Two Degree of Freedom Controller Design by AGTM\\AGMP Matching Method for Time Delay Systems

Abstract

This paper proposes the design of a general Two Degree Of Freedom (2-DOF) controller for time delay systems using a novel method which combines model order reduction, approximate model matching concepts as well as optimization techniques. The desired spectrum is embodied in the form of a transfer function which can be constructed from a set of time domain specifications. The problem of finding the parameters of the 2-DOF controller is formulated as that of obtaining the solution of a set of non-homogeneous linear equations. These set of non-homogeneous linear equations is obtained by using Approximate Generalized Time Moments (AGTM) matching concept, where closed loop response at certain frequency points in s-plane is matched with that of the desired model response. Using genetic algorithm optimum selection of frequency points (expansion points) in s-plane are obtained, which results in an optimum solution of controller parameters. This leads to a high degree of matching of the closed loop response with that of the desired model. The proposed method not only ensures the stability of the closed loop system with a 2-DOF controller but also satisfies the required performance criteria. The developed method does not pose any restriction on either the order of the model or on the structure/order of the controller transfer function. Moreover, this method is computationally simple and easy to implement. Simulation results demonstrate the effectiveness of the proposed method.