**4. Smith predictive controller**

152 Frontiers of Model Predictive Control

system with a fixed time constant. The time delay is also a problem that is not solved with

It was define a reference signal *r(t)* that is the desired hot water temperature and a water flow *wf(t)* with several step variations similar to the ones used in real applications. The cold

For testing the controllers it can be seen that error signal *e(t)=r(t)-hwt(t)* is around zero excepted in the input transitions. In reference step variations it can be seen that the overshoots for the different water flows are similar but the rise times are clearly different, for small water flows the controller presets bigger rise times. In water flow variations the control loop have some problems because of the variable time delay. This control loop only

With the proposed tests signals, the tuned adaptive PID control structure was tested in controlling the electric water heater. The APID control results are shown in figure 7.

*I*

*+*

*+*

*P*

*D*

water temperature was almost constant around 13,0 ºC.

P

*r(k)*

*+*

*wf(k)*

this control algorithm.

reacted when error appears.

**3.2 Adaptive PID control results** 

Fig. 7. Adaptive PID control results.


Fig. 6. APID controller constituent blocks.

*e(k)*

Electric Water Heater

*f((p(k)) hwt(k)*

The second control loop tested is the Smith predictive control algorithm. This control strategy is particularly used to control systems with time delay. First it is described the control structure and its parameters and second the control results are showed.
