(663a) Actuator and Sensor Fault Isolation of Nonlinear Systems Subject to Uncertainty

Actuator and sensor fault isolation of nonlinear systems subject to
uncertainty

Automatic control techniques have
been widely employed in industry to increase efficiency and profitability of the
processes. However, this comes at a price of increased impact of abnormalities
in major control equipment such as actuators and sensors. This realization has
motivated design of frameworks for fault detection and isolation (FDI) and
fault tolerant control (FTC). Important issues such as system nonlinearities
and existence of uncertainties must be considered in FDI and FTC design to be
able to successfully decrease or tackle the severity of the fault effects.

The FDI problem for nonlinear
systems has been considered widely in the literature during the past decade
(see, e.g., [1], [2], [3] and [4]). Most of the existing results, however,
focused on isolation of single actuator or single sensor faults. Recently,
results have enabled distinguishing between simultaneous sensor and actuator
faults, where the results are derived assuming no uncertainty (see e.g., [5]).

In [6], the problem of isolation of
complex actuator faults (occurrence of several actuator faults in same order of
differentiation) in the presence of uncertainty is handled by explicitly
characterizing the way the faults affect the nonlinear process system, and
driving the system to a point that enables fault isolation. The problem of FDI
in the presence of uncertainty has also been studied (see e.g., [7] and [8])
using adaptive estimation techniques. First a fault detection scheme is
designed which simply uses output estimation error as residual. Then, a bank of
fault isolation estimators is designed using adaptive estimation techniques.
The existing results, however, consider only single fault scenarios. In
summary, there is a lack of results for nonlinear systems subject to
uncertainty where the problem of fault detection and isolation for simultaneous
actuator and sensor faults is addressed.

Motivated by the above
considerations, this work considers the problem of actuator and sensor fault
isolation for simultaneous faults in the presence of uncertainty. This is
achieved by building a bank of residuals, each using an appropriate subset of
the available measurements (and associated state estimators), to determine the
expected behavior of the system and compare with the observed evolution. To
this end, at first we establish boundedness of estimation error for discretized
fashion high gain observer presented in [4] in the presence of uncertainty.
Next, we propose the fault detection and isolation design, which comprises a
bank of fault detection and isolation filters that trigger an alarm based on
appropriately defined residuals breaching their thresholds. Thresholds are
defined in a way that they account for the impact of the uncertainty on the
estimation error and the prediction of the expected system behavior. In this
way, the fault isolation mechanism explicitly accounts for effect of the uncertainty.
Then we present the detectability conditions for single and simultaneous
faults. The efficacy of proposed FDI framework in presence of uncertainty and
measurement noise is illustrated using a chemical reactor example.

References

[1] Prashant Mhaskar, Charles McFall, Adiwinata
Gani, Panagiotis D Christofides,
and James F Davis. Isolation and handling of actuator faults in nonlinear systems.
Automatica, 44(1):53-62, 2008.

[2] Chudong Tong, Nael
H El-Farra, Ahmet Palazoglu,
and Xuefeng Yan.
Fault detection and isolation in hybrid process systems using a combined
data-driven and observer-design methodology. AIChE
Journal, 60(8):2805-2814, 2014.

[3] Prashant Mhaskar, Jinfeng Liu, and P Christofides. Fault-tolerant process control. Springer,
2013.

[4] Miao Du and Prashant Mhaskar. Isolation and
handling of sensor faults in nonlinear systems. Automatica,
50(4):1066-1074, 2014.

[5] Miao Du, James Scott, and Prashant Mhaskar. Actuator and sensor
fault isolation of nonlinear process systems. Chemical Engineering Science,
104:294-303, 2013.

[6] Miao Du and Prashant Mhaskar. Active fault
isolation of nonlinear process systems. AIChE
Journal, 59(7):2435-2453, 2013.

[7] Xiaodong Zhang, Marios
M Polycarpou, and Thomas Parisini. Fault diagnosis of a class of nonlinear uncertain systems with
Lipchitz nonlinearities using adaptive estimation. Automatica,
46(2):290-299, 2010.

[8] Xiaodong Zhang. Sensor
bias fault detection and isolation in a class of nonlinear uncertain systems
using adaptive estimation. Automatic Control, IEEE Transactions on,
56(5):1220-1226, 2011.