A First Course in FUZZY and NEURAL CONTROL

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 61

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(^2468101214161820) t
Figure 2.25.y(t)=10u(t)− 10 e−^0.^8 tu(t)

2.7.2 Example:temperaturecontrol

In this section we discuss the developmentof the classical proportional-integral-
derivative (PID) control parameters for a temperature control problem. We
will extend this example in Chapter 6 to incorporate a neural controller. In
a conventional PID control system, the gains are allfixed, while with neural
networks, they can change.

System model The system comprises an electrical heater of heat capacity
Chconnected via a thermal resistanceRhoto the oven. The heat capacity of
the oven isC 0. At temperatureTe, the oven loses heat to the environment
through the thermal resistanceR 0 of its insulation. The temperature controller
adjusts the power dissipated in the heating elementsW, by comparing the oven
temperatureT 0 with the set-point temperatureTs.

Figure 2.26. System model

The symbols on the right side of the diagram in Figure 2.26 are thermal
components; the ones on the left are electrical devices. Dashed lines represent
transducers: a thermometer in one case, conversion of electrical currentflowing
through the heater into heat (thermal currentW) in the other. The thermome-