Optimal Tuning of Controllers Based on Ga and De

Abstract

In this paper a comparative study on the use of Genetic algorithms (GA) and Differential evolution (DE) for control systems design is presented. GA and DE are used for offline design of control schemes for continuous-time linear time invariant systems both in complex domain and time domain formulations. In the complex domain controller design, the design philosophy is based on approximate model matching in which a reference model is parameterized from time, frequency and complex domain specifications which ensure both stability and performance margin. The nominal plant model is known; the problems become to search the controller parameters through minimization of a scalar objective function, so that the augmented plant with controller matches the reference model. In time domain design, the sub-optimal control problem is considered in which the coefficients of the gain matrix is searched through minimization of a cost function developed on control input and state vector. GA and DE are used in both the design methods and applied in the single input single output (SISO) systems, Multi input and single output (MIMO) systems and systems with time delays. Examples are included to highlights the efficacy of the proposed methods.