Evolutionary Optimization of Controllers

Abstract

The aim of this paper is to describe a new optimization method that can create control equations of general regulators. For this type of optimization a new method was created and we call it Two-Level Transplant Evolution (TLTE). This method allowed us to apply advanced methods of optimization, for example direct tree reducing of tree structure of control equation. The reduction method was named Arithmetic Tree Reducing (ART). For optimization of control equations of general controllers is suitable combine two evolutionary algorithms. Main goal in the first level of TLTE is the optimization of structure of general controllers. In the second level of TLTE the concrete parameters are optimized and the unknown abstract parameters in structure of equations are set. The method TLTE was created by combination of Transplant Evolution method (TE) and Differential Evolution method (DE). The Transplant Evolution (TE) optimizes structure of solution with unknown abstract parameters and the DE optimizes the parameters in this structure. The parameters are real numbers. The real numbers are not easy find directly in TE without DE. For evaluation of quality of found control equation are described new methods, which allow evaluate their quality. It can be used in the case when the simulation of control process cannot be finished. In results are shown some practical application. In all results we received the control equation that reached better quality of control process, than classical PID controllers and Takahashi's modification of PID controller. © Springer-Verlag Berlin Heidelberg 2013.