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.

Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

“…Unlike loop transfer functions l ii (s), the ELTF captures the effective dynamics of the corresponding loop transfer function and interactions with other loops. The concept of ETLF can be considered an extension for centralized control of the equivalent open-loop process for decentralized control in [15], [33]. For the 2×2 case, the expressions of the ELTFs l 1 (s) and l 2 (s) are given by (2).…”

“…In [32], Karimi proposes a linear margin that ensures lower bounds for the previous classical margins, and develops an associated design methodology of SISO PID controllers based on linear programming. In [15], [33], this method is extended to decentralized PID controllers for stable MIMO systems by means of an iterative procedure.…”

A graphical tuning rule for higher-order systems with H∞ complementary sensitivity function framework

“…This method involves breaking down the system into individual SISO systems and implementing the control laws. An iterative approach for multi-variable systems is explored in Garrido et al (2021). The concept of an effective open-loop process is exploited in minimizing the loop interactions.…”

Grey-Box Modeling and Decoupling Control of a Lab Setup of the Quadruple-Tank System

“…In other cases where there is more interaction, and this is taken into account, the decentralized structure is still used. However, each controller is designed to incorporate the effects of the other loops on the corresponding process [8]. Before designing a decentralized control, it is important to choose a suitable pairing between input and output variables that presents as little interaction as possible.…”