Browsing by Subject "Robust stability"

Now showing 1 - 9 of 9

Open Access
Controller design for plants with internal delayed feedback
(Institute of Electrical and Electronics Engineers, 2022-05-01) Gündeş, A. N.; Özbay, Hitay
A special class of retarded and neutral time delay systems is considered. These are plants with internal delayed feedback, and they may have finitely many or infinitely many unstable poles. Stabilizing controllers are obtained from a particular interpolation. A parametrization of all stabilizing integral-action controllers is obtained. Examples are given to illustrate this simple design procedure and its robustness properties for various uncertainties.
Open Access
Dwell time optimization in switching control of parameter varying time delay systems
(IEEE, 2011) Yan, P.; Özbay, Hitay; Şansal, M.
It has been shown that parameter varying systems with time delays can be robustly stabilized by switching control, provided that the plant's parameter varies slowly enough such that the dwell time conditions of the switched controllers can be satisfied. In this paper, the minimization of dwell time is considered, where an iterative search algorithm is developed from the singular value perspectives. The local minimal dwell time obtained in this paper can be used to estimate the upper bound on how fast the plant's parameters can vary. Meanwhile, the switching controller synthesis with optimal dwell time is also discussed, where robust stabilizer design algorithm is presented to achieve robust stability at certain operating range, as well as the local minimal dwell time for controller switching. A numerical example is given to illustrate the proposed algorithm.
Open Access
Field of values of matrix polytopes
(Anadolu Üniversitesi, 2000) Özgüler, A. Bülent; Saadaoui, Karim
The tool of field of values (also known as the classical numerical range) is used to recover most results available in the literature and to obtain some new one s concerning Hurwitz and Schur stability of matrix polytopes. Some facts obtained by an application of the elementary properties of field of values are as follows. If the vertex matrices have polygonal field of values, then the matrix polytope is Hurwitz and Schur stable if and only if the vertex matrices are Hurwitz and Schur stable, respectively. If the polytope is nonnegative and the symmetric part of each vertex matrix is Schur stable, then the polytope is Schur stable. For polytopes with spectral vertex matrices, Schur stability of vertices is necessaryand sufficient for the Schur stability of the polytope.
Open Access
Implementation of stabilizing controllers for retarded delay systems
(Elsevier Ltd., 2024-11-26) Bonnet, C; Özbay, Hitay; Yeğin, Mustafa Oğuz; Gümüşsoy, S.
This paper proposes a way to efficiently implement stabilizing controllers for delay systems of the retarded type. We indeed choose a particular controller (central controller) in the set of all stabilizing controllers and decompose its transfer function in terms of stable delay systems and Finite Impulse Response (FIR) filters. The central controller is written in such a way that the corresponding Matlab/Simulink implementation scheme is obvious. We illustrate that all stabilizing controllers can be implemented by using stable components only around the central controller. We also discuss stability robustness in the presence of implementation errors. The method is illustrated in an example. Copyright (c) 2024 The Authors.
Open Access
On stability of interval matrices
(Institute of Electrical and Electronics Engineers, 1994-02) Sezer, M. E.; Siljak, D. D.
New sufficient, and sometimes necessary and sufficient conditions, are obtained for Schur- and Hurwitz-stability of interval matrices by relying on the concept of connective stability and M-matrices. The necessity part is broadened to include interval matrices with mixed signs of the off-diagonal elements, provided the sign patterns follow that of the Morishima matrix. The obtained results are extended to cover convex combinations of interval matrices.
Open Access
Robust sampled-data control
(1995) Ocalı, Ogan
Robust control of uncertain plants is a major area of interest in control theory. In this dissertation, robust stabilization of plants under various classes of structural perturbations using sampled-data controllers is considered. It is shown that a controllable system under bounded perturbations that satisfy certain structural conditions can be stabilized using high-gain sampled-data state feedback control, provided that the sampling period is sufficiently small, with generalizations to decentralized control of interconnected systems. This result is then modified so as to enable adapting the gain and the sampling periods of controllers online. Finally another design methodology is given which enables the controllers to operate on the sampled values of output only, instead of full state measurements.
Open Access
Robust Smith predictor design with finite dimensional filters
(2024-01) Yeğin, Mustafa Oğuz
The time delay is a widely recognized inherent phenomenon present in practical control systems, and it has been a subject of extensive research over the past century. Unless managed appropriately, even a minor delay can deteriorate performance and potentially lead to instability. Therefore, incorporating a model for time delay and designing the controller to mitigate its effects are crucial steps to attain the desired robustness and performance criteria in control theory. Additionally, owing to its infinitedimensional structure, the majority of predictor-based controllers comprise finite impulse response filters, necessitating approximation with finite-dimensional transfer functions for seamless integration into physical systems. Controller designs based on the Smith predictor can effectively cancel out the impact of dead-time delay. This study introduces an extension of the Smith predictor to formulate stabilizing controllers for Linear Time Invariant (LTI) Single-Input SingleOutput (SISO) systems with multiple unstable modes and time delay. The main contribution of this approach lies in the streamlining of previous predictor-based control designs intended for unstable plants. The main contribution of this methodology lies in the simplification of previous predictor-based control designs tailored for unstable plants. The predictor filters are crafted by solving a Nevanlinna-Pick interpolation problem to attain optimal robust stability. The process also upholds the fundamental essence of the Smith predictor scheme, allowing the design of a controller based on the non-delayed nominal plant. Despite the susceptibility of Smith predictor-based designs to uncertain delays, the robustness of the proposed configuration surpasses that of the H∞ optimal controller design, as demonstrated in the relevant section. The proposed design is also extensible to a category of distributed parameter SISO systems and Multi-Input Multi-Output (MIMO) plants. For distributed parameter SISO systems, it is assumed that the plant’s transfer function can be expressed through coprime factorization. The fundamental idea underlying this approach is treating the infinite-dimensional inner factor of the plant as a “time delay,” and, in turn, determining the predictor structure accordingly. The modeling and controller design steps expounded here are exemplified using a flexible beam model. Regarding MIMO systems, provided specific conditions are met, the tangential Nevanlinna-Pick interpolation technique can be employed to derive the controller and filters according to the proposed configuration. While numerous studies have addressed model order reduction in the context of H∞-norm error, achieving optimal H∞ approximation remains a challenging and unresolved problem. This study introduces an alternative model reduction method that seeks to minimize the H∞ norm of the difference between the reduced model and the original Finite Impulse Response (FIR) structure. The proposed method essentially reduces the order of a given function by one with the minimum H∞-norm error, employ ing a high-order Pade approximation of the time-delay term. As the method reduces the order by one, an iterative algorithm is devised to recursively decrease the order of a given plant from n to a desired order of m, repeating the procedure (n − m) times following the outlined steps. The main contribution of the proposed technique is that it provides a new perspective against H∞-norm approximation by using Chebyshev equioscillation theorem on rational functions. Various examples are provided to elucidate the methodology of the suggested controller design and the robust stability condition in the context of approximating the infinite-dimensional predictor structure. Furthermore, the proposed model order reduction method is compared with the most recent state-of-the-art techniques within the literature. Finally, potential avenues for further research are deliberated, encompassing both the controller structure and H∞ approximation.
Open Access
Stability robustness of linear systems: a field of values approach
(1997) Saadaoui, Karim
One active area of research in stability robustness of linear time invariant systems is concerned with stability of matrix polytopes. Various structured real parametric uncertainties can be modeled by a family of matrices consisting of a convex hull of a finite number of known matrices, the matrix poly tope. An interval matrix family consisting of matrices whose entries can assume any values in given intervals are special types of matrix polytopes and it models a commonly encountered parametric uncertainty. Results that allow the inference of the stability of the whole polytope from stability of a finite number of elements of the polytope are of interest. Deriving such results is known to be difficult and few results of sufficient generality exist. In this thesis, a survey of results pertaining to robust Hurwitz and Schur stability of matrix polytopes and interval matrices are given. A seemingly new tool, the field of values, and its elementary properties are used to recover most results available in the literature and to obtain some new results. Some easily obtained facts through the field of values approach are as follows. Poly topes with normal vertex matrices turn out to be Hurwitz and Schur stable if and only if the vertex matrices are Hurwitz and Schur stable, respectively. If the polytope contains the transpose of each vertex matrix, Hurwitz stability of the symmetric part of the vertices is necessary and sufficient for the Hurwiz stability of the polytope. If the polytope is nonnegative and the symmetric part of each vertex matrix is Schur stable, then the polytope is also stable. For polytopes with spectral vertex matrices, Schur stability of vertices is necessary and sufficient for the Schur stability of the polytope.
Open Access
Strongly stabilizing controller design for systems with time delay
(Natural Sciences Publishing Corporation, 2024) Özbay, Hitay
In this paper, some specific stable controller design techniques are reviewed for linear time invariant finite dimensional plants, and their extensions are discussed for systems with time delays. It is shown that under certain mild conditions, for strictly proper retarded delay systems with finitely many poles and zeros in C+, it is possible to obtain finite dimensional strongly stabilizing controllers. Illustrative examples are also given.