Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers

Abstract

This paper presents a sliding mode fault detection scheme for linear parameter varying (LPV) systems with uncertain or imperfectly measured scheduling parameters. In the majority of LPV systems, it is assumed that the scheduling parameters are exactly known. In reality due to noise or possibly faulty sensors, it is sometimes impossible to have accurate knowledge of the scheduling parameters and a design based on the assumption of perfect knowledge of the scheduling parameters cannot be guaranteed to work well in this situation. This paper proposes a sliding mode observer scheme to reconstruct actuator and sensor faults in a situation where the scheduling parameters are imperfectly known. The efficacy of the approach is demonstrated on simulation data taken from the nonlinear RECONFIGURE benchmark model . One approach to extending linear methods to make them work effectively across the whole plant operating range is to design (linear) observers at select operating points, and then schedule the gains with respect to certain parameters [4]. One of the main difficulties with gain scheduling is the selection of the operating points and how to choose the gains at intermediate points. Furthermore, formally, between the operating points the stability of the observer cannot be guaranteed.A more rigorous alternative approach is based on so-called linear parameter varying (LPV) system designs. In the LPV approach the gains are automatically scheduled with respect to the plant varying parameters. Another advantage is many nonlinear systems can be naturally approximated by LPV systems [13] [20]). However in all these papers the scheduling parameters are assumed to be perfectly known. However in reality this may not be the case: for example inaccurate sensors and/or faults can lead to imperfect knowledge of the parameters. The use of this corrupted information will affect the performance of the observer. The design of Luenberger-like observers in scenarios involving uncertain scheduling parameters has been investigated. In [21], using a Linear matrix inequality (LMI) framework an LPV observer was proposed. Later, a controller and a combined controllerobserver scheme for inexact continuous LPV polytopic systems was presented in [22], [23]. In [24], [25] H ∞ filters were employed to deal with uncertainty in the scheduling parameters; exploiting parameter dependent LMI methods. More recently, an H ∞ filter has been proposed to deal with both additive and multiplicative uncertainties in the LPV parameters in [26]. Recent applications of these ideas to aerospace systems have been explored in [27], [28]. A fault reconstruction scheme for LPV systems with perfect scheduling parameter knowledge, using H ∞ methods has been investigated in [29]. Very few papers have addressed specifically the fault reconstruction problem for LPV systems with uncertain scheduling parameters, notable exceptions are [30]. To the authors' knowledge,

H−/L∞ fault detection observer for linear parameter‐varying systems with parametric uncertainty

“…Theorem 3. For a known l > 0, given a scalar 0 < < 1, error dynamic system (6) satisfies conditions (i)-(iii) if there exist scalars > 0, 1 > 0, 2 > 0, 1 > 0, 2 > 0, symmetric matrices P 1 (h) = P T 1 (h) > 0, P 2 (h) = P T 2 (h), ∀h( (k)), h + ∶ = (h 1 ( (k + 1)), h 2 ( (k + 1)), … , h r ( (k + 1))), Q ∈ R n x ×n x , Q > 0 and matrices G ∈ R n x ×n x , S 1 ∈ R n x ×n x , S 2 ∈ R n x ×n x , S 3 ∈ R n ×n x , L(h) ∈ R n x ×n such that (15), (16) and the following inequality hold…”

“…Note that the conditions in Theorem 3 are nonlinear matrix inequalities and cannot be easily solved. Therefore, to facilitate the design, we convert (15), (16), and (29) into a set of LMIs.…”

“…Therefore, inequality (34) is a sufficient condition of inequality (29) in Theorem 3. Similarly, the left side of inequality (16) is equal to…”

Stabilization of linear impulsive systems under dwell-time constraints: Interval observer-based framework

“…The existing solutions in the literature are based on the assumption that the designed observers converge to the true values of the state. If only interval estimation is achievable, then the conventional approaches [49], [5], [54] cannot be applied, but interval observers demonstrated their efficiency for stabilizing control design in different classes of systems [23], [22], and in this work the approach is extended to impulsive systems. This paper sets out to make a contribution at two levels.…”

Observer design for sampled-data systems with unknown inputs and uncertainties based on quasi sliding motion

“…There have been a great number of papers concerning the problem of estimating state variables and unknown inputs for continuous-time systems using sliding mode approaches: see [1], [2], [3], [4], [5], [6], [7] and references therein. A typical property of these observers is that a sliding surface based on the output error is constructed and a nonlinear switching injection term is introduced to force the output errors to reach the sliding surface in finite time.…”