Browsing by Subject "Strong stabilization"

Now showing 1 - 11 of 11

Open Access
On stable controller design for robust stabilization of time delay systems
(IFAC, 2015) Yücesoy, Veysel; Özbay, Hitay
This paper studies the problem of robust stabilization of an infinite dimensional plant by a stable and possibly low order controller. The plant of interest is assumed to have only finitely many simple unstable zeros, however, may have infinitely many unstable poles. In the literature, it has been shown that the problem can be reduced to an interpolation problem and it is possible to obtain lower and upper bounds of the multiplicative uncertainty under which an infinite dimensional stable controller can be generated by a modified Nevanlinna-Pick formulation. We propose that the same interpolation problem can be solved approximately by a finite dimensional approach and present a finite dimensional interpolation function which can be used to find a stable controller. We illustrate this idea by a numerical example and additionally show the effects of the free design parameters of the rational interpolating outer function approach on the numerical example.
Open Access
On the real, rational, bounded, unit interpolation problem in ℋ∞ and its applications to strong stabilization
(Sage Publications, 2019) Yücesoy, Veysel; Özbay, Hitay
One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in 𝐻∞ satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.
Open Access
Remarks on strong stabilization and stable H∞ controller design
(Institute of Electrical and Electronics Engineers, 2005) Gümüşsoy, S.; Özbay, Hitay
A state space based design method is given to find strongly stabilizing controllers for multi-input-multi-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H∞ controller in terms of linear matrix inequalities (LMI) and the controller order is twice that of the plant A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFT).
Open Access
Sensitivity minimization by stable controllers for a class of unstable time-delay systems
(IEEE, 2006) Gümüşsoy, S.; Özbay, Hitay
In this paper sensitivity minimization problem is considered for a class of unstable time delay systems. Our goal is to find a stable controller stabilizing the feedback system and giving rise to smallest H∞ norm for the sensitivity function. This problem has been solved by Ganesh and Pearson (1986) for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to include possibly unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
Open Access
Sensitivity minimization by strongly stabilizing controllers for a class of unstable time-delay systems
(Institute of Electrical and Electronics Engineers, 2009) Gumussoy, S.; Özbay, Hitay
Weighted sensitivity minimization is studied within the framework of strongly stabilizing (stable) Hinfin controller design for a class of infinite dimensional systems. This problem has been solved by Ganesh and Pearson, for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to a class of unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
Open Access
Sensitivity reduction by stable controllers for mIMO infinite dimensional systems via the tangential nevanlinna-Pick interpolation
(IEEE, 2014) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C +, but they are allowed to possess infinitely many poles in C +. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method.
Open Access
Sensitivity reduction by strongly stabilizing controllers for MIMO distributed parameter systems
(Institute of Electrical and Electronics Engineers, 2011-12-09) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributed parameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm.
Open Access
Stable and robust controller synthesis for unstable time delay systems via ınterpolation and approximation
(Elsevier B.V., 2018) Yücesoy, V.; Özbay, Hitay
In this paper, we study the robust stabilization of a class of single input single output (SISO) unstable time delay systems by stable and finite dimensional controllers through finite dimensional approximation of infinite dimensional parts of the plant. The plant of interest is assumed to have finitely many non-minimum phase zeros but is allowed to have infinitely many unstable poles in the open right half plane. Conservatism of the proposed methods is illustrated by numerical examples for which infinite dimensional strongly stabilizing controllers are derived in the literature.
Open Access
Stable controllers for robust stabilization of systems with infinitely many unstable poles
(Elsevier, 2013) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation-minimization by a unit element. Next, by the modified Nevanlinna-Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.
Open Access
Strongly stabilizing controllers for a two-link robotic system
(2024-01) Andaç, Adile Merve
Strong stabilization is defined as finding a stable controller that stabilizes the feedback system for a given plant. This study addresses the strong stabilization of a robotic system called the “acrobot”, which is a two-linked underactuated planar robot system. The linearized system is fourth-order, with two poles and one zero in the right half-plane. In this thesis, stable second-order controllers designed with different methods have been investigated for this system. The sta-bility margins are analyzed with respect to various free parameters. In addition, the time-domain transient response analysis is illustrated through simulations. Furthermore, the effects of nonlinearities are studied by estimating the region of attraction for each linear controller considered.
Open Access
Tangential Nevanlinna-Pick interpolation for strong stabilization of MIMO distributed parameter systems
(IEEE, 2012-12) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding stable controllers that stabilize a multi-input multi-output distributed parameter system while simultaneously reducing the sensitivity of the system. The plants we consider have finitely many unstable transmission zeros, but they can possess infinitely many unstable poles. Using the tangential Nevanlinna-Pick interpolation with boundary conditions, we obtain both upper and lower bounds of the minimum sensitivity that can be achieved by stable controllers. We also derive a method to find stable controllers for sensitivity reduction. In addition, we apply the proposed method to a repetitive control system. © 2012 IEEE.