Single-objective optimization with gain scheduling control

This article presents a new method for adjusting the gain-scheduling controller, using the $\nu$-gap metric to reduce the number of gains in the gain-scheduling set and optimizing the proportional-integral-derivative (PID) values through single-objective optimization. For that, an algorithm was created with all the proposed steps, applying to a Peltier cell and comparing the results with two controllers: gain scheduling adjusted by a classical technique and PI controller adjusted with multiobjective optimization presented in [1]. With the reduced set, two new controllers were created: the first one optimizing a controller for each model in the set separately; the second one optimizing a single controller optimizing the whole set. As a result, it is observed that the separately optimized group is able to control almost as well as the gain scheduling adjusted by a classical technique and the PI controller tuning with multiobjective optimization, but both present a great effort in the control action. With a single controller, the response is slower, but the effort of the control action is significantly better.