Abstract
In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.
Highlights
Time-delay or hereditary systems are called systems with aftereffect or dead-time [1]
The NewtonRaphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and stability is checked by Nyquist plot and step response of closed-loop system
In two sub-sections we introduce rightmost characteristic root or stability determining characteristic roots and Nyquist plot which are of great role in this paper
Summary
Time-delay or hereditary systems are called systems with aftereffect or dead-time [1]. In a neutral time-delay system, the time-derivative of the state depends on both the current and delayed stated and the past derivative [9] Stability of this type of system is playing an increasingly important role in control engineering and has received considerable attention and has been studied extensively in the literature (see [10,11,12,13,14] and references therein). According to a survey paper [16], more than 90% of controllers are of PID structure; even complicated control techniques embed PID algorithms [17] It is the most common control law for SISO systems in control engineering [18]. We present an efficient approach for determining the stabilizing PID controller for neutral timedelay systems.
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