finite energy
disturbance d. Bd, Dd are the distribution matrices of the
unknown finite energy disturbance According to the test,
the window height is 435 mm, rising time is 5 s, so the
average rate of increase is 87 mm/s. The anti-pinch resign
is 4-200 mm, so the fault detection is achieved after the
window lifts 2.7 s. Bf, Df are the distribution matrices of
the possible fault.
The parameters of the DC can be got by experiments,
the process is:
Kt
(u  Ke )
Rm
The viscous friction coefficient B has less influence
on the torque, so it can be neglect. Choose the angular
velocity speed as a single state the motor control torque
speed can be reorganize as:
Ke Kt
JRm
0
0
Fault detection observer estimation for anti-pinch
window: Assume we select the reference residual model
is the following form (Zhong et al., 2007):
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
Table 1: Nominal value of the motor parameters
Motor parameters
Rm
Lm
Ke
Kt
Tn
J
Vc
The following three conditions hold:
Value
0.8500[S]
0.6490[mH]
0.1204[V•s/rad]
0.1204[V•s/rad]
9.3×10-3[s]
1.586×10-4[kg•m2]
12[V]
 x F (t )  AF x F (t )  BF f (t )

 rF (t )  C F x F (t )  DF f (t )
C
C
C
The coefficient matrix of the reference model can be
solved as follow:
(12)
 AF  ( R  X ) 1 M T

1
 BF  ( R  X ) K

T
 CF  N
D  T
 F
~
Choose x  [eT x F T ]T , using (3) and (12), the following
form can be obtained:
~~
~
 x (t )  Ax (t ) 

~~
 re (t )  Cx (t ) 
~
Bw(t )
~
Dw(t )
Lemma 2 transfers the existence condition of fault
detection filter into a solvability problem of linear matrix
inequalities. Equation (14) is a linear matrix inequalities
about scalar (, so it can be optimized as a variable ( by
solving the following optimization problem to get H4
filter:
(13)
For more resolve, two lemmas are given as following:
Lemma 1: Given a system as follow:
 min 

 constra int s : formula (14)
 x(t )  Ax (t )  Bw(t )

 z (t )  Cx (t )  Dw(t )
A is asymptotically stable, ||T(s)||4<(, if and only if
there exists a matrix P = PT>0 satisfying:
Trd
E14
E22
E23
E24
*
*
I
*
0
I
*
*
*
E11 = RA+ATR!ZC!CTZT
E12 = RA!ZC+ATX!CTY+M, E13 = Rbd!ZDd,
E14 = RBf!ZDf, E15 = CT!N,
E22 = ATX + XA!CTY!YTC, E23 = XBd!YDd,
E24 = XBf !YTDf+K, E45 = DfT!TT

 WF

   14633
.
CF = [0.6386 - 0.0154 0.0013], DF = [0.8655],
E15 
C T 
DdT   0

E45 
 I 
X-R > 0
 0.0575, Trf
  0.0001  0.000
0.000 


AF    0.00029  0.0921 0.0225 
 0.0009
 0.0335  0.0998
Lemma 2: For system (1), given (>0, if there exists
positive definite matrix R and X, the matrix K, M, N, T, Y
and Z, which satisfy the following LMI:
E13

 7.3967 
 0.0494 




H    0.0164 , BF    0.6203
  0.4900
 0.0201 
The system asymptotically stable and satisfy
||Tzw(s)||4<(, Tzw is the transfer function of w to r.
E12
(15)
Using the LMI toolbox in MATLAB, the index, the
observer gain and the coefficient matrix of the reference
model can be got:
 PA  A T P PB
CT 


T
  1I
D  0
 B P

C
D
  1 I 
 E11
 *

 *

 *
 *

For system (1), there exists a H4 filter.
The observer gain H = R-1Z.
The system (13) asymptotically stable and satisfy
||re||2 < (||w||2, namely the index J<(.
(14)
Design of threshold: The basic method of the fault
detection is to construct an optimal fault detection
observer to acquire a residual. By comparing the residual
evaluation value with a threshold, the occurrence of pinch
can be detected. So we first decide the threshold based on
the normal states of the window. From Eq. (4) we know
the feature of residual is:
r(s) = Trd(s)d(s)+Trf(s)f(s)
When no fault occurs, there is also a certain load
torque in window control system. So according to the
2559
600
550
500
450
400
350
300
250
200
150
100
0.0
Pinch angular velocity
Normal angular velocity
6
Torque rate (Nm/s)
Angular velocity (deg/s)
Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
0.5
24
1.0
1.5 2.0 2.5 3.0 3.5
Time [sec]
4.0
4.5
2
0
-2
-6
0.0
5.0
Residual
12
4.5
5.0
-0.4
-0.6
-0.8
8
-1.0
4
-1.2
1.5 2.0 2.5 3.0 3.5 4.0
Time [sec]
1.5 2.0 2.5 3.0 3.5 4.0
Time [sec]
0
-0.2
16
1.0
1.0
0.2
Pinch torque
Normal torque
0.5
0.5
Fig. 5: Pinch torque rate
20
Torque (Nm)
4
-4
Fig. 3: Pinch angular velocity
0
0.0
Pinch torque rate
Normal torque rate
4.5
-1.4
-1.6
0.0
5.0
0.5
1.0
1.5
2.0 2.5 3.0
Time [sec]
3.5
4.0
4.5
Fig. 4: Pinch torque
Fig. 7: Normal residual signal
theory of fault detection, with the absence of fault and the
input voltage is a constant value case, Truu(s) + Trdd(s) =
0. The Eq. (16) can be obtained in the normal state:
r ( s)  Trf ( s) f ( s)
(16)
Solving the steady-state value of residual signal in
normal and taking the averag value of it as Jr. Because the
residual strikes in a certain range, we select threshold for
the average of 20% margin, namely the threshold meets
(Jr!Jth)/Jr = 20%.
SIMULATION AND RESULT ANALYSIS
MATLAB simulation results: When the fault occurs, the
angular velocity, torque and torque rate change as follow
Fig. 3 to 5, we can see at the pinch condition 2.7 s, the
rate changes dramatically. So by considering the
torque rate as criterion of pinch detection, the system
could improve the reliability of pinch detection even in
the presence of disturbance.
Using Simulation toolbox to build the robust fault
diagnosis system model of anti-pinch window, the input
is angular velocity and output is residual signal, shown in
Fig. 6. The model bases on the residual generator.
The Fig. 7 shows the normal residual when the
window lifts without fault. After 0.2 s the residual reaches
the steady-state value, taking the average of the residual
signal between 0.2~4.5 s. Based on the former analysis
we design the threshold as 0.8*-1.03823 (the average
value) = !0.8306.
When the force from the external obstacles is large,
the residual signal is shown as Fig. 8. After the pinch
occurs at 2.7 s, it can be detected with 70 ms timely in the
margin 20% as the Fig. 8 shown, which meets the
requirements that the residual has high sensitivity to fault.
When the force from the external obstacles is small,
the residual signal is shown as Fig. 9. The anti-pinch
Fig. 6: Simulink model of anti-pinch window
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
Residual
Threshold
Pinch detection
-0.4
Pinch occurs
X: 2.77
Y: -0.7988
-0.8
-1.0
-0.4
-0.6
Pinch occurs
X: 2.78
Y: -0.7964
-0.8
-1.0
-1.2
-1.2
-1.4
-1.6
0.0
Pinch detection
-0.2
Residual
Residual
-0.6
Residual
Threshold
0.2
0
0.5
1.0
1.5
2.0 2.5 3.0
Time [sec]
3.5
4.0
-1.4
-1.6
0.0
4.5
0.5
1.0
1.5
2.0 2.5 3.0
Time [sec]
3.5
4.0
4.5
Fig. 8: Fault residual signal with large obstacles
Fig. 9: Fault residual signal with small obstacles
condition can also be detected with 80 ms timely in the
margin 20%. So we consider the proposed algorithm
detects the pinched condition relatively fast in spite of the
disturbance and noise, which meets our requirements that
the residual has strong robustness to uncertainties.
Co-simulation results on CANoe-MATLAB: The CAN
bus technology has been widely applied in the pure
electric vehicles system at present (Duan et al., 2010). We
verify the anti-pinch algorithm in realistic window system
by using CANoe-MATLB interface connected with
Simulation node
LFD_ECU
MATLAB/Simulink
CANoe
CANopen
network
Motor
CANoe/
MATLAB
interface
Left rear view mirror Right rear view mirror
Door Lock
CANcaseXL USB 2.0
Interface card
Control switch
CAN Bus
Fig. 10: The co-simulation of anti-pinch window
2561
Control
algorithm
Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
1.2
current and the angular velocity is considered as a fault to
generate a residual which can be effectively detected and
guarantee the robustness in the method. By CANoeMatlab interface we realize the Co-simulation of the real
(CAN) hardware in a networked environment and the
function of anti-pinch. The simulation results show the
observer can detect the fault after it occurs 0.16 s and the
bus load rate is 3.49%. All of these valid the proposed
method can be used for anti-pinch detection on pure
electric vehicles.
Pinch detection
1.0
Residual
0.8
0.6
0.4
Pinch occurs
0.2
0.0
-0.2
-0.4
0.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Time [sec]
ACKNOWLEDGMENT
5.0
Fig. 11: Residual of pinch condition
MATLB/Simulink which has power modeling functions
and CANoe which has perfect functions of bus
simulation.
CANoe-MATLAB interface can be operated in two
different modes: one is offline mode, the other is
Hardware-in-the-Loop (HIL) mode. The whole system
simulation process is based on HIL mode as shown in Fig.
10. In HIL mode, CANoe runs as MATLAB/Simulink
subsidiary mode. When the time starts running simulink
model, CANoe will automatically open the bus monitor
and display bus message value and signal value. With the
Simulink Real-Time Workshop we can target CANoe and
produce a Windows DLL which can be loaded in
CANoe's simulation environment. One DLL must be
generated per node. With this approach it is possible to
test and verify a design with real (CAN) hardware in a
networked environment. The simulation can be used as a
simulation of the remainder of the bus in a real-time
environment. Several Electronic Control Units (ECUs)
can be simulated simultaneously the remaining bus in real
time. The simulation results are as follows.
Figure 11 shows the residual signal in co-simulation.
We can see the results are similar as the MATLAB
Simulation results. The residual changes dramatically
under the pinch condition which exceeds the threshold as
former results.
CONCLUSION
In this study, the pinch torque rate detection
algorithm based on H4 filter fault detection is proposed. A
performance index which includes both robustness against
disturbances and sensitivity against fault is used. By using
some results of H-infinity optimization, the H4 filter
design problem is formulated as an H-infinity
optimization problem. By using the LMI toolbox of
MATALB, we get the indices, the observer gain and the
coefficient matrix of the reference model. The designed
observer considers both robustness against disturbances
and sensitivity to fault. The simulation results show the
observer can detect the fault after it occurs 70 ms.
Compared with the former methods mentioned in the
instruction, we can see torque rate not the motor control
This study was supported by the National High
Technology Research and Development Program of China
(863 Program) (Grant No. 2001AA501310) and the
Specialized Research Fund for the Doctoral Program of
Higher Education of China (No. 20101201120001)”.
REFERENCES
Adil, A., D. Mohamed and B. Mohamed, 2010. Design of
robust H-reduced-order unknown-input filter for a
class of uncertain linear neutral systems. IEEE
T. Automat. Contr., 55(1): 6-19.
Angelo, C., G. Bossio, J. Solsona, G.O. Garcia and M.I.
Valla, 2006. Mechanican sensor-less speed con
control of permanent magent AC motors driving an
unkonwn load. IEEE T Ind. Electron., 53(2):
406-414.
Buja, G.S., R. Menis and M.I. Valla, 1995. Disturbance
torque estimation in a sensorless DC drive. IEEE T
Ind. Electron ., 42(4): 351-357.
Duan, J., H. Deng and Y. Yu, 2010. Co-Simulation of
SBW and FlexRay Bus Based on CANoe_MATLAB.
Proceedings of the 2010 IEEE International
Conference on Automation and Logistics, Hong
Kong and Macau, August, pp: 16-20.
Doh, T. and J. Ryoo, 2008. Robust stability condition and
analysis on steady-state tracking erors of repetitive
control systems. Int. J. Cont. Autom., 6(6): 960-967.
Henry, D. and A. Zolghadri, 2005. Design and analysis of
robust residual generators for systems under feedback
control. Automatica, 41(2): 251-264.
Isermann, R., 2005. Model-based fault detection and
diagnosis-status and application. Annu. Rev. Cont.,
29: 71-85.
Lee, Hye-Jin, R. Won-sang, Y. Tae-Sung and P. Jin-Bae,
2008. Practical pinch torque detection algorithm for
anti-pinch window control system application. IEEE
T. Ind. Electron., 55: 1376-1384.
Ma, W., S. Zhang and H. Wang, 2008. The design of antipinch car window using Hall sensor. Automot. Eng.,
35(12): 1256-1260.
Niaki, S. and A. Taghi, 2009. Decision-making in
detecting and diagnosing faults of multivariate
statistical quality control systems. Int. J. Adv. Manuf.
Tech., 42(8): 713-724.
2562
Res. J. Appl. Sci. Eng. Technol., 4(15): 2555-2563, 2012
Syed-Ahmad, N. and F.M. Wells, 1993. Torque
estimation and compensation for speed control of a
DC motor using an adaptive approach. Proceedings
of the 36th Midwest Symposium on Circuits and
Systems, pp: 68-71.
Yang, H., J. Mathew and L. Ma, 2005. Fault diagnosis of
element bearing using basis pursuit. Mech. Syst.
Signal., 19: 341-356.
Zhang, X.Z. and Y.N. Wang, 2011. A novel positionsensorless control method for brushless DC motor.
Energ. Convers. Manage., 52(3): 1669-1676.
Zheng, Q. and F. Wu, 2009. Nonlinear H- infinity control
designs with axisym metric spacecraft control. J.
Guid. Contr. Dynam., 32(3): 850-859.
Zhong, M., S.X. Ding, J. Lam and W. Haibo, 2007. An
LMI approach to design robust fault detection filter
for uncertain LTI systems. Automatica, 39: 543-550.
2563