Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning

• We present an evolutionary multiobjective optimisation approach for PI controller tuning.
• This approach incorporates designer’s preferences into the optimisation process.
• The methodology is evaluated in a multivariable process.
• It is possible to improve pertinency of the approximated Pareto front.

Multi-objective optimisation design procedures have shown to be a valuable tool for control engineers. They enable the designer having a close embedment of the tuning process for a wide variety of applications. In such procedures, evolutionary multi-objective optimisation has been extensively used for PI and PID controller tuning; one reason for this is due to their flexibility to include mechanisms in order to enhance convergence and diversity. Although its usability, when dealing with multi-variable processes, the resulting Pareto front approximation might not be useful, due to the number of design objectives stated. That is, a vast region of the objective space might be impractical or useless a priori, due to the strong degradation in some of the design objectives. In this paper preference handling techniques are incorporated into the optimisation process, seeking to improve the pertinency of the approximated Pareto front for multi-variable PI controller tuning. That is, the inclusion of preferences into the optimisation process, in order to seek actively for a pertinent Pareto front approximation. With such approach, it is possible to tune a multi-variable PI controller, fulfilling several design objectives, using previous knowledge from the designer on the expected trade-off performance. This is validated with a well-known benchmark example in multi-variable control. Control tests show the usefulness of the proposed approach when compared with other tuning techniques.