Passing from a Gas to an Electric Water Heater System: Adaptive PID Versus Smith Predictive Control

This paper presents the control results of an electric water heater system using two approaches: adaptive proportional integral derivative and Smith predictive control based on the physical internal model control structure. The electric water heater was modelled with two variable blocks connected in series: a first order system and a time delay. In fact, the gain, the tune constant and the time delay of the system change linearly with the water that flows in the permutation chamber. The physical model of the electric water heater system was retched based on energy dynamic equations and validated with open loop data of the system in a similar way that was made in a previews study about modelling and controlling a gas water heater. The two different control algorithms explored are the adaptive proportional integral derivative (APID) and the Smith predictive control (SPC) based on the internal physical model control algorithm. The first approach has some problems dealing with the time constant and the time delay variations of the system. This solution can control the overshoot for all different water flows but the time constant of the close loop systems changes with the water flow. The APID does not deal well with water flow variations. The second approach is more adequate to control this kind of systems (first order system followed by a time delay that changes in time). The SPC loop is indicated for control time delay systems and with the a priori knowledge of the physical model we can achieve a very good control result. Finally, these two algorithms are applied in controlling the system and the results are compared using the mean square error criterion.