Observer-Based Control of Discrete-Time LPV Systems With Uncertain Parameters $ $

Heemels, W.P.M.H.; Daafouz, Jamal; Millérioux, Gilles

doi:10.1109/tac.2010.2051072

Cited by 189 publications

(126 citation statements)

References 21 publications

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“…Proof: The proof is given in [16]. The following corollary can be obtained immediately from the above theorem in case the full state x k is known (i.e.…”

Section: N Is Iss With Respect To E and V And Vmentioning

confidence: 98%

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Design of observer-based controllers for LPV systems with unknown parameters

Heemels

Daafouz

Millérioux

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-Output-based feedback control of LPV systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. In this paper we consider this problem in the case of discrete-time LPV systems for which the parameters are not exactly known, but only available with a finite accuracy or affected by noise during their measurement. The controllers are obtained using a separate design of an observer and a state feedback and the interconnection is proven to stabilize the LPV system despite the mismatch between the true and available parameters. The approach allows to maximize the parameter uncertainty while still guaranteeing closed-loop stability. In addition, it is possible to make tradeoffs between the admissible level of mismatch on the one hand and the performance in terms of decay factors on the other. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.

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“…Proof: The proof is given in [16]. The following corollary can be obtained immediately from the above theorem in case the full state x k is known (i.e.…”

Section: N Is Iss With Respect To E and V And Vmentioning

confidence: 98%

“…The ISS gain γ can be taken linear as γ(s) = σ ev s. Proof: The proof can be found in [16]. In case the conditions of Theorem 4 hold, the polytopic observer (8) guarantees GES of the error dynamics (9) …”

Section: Observer Designmentioning

confidence: 99%

Design of observer-based controllers for LPV systems with unknown parameters

Heemels

Daafouz

Millérioux

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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“…The LQR optimal control method possesses the advantage of computing the feedback control gain matrix [32] by providing a whole set of systems based on optimal control theory. Compared with general optimal control problems, linear quadratic type optimal control problems have two distinct features.…”

Section: Lqr Scheduling Control Algorithm Based On Lpv Modelmentioning

confidence: 99%

Research on the Common Rail Pressure Overshoot of Opposed-Piston Two-Stroke Diesel Engines

Zhao

Zuo

et al. 2017

Energies

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Abstract:The common rail pressure has a direct influence on the working stability of Opposed-Piston Two-Stroke (OP2S) diesel engines, especially on performance indexes such as power, economy and emissions. Meanwhile, the rail pressure overshoot phenomenon occurs frequently due to the operating characteristics of OP2S diesel engines, which could lead to serious consequences. In order to solve the rail pressure overshoot problem of OP2S diesel engines, a nonlinear concerted algorithm adding a speed state feedback was investigated. First, the nonlinear Linear Parameter Varying (LPV) model was utilized to describe the coupling relationship between the engine speed and the rail pressure. The Linear Quadratic Regulator (LQR) optimal control algorithm was applied to design the controller by the feedback of speed and rail pressure. Second, cooperating with the switching characteristics of injectors, the co-simulation of MATLAB/Simulink and GT-Power was utilized to verify the validity of the control algorithm and analyze workspaces for both normal and special sections. Finally, bench test results showed that the accuracy of the rail pressure control was in the range of ±1 MPa, in the condition of sudden 600 r/min speed increases. In addition, the fuel mass was reduced 76.3% compared with the maximum fuel supply quantity and the rail pressure fluctuation was less than 20 MPa. The algorithm could also be appropriate for other types of common rail system thanks to its universality.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Chandra¹,

Alwi

Edwards

2017

European Journal of Control

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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,

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Observer-Based Control of Discrete-Time LPV Systems With Uncertain Parameters $ $

Cited by 189 publications

References 21 publications

Design of observer-based controllers for LPV systems with unknown parameters

Design of observer-based controllers for LPV systems with unknown parameters

Research on the Common Rail Pressure Overshoot of Opposed-Piston Two-Stroke Diesel Engines

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

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