Consider the oven temperature control system of Example 3.5 with transfer function
(a) Design a proportional controller for the system to obtain a percentage overshoot less than 5%.
(b) Design a controller for the system to reduce the steady-state error due to step to zero without significant deterioration in the transient 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.
