The conceptual block diagram of a gas-fired heater is shown in Figure below. The commanded fuel pressure is proportional to the desired temperature. The difference between the commanded fuel pressure and a measured pressure related to the output temperature is used to actuate a valve and release fuel to the heater. The rate of fuel flow determines the temperature. When the output temperature equals the equivalent commanded temperature as determined by the commanded fuel pressure, the fuel flow is stopped and the heater shuts off. If the transfer function of the heater. GH(s). is The transfer function of the fuel valve Gy(s) is,

(a) Design the temperature feedback path with a suitable state feedback controller that yields 5% overshoot and a setting time of 10 minutes.

GH(S) = 1 (s+0.4) (s+0.8) degrees F ft/min G,(s) 5 ft/min s+5 psi