Consider the oven temperature control system described in Example 3.5 with transfer function

(a) Obtain the step response of the system with a PD cascade controller with gain 80 and a zero at 25.

(b) Obtain the step response of the system with PD feedback controller with a zero at 25 and unity gain and forward gain of 80.

(c) Why is the root locus identical for both systems?

(d) Why are the time responses different although the systems have the same loop gains?

(e) Complete a comparison table using the responses of (a) and (b), including the percentage overshoot, the time to first peak, the settling time, and the steady-state error. Comment on the results, and explain the reason for the differences in the response.

EXAMPLE 3.5

Find the z-domain transfer function of the furnace sketched in Figure 3.12, where the inside temperature Ti is the controlled variable, Tw is the wall temperature, and To is the outside temperature. Assume perfect insulation so that there is no heat transfer between the wall and the environment with heating provided through a resistor. The control variable u has the dimension of temperature scaled by an amplifier with gain K. The sampling period T = 5 1 s.