Citation: Taherkhani, A.; Bayat, F.;
Hooshmandi, K.; Bartoszewicz, A.
Generalized Sliding Mode Observers
for Simultaneous Fault
Reconstruction in the Presence of
Uncertainty and Disturbance.
Energies 2022, 15, 1411. https://
doi.org/10.3390/en15041411
Academic Editor: Sergio
Nesmachnow
Received: 8 January 2022
Accepted: 4 February 2022
Published: 15 February 2022
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Article
Generalized Sliding Mode Observers for Simultaneous Fault
Reconstruction in the Presence of Uncertainty and Disturbance
Ashkan Taherkhani
1
, Farhad Bayat
1,
* , Kaveh Hooshmandi
2
and Andrzej Bartoszewicz
3
1
Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran;
ashkantaherkhani7@gmail.com
2
Department of Electrical Engineering, Arak University of Technology, Arak 38181-46763, Iran;
k.hooshmandi@arakut.ac.ir
3
Institute of Automatic Control, Lodz University of Technology, 90924 Lodz, Poland;
andrzej.bartoszewicz@p.lodz.pl
* Correspondence: bayat.farhad@znu.ac.ir
Abstract:
In this paper, a generalized sliding mode observer design method is proposed for the
robust reconstruction of sensors and actuators faults in the presence of both unknown disturbances
and uncertainties. For this purpose, the effect of uncertainty and disturbance on the system has
been considered in generalized state-space form, and the LMI tool is combined with the concept
of an equivalent output error injection method to reduce the effects of them on the reconstruction
process. The upper bound of the disturbance and uncertainty are minimized in the design of the
sliding motion so that the reconstruction of the faults will be minimized. The design method is
applied for actuator faults in the generalized state-space form, and then with some suitable filtering,
the method extends as sensors and actuators coincidentally faults. Since in the proposed approach,
the state trajectories do not leave the sliding manifold even in simultaneous sensors and actuators
faults, then the faults are reconstructed based upon information retrieved from the equivalent output
error injection signal. Due to the importance of the robust fault reconstruction in the wind energy
conversion system (WECS), the proposed approach is successfully applied to a 5 MW wind turbine
system. The simulation results verify the robust performances of the proposed approach in the
presence of unknown perturbations and uncertainties.
Keywords:
sliding mode observer; fault detection; robust fault reconstruction; linear matrix inequali-
ties (LMIs)
1. Introduction
In recent decades, industrial processes are becoming more and more complex; thus,
ensuring the operational reliability of these processes is an important task. Among them,
fault detection and isolation (FDI) methods play a pivotal role in making the process reli-
able. The sensor and actuator faults are known as the most frequent faults that occur in
many control systems such as satellite/aircraft [
1
,
2
], wind turbines [
3
,
4
], vehicles suspen-
sion
system [5,6],
offshore platforms [
7
], motor drives [
8
], power systems, and renewable
energies [
9
,
10
]. In the event of a fault occurrence, the reliability and efficiency of the system
are severely affected, and thus, the fault reconstruction is an important issue in the context
of FDI approaches, and various types of research have been done in this field. However,
when the system is subject to the uncertainty and disturbance, at the same time, identifying
and reconstructing simultaneous sensor and actuator faults are still challenging issues that
need to be addressed carefully.
In [
11
], a PI observer is proposed for fault estimation purposes based on convex
structures and by employing nonquadratic Lyapunov functions. As a result, less conser-
vative conditions in the form of LMIs are obtained. In [
12
], the sensor and actuator faults
reconstruction problem is addressed by only considering the uncertainty in the model.
Energies 2022, 15, 1411. https://doi.org/10.3390/en15041411 https://www.mdpi.com/journal/energies
