Browsing by Subject "Linear time-invariant"

Now showing 1 - 3 of 3

Open Access
PID controller synthesis for a class of unstable MIMO plants with I/O delays
(Elsevier, 2006-07) Gündeş, A. N.; Özbay, Hitay; Özgüler, A. Bülent
Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional + Integral + Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability. Copyright © 2006 IFAC.
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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.
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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.