Iterative Method for Tuning Multiloop PID Controllers Based on Single Loop Robustness Specifications in the Frequency Domain

Abstract

Multiloop proportional-integral-derivative (PID) controllers are widely used for controlling multivariable processes due to their understandability, simplicity and other practical advantages. The main difficulty of the methodologies using this approach is the fact that the controllers of different loops interact each other. Thus, the knowledge of the controllers in the other loops is necessary for the evaluation of one loop. This work proposes an iterative design methodology of multiloop PID controllers for stable multivariable systems. The controllers in each step are tuned using single-input single-output (SISO) methods for the corresponding effective open loop process (EOP), which considers the interaction of the other loops closed with the controllers of the previous step. The methodology uses a frequency response matrix representation of the system to avoid process approximations in the case of elements with time delays or complicated EOPs. Consequently, different robustness margins on the frequency domain are proposed as specifications: phase margin, gain margin, phase and gain margin combination, sensitivity margin and linear margin. For each case, a PID tuning method is described and detailed for the iterative methodology. The proposals are exemplified with two simulations systems where the obtained performance is similar or better than that achieved by other authors.