New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers

Abstract

This paper presents a robust actuator fault reconstruction scheme for linear uncertain systems using sliding mode observers. In existing work, fault reconstruction via sliding mode observers is limited to either linear certain systems subject to unknown inputs, relative degree one systems or a specific class of relative degree two systems. This paper presents a new method that is applicable to a wider class of systems with relative degree higher than one, and can also be used for systems with more unknown inputs than outputs. The method uses two sliding mode observers in cascade. Signals from the first observer are processed and used to drive the second observer. Overall, this results in actuator fault reconstruction being feasible for a wider class of systems than using existing methods. A simulation example verifies the claims made in this paper. as to whether a fault condition is present and also an attempt is made to determine its location.A useful alternative to residual generation is fault reconstruction [8-10], which not only detects and isolates the fault, but also provides an estimate of the fault so that its shape and magnitude can be better understood and more precise corrective action can be taken. However, a fault reconstruction scheme is usually designed about a model of the system. This model usually does not perfectly represent the system, as certain dynamics are either unknown or do not fit exactly into the framework of the model. These dynamics are usually represented as a class of disturbances within the model [11]. The disturbances corrupt the reconstruction, and could produce a non-zero reconstruction when there are no faults, or worse, mask the effect of a fault, producing a 'zero' reconstruction in the presence of faults. Therefore, the scheme needs to be designed so that the reconstruction is robust to disturbances.Edwards et al. [8,9] used a sliding mode observer [12] to reconstruct faults, but there was no explicit consideration of the disturbances. Tan and Edwards [13] built on the work in [8,9] and presented a design algorithm for the observer, using linear matrix inequalities (LMIs) [14], such that the L 2 gain from the disturbances to the fault reconstruction is minimized. Saif and Guan [10] aggregated the faults and disturbances to form a new 'fault' vector and used a linear observer to reconstruct the new 'fault' vector. One of the necessary conditions in [8-10, 13] is that the transfer function from the faults to the output has a relative degree of one. This limits the class of systems where the schemes [8-10, 13] are applicable.Recently, there have been developments in the area of fault reconstruction for systems with relative degree greater than one. Floquet and Barbot [15] transformed the system into an 'output information' form such that existing sliding mode observer techniques could be implemented to perfectly estimate the states in finite time and reconstruct faults. However, their algorithm does not consider disturbances (unless as in [10] the unknown inputs (faults) are a...

Sliding mode methods for fault detection and fault tolerant control with application to aerospace systems

“…In this section the faults and disturbances are treated differently. Using similar techniques as Ng et al (2007) did, measurable signals from an observer are used as outputs of a fictitious system. The next observer is designed for the fictitious system, and the known signals from this observer are used as outputs of another fictitious system.…”

“…The technique proposed by Tan and Edwards (2003) is then used to robustly reconstruct the fault. This results in a robust fault scheme reconstruction applicable to a wider class of systems than in the work of Ng et al (2007).…”

“…This limits the class of systems for which the results are applicable. Ng et al (2007) extended the work of Tan and Edwards (2003) exploiting two sliding mode observers in cascade. Known signals from the first observer were considered as outputs of a 'fictitious' system which has a full rank (first) Markov parameter.…”

“…This enables robust fault reconstruction for systems where the number of disturbances and faults exceeds that of outputs. The next section builds on the results of Ng et al (2007) using multiple observers in cascade.…”

An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An

“…• If actuator fault reconstruction is considered, fault * Corresponding author estimation is possible without sensor faults (Edwards et al, 2000;Ng et al, 2007;Tan and Edwards, 2003b;Dhahri et al, 2012;Raoufi et al, 2010;Xing-Gang and Edwards, 2007a).…”