Multiloop PI/PID controller design based on Gershgorin bands

A new definition of the ultimate point is proposed for diagonally dominant, MIMO systems. Analytical formulas are developed for the new ultimate gains and ultimate frequencies based on the system frequency response and Gershgorin bands. Decentralized PI and PID controllers with set-point weighting factors can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. The proposed design method is simple and easy to implement. Two simulation examples compare the performance of the proposed multiloop design method with alternative techniques.