4. FIGURE 5 shows an electrically heated oven and its associated control circuitry. The current, I, to the oven's heating element is fed from a voltage-controlled power amplifier such that I = εK1. A voltage, VD, derived from a potentiometer, sets the desired oven temperature, TD. The oven temperature is measured using a thermocouple that, for simplicity, is assumed to generate a constant emf of 10 μV per degree Celsius. The effect of the ambient temperature is ignored.

(a) Represent the arrangement by a conventional control-system block diagram. Identify the following elements in the block diagram:

input; error detector (comparator); controller; controlled element; detecting element and feedback loop.

(b) Derive an expression for the transfer function of the system, in terms of the system parameters k1, k2, kO and kt.

(c) Using the data given in TABLE A, calculate the oven temperature when the potentiometer is at its mid-point.