Discrete-Time Nonlinear Singularly Perturbed System Identification Using Coupled Multimodel Representation

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Asma Ben Rajab ◽  
Nesrine Bahri ◽  
Majda Ltaief
Keyword(s):  
Discrete Time ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
System Model ◽  
Model Parameters ◽  
Singularly Perturbed Systems ◽  
Perturbed System ◽  
Marquardt Algorithm ◽  
Perturbed Systems ◽  
Full Knowledge

Abstract Many control and observability theories for singularly perturbed systems require the full knowledge of system model parameters exceptionally if the system is considered as black box. To overcome this problem and to obtain an accurate and faithful model, this paper describes a new identification method for discrete-time nonlinear singularly perturbed systems (NLSPS) using the coupled state multimodel representation. The Levenberg–Marquardt algorithm is used to identify not only the submodels parameters but also the perturbation parameter ε. Two cases are considered to identify these systems. The first one supposes that the perturbation parameter ε of the real system is known and thus only the submodels parameters are identified. The second case supposes that this perturbation parameter is unknown and has to be identified with the other submodels parameters. The simulation example demonstrates the effectiveness of the proposed identification.

scholarly journals Diagnosis of Discrete-Time Singularly Perturbed Systems Based on Slow Subsystem

2014 ◽  
Vol 8 (4) ◽  
pp. 175-180 ◽  
Author(s):  
Adel Tellili ◽  
Nouceyba Abdelkrim ◽  
Bahaa Jaouadi ◽  
Mohamed Naceur Abdelkrim
Keyword(s):  
Discrete Time ◽  
Diagnostic Algorithm ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Order System ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems ◽  
Parity Space ◽  
The One ◽  
Slow Subsystem

Abstract This paper deals with the diagnosis of discrete-time singularly perturbed systems presenting two time scales property. Parity space method is considered to generate the fault detection residual. The focus is in two directions. First, we discuss the residual illconditioning caused by the singular perturbation parameter. Then, the use of the slow subsystem is considered to make the fault diagnosis easier. It is shown that the designed diagnostic algorithm based on reduced order model is close to the one synthesized using the full order system. The developed approach aims at reducing the computational load and the ill-conditioning for stiff residual generation problem. Two examples of application are used to demonstrate the efficiency of the proposed method.

Stabilization of Discrete Singularly Perturbed Systems Under Composite Observer-Based Control

1999 ◽  
Vol 123 (1) ◽  
pp. 132-139 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Jiing-Dong Hwang ◽  
Shing-Tai Pan
Keyword(s):  
Singular Perturbation ◽  
Stability Criterion ◽  
Original System ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Stability Conditions ◽  
Singularly Perturbed Systems ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Perturbed Systems

New stability conditions for discrete singularly perturbed systems are presented in this study. The corresponding slow and fast subsystems of the original discrete singularly perturbed system are first derived. The observer-based controllers for the slow and the fast subsystems are then separately designed and a composite observer-based controller for the original system is subsequently synthesized from these observer-based controllers. Finally, a frequency domain ε-dependent stability criterion for the original discrete singularly perturbed system under the composite observer-based controller is proposed. If any one condition of this criterion is fulfilled, stability of the original system by establishing that of its corresponding slow and fast subsystems is thus investigated. An illustrative example is given to demonstrate that the upper bound of the singular perturbation parameter ε can be obtained by examining this criterion.

scholarly journals Control of Discrete-Time Singularly Perturbed Systems via Static Output Feedback

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dan Liu ◽  
Lei Liu ◽  
Ying Yang
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Static Output Feedback ◽  
Singularly Perturbed Systems ◽  
Closed Loop System ◽  
Perturbed Systems ◽  
Norm Bound ◽  
Static Output

This paper concentrates on control problems of discrete-time singularly perturbed systems via static output feedback. Two methods of designing an controller, which ensures that the resulting closed-loop system is asymptotically stable and meets a prescribed norm bound, are presented in terms of LMIs. Though based on the same matrix transformation, the two approaches are turned into different optimal problems. The first result is given by an -independent LMI, while the second result is related to . Furthermore, a stability upper bound of the singular perturbation parameter is obtained. The validity of the proposed two results is demonstrated by a numerical example.

scholarly journals Passive Control andε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Linna Zhou ◽  
Chunyu Yang
Keyword(s):  
Singular Perturbation ◽  
Passive Control ◽  
Controller Design ◽  
Design Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Storage Function ◽  
Rlc Circuit ◽  
Perturbed Systems

This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameterε, a new method is proposed to estimate theε-bound, such that the system is passive when the singular perturbation parameter is lower than theε-bound. Furthermore, a controller design method is proposed to achieve a predefinedε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.

scholarly journals On Output Feedback Multiobjective Control for Singularly Perturbed Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-28
Author(s):  
Mehdi Ghasem Moghadam ◽  
Mohammad Taghi Hamidi Beheshti
Keyword(s):  
Numerical Simulations ◽  
Output Feedback ◽  
Design Procedure ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Dynamic Output Feedback ◽  
Singularly Perturbed Systems ◽  
Dynamic Output ◽  
Perturbed Systems ◽  
And Performance

A new design procedure for a robust and control of continuous-time singularly perturbed systems via dynamic output feedback is presented. By formulating all objectives in terms of a common Lyapunov function, the controller will be designed through solving a set of inequalities. Therefore, a dynamic output feedback controller is developed such that and performance of the resulting closed-loop system is less than or equal to some prescribed value. Also, and performance for a given upperbound of singular perturbation parameter are guaranteed. It is shown that the -dependent controller is well defined for any and can be reduced to an -independent one so long as is sufficiently small. Finally, numerical simulations are provided to validate the proposed controller. Numerical simulations coincide with the theoretical analysis.

Duck Trajectories of Three-Dimensional Singularly Perturbed Systems

2007 ◽  
Vol 14 (2) ◽  
pp. 341-350
Author(s):  
Nikolai Kh. Rozov
Keyword(s):  
Three Dimensional ◽  
Slow Motion ◽  
Singularly Perturbed ◽  
Fast Variable ◽  
Singularly Perturbed Systems ◽  
Singularly Perturbed System ◽  
Motion Trajectories ◽  
Perturbed System ◽  
General Manner ◽  
Perturbed Systems

Abstract For the singularly perturbed system of three equations with one fast variable and two slow ones the problem of the emergence of duck trajectories is considered in the case with two different slow motion trajectories intersecting in a general manner.

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