A New Point of View in Multivariable Controller Tuning Under Multiobjective Optimization by Considering Nearly Optimal Solutions

Abstract

In this paper, we present the adjustment of controller parameters using multiobjective optimization techniques. Unlike other works, where only the Pareto optimal solutions are considered, we also consider the set of nearly optimal solutions nondominated in their neighborhood. These solutions are potentially useful for two reasons: 1) they are similar to the optimal solutions for the optimized objectives, and; 2) they differ significantly in their parameters. This last point makes them interesting, since they bring diversity and different characteristics to the set of solutions for analyzing in the decision stage. In problems of controller parameter adjustment, especially for multivariable processes, there are many conflicting objectives. To simplify the optimization problem and decision stage, it is common to aggregate some of the objectives, and so simplify the initial problem. In this scenario, some controllers that were optimal for the initial problem can become nearly optimal in the simplified case. When these controllers are nondominated in their neighborhood, they are especially interesting because they usually present a different trade-off for the initial objectives. For the calculation of nearly optimal solutions nondominated in their neighborhood, the evolutionary algorithm nevMOGA was used. In this paper, the usefulness of considering these solutions is revealed in two controller design problems: the Wood & Berry distillation column and the CIC2018 control benchmark.

Keywords

• Multiobjective optimization
• multivariable control systems
• nearly optimal solutions