PARITY SPACE METHOD BASED DESIGN OF
UNKNOWN INPUT OBSERVERS FOR FAULT
DETECTION IN VEHICLE LATERAL DYNAMICS
CONTROL SYSTEM
S. Schneider
a,b
, N. Weinhold
b
, S.X. Ding
b
, H.-G. Schulz
b
, E. L. Ding
a
, A. Rehm
c
aDept. of Physical Engineering, University of Applied Sciences Gelsenkirchen,
45877 Gelsenkirchen, Germany
bInstitute for Automatic Control and Complex Systems, Faculty 5, Univerity Duisburg-Essen,
47048 Duisburg, Germany
cRobert Bosch GmbH, Stuttgart, Germany
Keywords: Fault detection, UIO, parity space approach, vehicle lateral dynamics
ABSTRACT
In this paper an approach to the design and implementation of a fault detection system (FDS) for vehicle lateral
dynamics control systems is presented. The basic idea is to design the FDS using the parity space methods.
At the implementation stage, the FDS is ¯rst transformed into an observer and then realised in a closed-loop
structure. Simulation results generated with the software CarSim are used to illustrate the proposed approach.
1. INTRODUCTION
The increasing use of automatic systems in vehicle driv-
ing control like for example ABS (Anti-lock Breaking Sys-
tem), ESP (Electronic Stability Program), ACC (Adaptive
Cruise Control) and ASC (Anti Slip Control) improves, on
the one side, the vehicle dynamics signi¯cantly, requires, on
the other side, the integration of an e®ective fault detec-
tion and supervision system. The focus of this paper is on
an early detection of sensor faults in the vehicle dynamics
stabilisation systems.
The objective of this paper is to develop an approach to
the design and implementation of a fault detection system
(FDS) for vehicle lateral dynamics control systems. This
work has been strongly motivated by the following two facts:
² Observer based FD technique is a powerful tool to solve
FDI problems in mechatronic systems like vehicle lat-
eral dynamics control systems;
² It is often the case that due to the lack of needed knowl-
edge in advanced control theory engineers have di±cul-
ties with the design of observer based FD.
The basic idea of the approach proposed in this paper is to
design an observer based FD system with the aid of the so-
called parity space methods. A signi¯cant advantage of the
parity space methods is that only computation of some well-
de¯ned algebraic equations is involved by the FD system
design. For our purpose, the well-established relationships
between the parity space based and the observer based FD
systems will be used.
2. PROBLEM FORMULATION AND
VEHICLE MODEL
In this chapter, we ¯rst describe the main problems which
are focused in this paper and then introduce the model used
for the FDS.
2.1. Problem Formulation
As mentioned above the main goal is to detect faults in the
sensors used for the vehicle lateral dynamics control sys-
tems. The sensors to be supervised are the lateral accelera-
tion sensor and the yaw rate sensor. The sensor signals are
corrupted by noise and are also in°uenced by the total roll
angle (road bank angle + vehicle roll angle) of the vehicle,
which can be regarded as an unknown input. Hence the FD
system must be robust against noise and the unknown input
while being sensitive to the faults.
To solve this design problem the optimization (1) can
be used. It has been proven that the performance index
of the system gets better with the increase of the order of
the parity vector[Ding et al. 1999b, Ding et al. 2000]. The
optimal solution of (1) results in a high order parity vector
requiring a high amount of online computation.
min
v
T
p2Ps
J = min
v
T
p2Ps
vT
pHd;sHT
d;svp
vT
pHf;sHT
f;svp
mit Ps = fvT
pjvT
pH0;s = 0g
(1)
For a practical solution this amount of online-computation
must be reduced. Therefore we use an alternative approach,
the residual is computed by:
r(k) = vT
p(ys(k) ¡ Hu;sus(k)): (2)
.....