Physical Modeling and Control of a Distributed Parameter System

The aim of this work was to test model based controllers with pilot-scale water heating equipment. The controlled variable is the outlet temperature, and the manipulated variable is the volumetric flow rate. The main disturbances are the heat duty and the inlet temperature. The power of the electric heater can be manipulated to imitate solar radiation, thus our system could be the physical model of a solar collector. The first principle based dynamic modeling of the system yields partial differential equations (PDEs). One way to simplify the model is integrating the heat balance equation along the geometric space, and estimating the needed average variables using the measured signals. Another approach is to divide the geometric space into discrete units, thus transforming the PDE into a system of ordinary differential equations (ODEs). Controller structures were synthesized using the constrained inversion technique, which yields nonlinear feed-forward controllers that accomplish a pre-defined control specification (relation between the setpoint and the controlled variable). Perfect models are not available, and IMC structure has been used for feedback compensation of the model error. Constrained PI controller has been used as reference. The effect of different modeling techniques and the different control specifications were examined. All the model based controllers outperformed the fixed parameter PI controller.