Optimization of PI parameters using biogeography based optimization and differential evolution for non minimum phase quadruple tank process

Differential Evolution (DE) algorithm is a new technique for finding optimal solutions to multivariable Quadruple Tank Process (QTP) which has a Right Half Plane (RHP) zero when operated in Non-Minimum Phase (NMP) mode. Due to interaction, there is a third hidden feedback control loop which causes the instability problem of the closed loop system and making the controller tuning more difficult, since both controllers affect both outputs. Because of the presence of nonlinearity, time delay and pole-zero locations, the proper tuning of the Proportional Integral (PI) controller settings are difficult. Recently several meteheuristics algorithms such as evolutionary algorithms and Biogeography Based Optimization (BBO) are used. In this paper, BBO and DE are employed to search for optimal PI controller parameters to get the global optimum value of the fitness function. The efficacy of the proposed scheme is demonstrated by conducting simulation studies on QTP to prove DE is significantly superior to others in terms of better tracking, rejecting the disturbances with better quality and performance indices.