H∞ generalized dynamic unknown inputs observer design for discrete LPV systems. Application to wind turbine

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.

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“…, M of Θ and Φ, respectively. Thereupon, let us consider the regions (8) and (18) and the inclusion E ⊆ V described by (19) to obtain (32).…”

Section: Theoremmentioning

confidence: 99%

“…Notably, many nonlinearities can be represented as varying parameters that depend on endogenous signals, for example, states and inputs [17], which broadens the applicability of the design methodology to nonlinear plants. Examples of successful applications of the LPV paradigm are-wind turbines [18], vehicles [19,20] and drones [21].…”

Section: Introductionmentioning

confidence: 99%

Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

Ruiz¹,

Rotondo

Morcego³

2019

Applied Sciences

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“…This research is funded by Funds for Science and Technology Development of the University of Danang under project number B2020-DN06- 21. research trend in the LPV community [2]. In the literature, the observers of this new class take various structures, from the classical form [3], the descriptor form [4], [5] to the two-DOF [6] or the generalized one [7], [8]. The main objective of this work is to extend the unified formulation of unknown input observers [9], [10] for NLPV systems.…”

Section: Introductionmentioning

confidence: 99%

Unified Generalized H ₂ Nonlinear Parameter Varying Observer: Application to Automotive Suspensions

Tran

Pham

Sename

2023

IEEE Control Syst. Lett.

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This paper extends the unified observer design problem to the class of Nonlinear Parameter Varying (NLPV) systems with parameter dependence in both the dynamics and the control input matrices. First, parameterization of the observer matrices, herein generalized for the NLPV case, allows us to decouple the input disturbance from the estimation error. Then, the vanishing disturbance caused by the nonlinearity is bounded by the Lipschitz property and the effect of measurement noise on the error is minimized using the generalized H2 condition. Both objectives are combined into a single framework thanks to the S-procedure. Furthermore, the asymptotic stability of the error is tackled using a parameter-dependent Lyapunov function, then a grid-based Linear Matrix Inequalities (LMIs) solution is provided, which reduces conservatism. The efficiency of this observer is illustrated and compared with an LPV observer through the damper force estimation problem, a crucial topic in semi-active suspensions.

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“…Since then, numerous studies have explored the application of this type of observer in the continuous‐time domain, as evidenced by various works in the literature such as those by Naami et al, 33 Gao et al, 34 Boutat‐Baddas et al, 35 and Osorio‐Gordillo et al 36 However, limited attention has been paid to its discrete‐time equivalent. Notably, Reference 37 studied this observer for linear systems, while Reference 38 focused on linear parameters‐varying (LPV) systems. Nevertheless, these earlier studies did not take into account nonlinear terms and delays, which served as the main motivation for our current work.…”

Section: Introductionmentioning

confidence: 99%

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

Naami,

Ouahi

2023

Optim Control Appl Methods

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This study explores the development of dynamic observer (HDO) for discrete‐time nonlinear systems (DTNLS) with time‐varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen‐based inequality (JBI) and the Wirtinger‐based inequality (WBI). These lead to less conservative time‐dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.

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H∞ generalized dynamic unknown inputs observer design for discrete LPV systems. Application to wind turbine

Cited by 15 publications

References 39 publications

Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

Unified Generalized H ₂ Nonlinear Parameter Varying Observer: Application to Automotive Suspensions

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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H∞ generalized dynamic unknown inputs observer design for discrete LPV systems. Application to wind turbine

Cited by 15 publications

References 39 publications

Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

Design of State-Feedback Controllers for Linear Parameter Varying Systems Subject to Time-Varying Input Saturation

Unified Generalized H 2 Nonlinear Parameter Varying Observer: Application to Automotive Suspensions

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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Unified Generalized H ₂ Nonlinear Parameter Varying Observer: Application to Automotive Suspensions

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays