Finite time functional observers for descriptor systems. Application to fault tolerant control
01 Jul 2019-pp 165-170
TL;DR: A new finite-time convergent functional dynamical observer design for descriptor systems that is applied to the sensor and actuator faults detection and estimation and used in the observer-based fault tolerant control design.
Abstract: In this paper a new finite-time convergent functional dynamical observer design for descriptor systems is presented. The conditions for its existence and stability are given. This observer is then applied to the sensor and actuator faults detection and estimation. This estimation is used in the observer-based fault tolerant control design. All the obtained results are illustrated by numerical examples.
Citations
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TL;DR: A sliding mode observer (SMO) for robustly reconstructing faults affecting a class of nonlinear non-infinitely observable descriptor systems and preliminary transformations are utilised to re-express the system such that the design freedom in its structure is easier to exploit.
Abstract: This paper presents a sliding mode observer (SMO) for robustly reconstructing faults affecting a class of nonlinear non-infinitely observable descriptor systems. Preliminary transformations are utilised to re-express the system such that the design freedom in its structure is easier to exploit. An infinitely observable system is formed by treating some states as unknown inputs. The faults are then reconstructed from measurable inputs and outputs using a SMO. The structure of the SMO bounds the nonlinear components of its estimation errors. The effect of disturbances on the fault reconstruction is minimised using linear matrix inequality techniques. A summarised design procedure for the SMO scheme is presented. Finally, a simulated example is carried out to showcase the efficacy of the scheme.
34 citations
TL;DR: In this article , the authors proposed an LMI-based approach to design a bank of residual generators for functional observers to detect load-altering attacks in a large-scale smart grid.
4 citations
TL;DR: In this paper , the design of a generalized functional observer for Takagi-Sugeno descriptor systems is described, which provides additional degrees of freedom in the observer design, which allows for improvements in the estimation against parametric uncertainties.
Abstract: This paper concerns the design of a generalized functional observer for Takagi–Sugeno descriptor systems. Furthermore, a generalized structure is herein introduced for purposes of estimating linear functions of the states of descriptor nonlinear systems represented into a Takagi–Sugeno descriptor form. The originality of the functional generalized observer structure is that it provides additional degrees of freedom in the observer design, which allows for improvements in the estimation against parametric uncertainties. The effectiveness of the developed design is illustrated by a nonlinear model of a single link robotic arm with a flexible link. A comparison between the functional generalized observer and the functional proportional observer is given to demonstrate the observer performances.
1 citations
01 Oct 2020
TL;DR: This paper proposes a new approach to design a functional observer for delayed non-linear singular systems using the Takagi-Sugeno multiple model principle and proves its effectiveness on a numerical example.
Abstract: In this paper, we propose a new approach to design a functional observer for delayed non-linear singular systems. Delay functions are considered in both state and input vectors. Using the Takagi-Sugeno multiple model principle, we propose to extend observer design for linear singular delayed systems to the non-linear singular delayed representation. Sufficient conditions of stability are given to develop the designed observer gain. Such proposed observer proves its effectiveness on a numerical example.
1 citations
TL;DR: In this paper , a robust sliding mode observer (SMO) is designed to estimate the states of the DS in a realistic setting, and a sliding surface is constructed with the estimated states, following the integral sliding mode control (ISMC) principle.
Abstract: The problem of designing an observer-based fault-tolerant control allocation mechanism for a multi-input multi-output (MIMO) uncertain descriptor system (DS) subjected to actuator faults/failures and external uncertainties is discussed in this paper. The proposed approach guarantees system performance and closed-loop stability using the integral sliding mode control (ISMC) and a fixed control allocation (CA) strategy. A robust sliding mode observer (SMO) is designed to estimate the states of the DS in a realistic setting. The sliding surface is constructed with the estimated states, following the ISMC principle. To meet the admissibility conditions of DS, a multivariable super-twisting sliding mode control (STSMC) algorithm is designed. The CA technique reallocates the control effort to the remaining healthy actuators on the occurrence of any fault/failure. Lyapunov-based stability is established for the closed-loop system with the controller–observer pair. Finally, the proposed design is validated by evaluating various actuator fault/failure situations.
References
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22 Nov 2017
TL;DR: For some reasons, this unified algebraic approach to control design tends to be the representative book in this website.
Abstract: 1. Introduction 2. Linear Algebra Review 3. Analysis of First-order Information 4. Second-order Information in Linear Systems 5. Covariance Controllers 6.Covariance Upper Boundary Controllers 7. H-Controllers 8. Model Reduction 9. Unified Perspective 10. Projection Methods 11. Successive Centring Methods 12. A: Linear Algebra Basics 13. B: Calculus of Vectors and Matrices 14. C: Balanced Model Reduction
1,119 citations
"Finite time functional observers fo..." refers background in this paper
...4: The necessary and sufficient condition for the existence of a solution to (5) is given by (see [19])...
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TL;DR: It is shown that a continuous-time observer can observe the state of an nth order linear system in finite time D exactly, and any convergence time D can be assigned, independent of the observer eigenvalues.
Abstract: It is shown that a continuous-time observer, which comprises two standard nth order observers and a delay D, can observe the state of an nth order linear system in finite time D exactly. In particular, (almost) any convergence time D can be assigned, independent of the observer eigenvalues.
256 citations
"Finite time functional observers fo..." refers background in this paper
...Finite-time convergence, is not restricted to sampling and discrete time techniques, thus, finite-time convergence is an appealing topic of study [1]....
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TL;DR: In this note simple and straightforward methods to design full- and reduced-order observers for linear time-invariant descriptor systems are presented.
Abstract: In this note simple and straightforward methods to design full- and reduced-order observers for linear time-invariant descriptor systems are presented. The approach for the reduced-order observer design is based on the generalized Sylvester equation. Sufficient conditions for the existence of the observers are given. An illustrative example is included. >
256 citations
Book•
24 Sep 2011
TL;DR: In this article, a Parametric Approach to the Design of Reduced-Order Linear Functional Observers (RFLO) is presented. But this approach is not suitable for nonlinear systems.
Abstract: Introduction.- State Observers for Different Types of Systems.- Linear Functional Observers.- A Parametric Approach to the Design of Reduced-Order Linear Functional Observers.- Functional Unknown Input Observers: Further Results and Applications.- Functional State and Unknown Input Observers for Nonlinear Systems.- Simultaneous State and Input Estimation.- Further Notes on Functional Observers.
199 citations
"Finite time functional observers fo..." refers background in this paper
...This feature is particularly advantageous in state feedback control (as it can be seen in [7]–[9] )and can be exploited for other control applications such as fault detection [10] or fault tolerant control [11]....
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TL;DR: The necessary and sufficient conditions for the existence of the rth-order observers are given and a systematic design method of these observers is presented.
Abstract: This paper is concerned with the design of linear functional state observers for systems with delays in state variables. In particular, the necessary and sufficient conditions for the existence of the rth-order observers are given. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix-in-equality formulation. A systematic design method of these observers is presented. Numerical examples are given to illustrate this method.
188 citations
"Finite time functional observers fo..." refers background in this paper
...is given by X = BA−Z(I−AA), where Z is an arbitrary matrix of appropriate dimensions ( [17], [18])....
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