Browsing by Subject "Unstable system"

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    PID and low-order controller design for guaranteed delay margin and pole placement
    (John Wiley & Sons Ltd., 2021-04-03) Özbay, Hitay; Gündeş, A. N.
    This article provides a simple low-order controller design method (including PID controllers as special cases) for a class of unstable systems. First, PID controller design is considered for systems with two unstable poles and pole placement and delay margin issues are discussed. Then, a chain of integrators is considered with arbitrary stable dynamics in cascade. For a given desired minimum delay margin for this class of plants, a PID and low-order controller design method is obtained in terms of an inequality constraint on the sum of k of the desired closed-loop poles, where k is number of the integrators in the open-loop transfer function.
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    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.