**2. The electric water heater**

The overall system has three main blocks: the electric water heater, a micro-controller board and a personal computer (see figure 1).

The micro-controller board has two modules controlled by a flash-type micro-controller from the ATMEL, ATMEGA168 with 8Kbytes on FLASH. The interface module has the necessary electronics to connect the sensors and control the actuator. The communication module has the RS232 interface used for monitoring and acquisition of all system variables in to a personal computer.

After this small description of the prototype system, the electric water heater characteristics are presented and its first principles equations are presented.

Fig. 1. System main blocks.

146 Frontiers of Model Predictive Control

that used a neuro-fuzzy compensator based in Smith predictive control to achieved better results. Or other solutions for unknown dead time delays like (Dong-Na, Guo, et al., 2008) that use gray predictive adaptive Smith-PID control because the dead time variation is unknown. There is an interesting solution to control processes with variable time delay using EPSAC (Extended Prediction Self-Adaptive Control) (Sbarciog, Keyser, et al., 2008) that could be used in this systems because the delay variations is caused by fluid

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

This chapter 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 in time and gives an interpretable model

This chapter starts, in section 2, with a full description of the implemented system to control the electric water heater, including a detailed description of the heater and its physical equations allowing the reader to have a comprehension of the control problems that will be

Section 3 and 4, describes the two control algorithms presented: the adaptive proportional integral derivative control structure and the Smith predictive control based in the physical models of the heater. These sections show the control results using the two approaches applied in to a domestic electric water heater system. Finally, in section 5, the conclusions

The overall system has three main blocks: the electric water heater, a micro-controller board

The micro-controller board has two modules controlled by a flash-type micro-controller from the ATMEL, ATMEGA168 with 8Kbytes on FLASH. The interface module has the necessary electronics to connect the sensors and control the actuator. The communication module has the RS232 interface used for monitoring and acquisition of all system variables

After this small description of the prototype system, the electric water heater characteristics

simple adaptive model was achieved (the physical model white box modelling).

that facilitate its integration on any control schemes.

explained in later sections.

**2. The electric water heater** 

in to a personal computer.

and a personal computer (see figure 1).

are presented and its first principles equations are presented.

are presented.

transportation.
