Abstract—This paper presents the control results of an electric water heater system using two approaches: adaptable proportional integral derivative and Smith predictive control based in 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 time 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 in 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 in 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 à 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. Index terms—adaptive PID, electrical water heater, physical model identification, Smith predictive control and time delay system. I. INTRODUCTION Industry control processes presents many challenging problems, including non-linear or variable linear dynamic behaviour, variable time delay that means time varying parameters. One of the alternatives to handle with time delay systems is to use prediction technique to compensate the negative influence of the time delay. Smith predictor control J. A. Vieira is with Department of Electrotecnica of the Escola Superior de Tecnologia, Av. Empresário, 600-767 Castelo Branco, Portugal (corresponding author phone: 272 339300; fax: 272 339399; email: zevieira@est.ipcb.pt). A. M. Mota is with Department of Electrónica, Telecomunicações e Informatica of the Universidade de Aveiro, Campus Santiago, 3810 Aveiro, Portugal (alex@det.ua.pt). (SPC) is one of the simplest and most often used strategies to compensate time delay systems. In this algorithm it is important to choose the right model representation of the linear/non-linear system. The model should be accurate and robust for all working points, with a simple mathematical and transparent representation that makes it interpretable. This work is based in a previews study made in modelling and controlling a gas water heater system. The problem was to control the output water temperature even with water flow, cold water temperature and desired hot water temperature changes. To succeed in this mission one non-linear model based Smith predictive controller was implemented. The main study was to identify the best and simple model of the gas water heater system. It has been shown that many variable industry linear and non- linear processes are effectively modelled with neural and neuro-fuzzy models like the chemical processes [1]. Hammerstein and Wiener models like pH-neutralization, heat exchangers and distillation columns [2]-[3]. And hybrid models like heating and cooling processes, fermentation [4], solid drying processes [5] and continues stirred tank reactor (CSTR) [6]. In this previews work there were explored this three different modelling types: neuro-fuzzy [7], Hammerstein [8] and hybrid [9] and [10] models that reflex the evolution of the knowledge about the first principles of the system. These kinds of models were used because the system had a non-linear actuator and time varying linear parameters. At the beginning there was no knowledge about the physical model and there were used black and grey box model approaches. Finally, the physical model was found and a much simple adaptive model was achieved (the physical model white box modelling). This paper presents two different control algorithms to control the output water temperature in an electric water heater system. The first approach is the adaptive proportional integral derivative controller and second is the Smith predictive controller based on the physical model of the system. From the previews work it is known that the first control approach is not the best algorithm to use in this system, it was used just because it has a simple mathematical structure and serves to compare results with the Smith predictive controller results. The Smith predictive controller has a much more complex mathematical structure because it uses three internal physical models (one inverse and two directs) and deals with the variable time delay of the system. The knowledge of the physical model permits varying the linear parameters correctly PASSING FROM A GAS TO AN ELECTRIC WATER HEATER SYSTEM: ADAPTABLE PID VERSUS SMITH PREDICTIVE CONTROL José Vieira 1 and Alexandre Mota