Novel Design Method for Two Degree of Freedom Controllers

Abstract

This paper proposes the design of a general Two Degree of Freedom (2-DOF) controller and a 2-DOF PID controller using a novel method which combines model order reduction, 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 such as rise time, settling time, peak over shoot, etc. Another approach to create the model transfer function could be to use the Linear Quadratic Gaussian (LQG) theory for a given set of weighting matrices. The proposed method not only ensures stability of the closed loop system with 2-DOF controller but also guarantees 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. Since it is an algebraic method, the problem of finding the parameters of 2-DOF controller is formulated as that of finding the solution of linear non-homogeneous equations. The proposed method yields an output feedback controller instead of an optimal state feedback one. Simulation results demonstrate the effectiveness of the proposed method.