The oven given in the figure is heated with a heat source having the heat flow rate Q. The total heat capacity of all objects in the oven is C and the thermal isolation between the oven and its environment is R. T o is the temparature of the medium around the oven (air). The temperature in the oven is T. The heat flow rate can be controlled electrically as Q=K 1 V 1, where V 1 is the applied voltage and K 1 is the control coefficient. The temperature of the oven is measured by a thermistor as the voltage V 2 and V 2 =K 2 T, where K 2 is the sensor constant. o o Problem The heat loss between the oven and its environment is 0.5 kJ/s for the difference of 1 ̊ C. The heat required to increase the temperature of the objects of 1 ̊ C in the oven is 2 kJ. The heat flow rate is obtained as Q=30 kJ/s when 4 volts are applied to the heat source. The thermistor gives 4 volts for 80 o C temperature in th eoven. HOMEWORK-01 Obtain the closed loop control diagram. G c (s)=K p Answer: Heat transfer to environment Heat transfer to objects in the oven Q Q oven Q wall Q  Watt H  Joule

Hot water source Electro-pneumatic member Controller Heat exchanger Aspirator Air inlet, T Ai Heated air, T Ao Temperature sensor, T s Problem (Kuo, p.195) T w : Water temperature Answer: Fill the missing blocks for the closed loop control diagram of the air heating system: Sensor Heat Exchanger

The water tank shown in the figure is filled with a source having the flow rate Q 1. The capacity of the tank is C=A/ρg. A is the cross section area of the tank, ρ is the density of the fluid and g is the gravity. The output flow rate is Q 2. The pressure drop at the outlet is ∆p 2 =RQ 2 and the water level in the tank is h 1. The open loop control diagram is given below as the V 1 is input and V 2 is the output. V 1 is the input voltage (command signal) and V 2 is the measured voltage (sensor output). Q d is the uncontrolled input (disturbance). Obtain the closed loop control diagram of the fluid- level control system. Problem Answer: Transfer function from Q=Q 1 +Q d to h 1 C