A sequential optimization procedure to tune MIMO PID controllers

Due to the presence of interactions in Multiple-Input Multiple-Output (MIMO) systems, the application of conventional Proportional-Integral-Derivative (PID) controllers for such systems becomes difficult in terms of tuning. The Genetic Algorithm has been extensively used in the literature in order to obtain the optimum multivariable PID tuning parameters based on simultaneous step changes in the set points of the system; however, they lead to sluggish responses when individual step changes are applied. This project investigates the application of sequential optimization procedure to obtain the tuning parameters for a multivariable PI controller applied to 2×2 MIMO transfer function that represents a binary distillation column. The top and bottom composition set points were individually step changed and the Genetic Algorithm was applied to minimize the Integral Averaged Error (IAE) until convergence was observed. The sequential optimization has shown to provide faster and less oscillatory response than the simultaneous procedure; however, the new methodology showed poor performance for disturbance rejection when simultaneous step changes were applied to the set points.