ORDER REDUCTION OF DISCRETE SYSTEMS AND ITS APPLICATION FOR DESIGNING A PID CONTROLLER

Abstract

Order reduction of linear time invariant discrete systems with constant sampling rate was attempted in this work using step response matching technique. Altogether three methods were tried using a common criteria of forced matching of steady state error. In two of the methods, the dominant poles were retained whereas in one method the new poles were synthesized. Similarly for calculating the zeroes of the reduced order system, in two methods the transient error was minimized whereas one method was based on point to point matching of transient parts of the unit step response. Results obtained after trying all the method on some common examples were compared. Finally a PID controller was designed using a reduced order model obtained with all the three methods developed. The three unknown parameters Kp, Kj and Kd are determined using low order model obtained from the original high-order system, by Ziegler-Nichols tuning rule. Then the same PID controller was used in the original high order system to calculate the integral square error between the original and reduced system performance analysis. Results obtained on a number of examples were satisfactory. Conclusions were drawn in terms of system performance by using all the order reduction methods developed. Further its applications for designing a controller by using the same set of examples of different varieties was taken up. The work lead to ideas which can be tried in future by other workers in this field both towards methodology of order reduction and its application in describing a PID controller.