A direct method for multi-loop PI/PID controller design

Difficulties caused by the interactions are always encountered in the design of multi-loop control systems for MIMO processes. To overcome the difficulties, a multi-loop system is decomposed into a number of equivalent single loops for design. For each equivalent single loop, an effective open-loop process (EOP) is formulated without prior knowledge of controller dynamics in other loops, and, hence, controller can be designed directly and independently. Based on the derived EOPs, a model-based method aims at having reasonable gain margins (e.g.≥ 2) and phase margins (e.g. ≈60°) are presented to derive multi-loop PI/PID controllers. This proposed method is formulated in details for the EOPs of 2-loop systems. Extension to higher dimensional systems needs further simplification and is illustrated with formulation for 3-loop systems. Simulation results show that this presented method is effective for square MIMO processes, especially, for low dimensional ones.