JIC_V3_N3_RP2 C. Ravi Kishore R. Padma Sree Journal on Instrumentation & Control Engineering 2321 – 1148 3 3 21 30 Unstable System, Second Order System, Time Delay, Equating Coefficient Method, PID Controller Design of Proportional Integral Derivative (PID) controllers for Unstable Second Order systems Plus Time Delay (USOPTD) with/without a zero using equating coefficient method is proposed in this paper. The method is based on equating the corresponding coefficients of s , s2 , s3 of the numerator of the closed loop transfer function for servo problem to α1 ,α 2, α3 times that of the denominator. The time delay term in the denominator of the closed loop transfer function is written as, and it is expanded using Taylor series expansion upto four terms both in the numerator and denominator. This makes the numerator and denominator as polynomial of s. The time delay term in the numerator shifts the response on time axis and is not considered in the design problem. By equating the corresponding coefficients of s, s2 and s3 in the numerator with α , α2 , and α3 times that of the denominator; three linear equations are formulated and solved for the PID controller parameters. In the proposed work, the coefficients α , α2 , and α3 are obtained by minimizing Integral Time weighted Absolute Error (ITAE) for servo problem using fminunc of Matlab. Simulation results on various transfer function models and on the nonlinear model equations of jacketed CSTR (Continuous Stirred Tank Reactor) carrying out first order exothermic reaction are given to demonstrate the effectiveness of the proposed method. The smooth functioning of the controller is expressed interms of total variation. The controller performance is expressed in terms of ITAE. Nominal control performance of the proposed method is better than the existing methods. May - July 2015 Copyright © 2015 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=3579