Stability and performance of feedback control systems with time delays

Abstract

Abstract-This paper investigates the time delay effects on the stability and performance of active feed back control systems for engineering structures. A computer algorithm is developed for stability analy sis of a SDOF system with unequal delay time pair in the velocity and displacement feedback loops. It is found that there may exist multiple stable regions in the plane of the time delay pair, which contain time delays greater than the maximum allowable values obtained by previous studies. The size, shape and location of these stable and unstable regions depend on the system parameters and the feedback control gains. For systems with multiple stable regions, the boundaries between the stable and unstable regions in the plane of the time delay pair are explicitly obtained. The delay time pairs that forms these boundaries are called the critical delay time pairs at which the steady-state response becomes unbounded. The conclusions are valid for both large and small delay times. For any system with mul tiple stable regions, preliminary guidelines obtained from an explicit formula are given to find the desir able delay time pair(s). When used, these desirable delay time pair(s) not only stabilize an unstable system with inherent time delays, but also significantly reduce the system response and control force. For any system with multiple stable regions, these desirable delay time pair(s) are above the maximum allowable delay times obtained by previous studies. Numerical results, for both steady-state and transi ent analysis, are given to investigate the performance of delayed feedback control systems subjected to both harmonic and real earthquake ground motion excitations. ~O 1997 Published by

A method of continuous time approximation of delayed dynamical systems

“…Yang and Wu [3] and Stepan [4] have studied structural systems with time delay. A study on stability and performance of feedback controls with multiple time delays is reported in [5] by considering the roots of the closed loop characteristic equation. For deterministic delayed linear systems a survey of recent methods for stability analysis is presented in [6].…”

Control studies of time-delayed dynamical systems with the method of continuous time approximation

“…Yang and Wu [4] and Stepan [5] have studied structural systems with time delay. A study on stability and performance of feedback controls with multiple time delays is reported in [6] by considering the roots of the closed-loop characteristic equation. A method using Chebyshev polynomials to approximate general nonlinear functions of time has been developed to handle linear and nonlinear time-delayed dynamical systems with periodic coefficients [7][8][9][10].…”

Internal and External Feedback Circuits for Skilled Forelimb Movement

“…The first challenge, documented extensively in the realm of engineering control theory, is that feedback delays destabilize output and result in oscillations and a degradation in performance (Kawato and Gomi 1992; Wolpert and Miall 1996; Ali et al 1998). One effective means of avoiding motor instability is to limit the impact of sensory feedback on motor output through reduced feedback gain (Stein and Oğuztöreli 1976).…”