RNGA based Centralized PI Controller for Multivariable Non Square Systems using Direct Synthesis Method

Abstract

Design of centralized PI controllers for multivariable non square systems is proposed in the present work. The centralized controller is designed based on the direct synthesis method. The method includes approximating the inverse of the process transfer matrix with the effective transfer function matrix. The effective transfer function for each element in the process transfer function matrix is derived by using the relative normalized gain array (RNGA), and relative average residence time array (RARTA) concepts proposed by Cai et al [1]. The transfer function models used in the present work include first order processes with time delay (FOPDT). Maclaurin series is applied to reduce the resulting controllers in to standard PI forms. The design method requires a single tuning parameter (filter time constant) to adjust the performance of the controller. Simulation study is carried out for various case studies and the results show the advantage of proposed method over the literature reported methods. The control algorithms are comparatively analyzed using standard robust stability measure. The designed controllers give a good performance with lesser interaction compared to the literature methods, Davison Method [2] and Tanttu and Lieslehto’s method [3].