Parameter Optimization of Control with Feedback Linearization for a Model of Thermoelectric Processes in Cylindrical Bodies

In this paper, mathematical modeling of transient processes and parameter optimization of control laws for heat transfer in a conductive solid structure are considered. In accordance with an implementation of an experimental setup, a nonlinear model is proposed for the thermoelectric process in a Peltier element arranged in between of two metal cylinders. The method of separation of variables is applied to reduce the spatially three-dimensional system to a finite set of ordinary differential equations. The nonlinearity of the resulting equations with respect to the temperature state is eliminated by introducing feedback control in the form of a voltage proportional to the temperature drop on the Peltier element. Additionally, a feedforward control law defined by a piecewise constant function of time is optimized to bring the system, which is still nonlinear w.r.t. this voltage input, as closely as possible to a prescribed terminal steady state.