A Loop Pairing Method for Non-Linear Multivariable Control Systems under a Multi-Objective Optimization Approach

In the multivariable control literature there are few techniques that face the problem of selecting suitable loop pairings in non-linear multivariable systems. Most techniques analyze the linearized system at a specific operating point. This paper proposes a new methodology to optimally and simultaneously select the loop pairings and the tuning of the parameters of the decentralized control by applying a multi-objective optimization approach directly on the non-linear system. The main contribution of this work is that the proposed methodology enables a detailed multi-dimensional analysis of the performances and trade-offs in the available loop pairings to control a multivariable non-linear system. The methodology is applied in this paper to three examples that analyze how the different types of loop pairings conflict. In one of the examples, the proposed methodology was applied first in the linearized system and later in the non-linear system. The results were contradictory and show how the application of loop pairing techniques for linear systems can be inaccurate when they are applied on a non-linear system previously linearized at an operating point. The following examples show that the operating point of a non-linear system, the design objectives of each multi-objective problem, as well as the designer's preferences have important roles in the selection of an optimal loop pairing.