o Problem 01-01 Qoven Obtain the closed loop control diagram. Gc(s)=Kp HOMEWORK-01 Problem 01-01 o 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. To 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=K1V1 , where V1 is the applied voltage and K1 is the control coefficient. The temperature of the oven is measured by a thermistor as the voltage V2 and V2=K2T , where K2 is the sensor constant. 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 oC temperature in th eoven. Qoven Obtain the closed loop control diagram. Gc(s)=Kp Q Heat transfer to environment Heat transfer to objects in the oven Qwall Answer: QWatt HJoule

Electro-pneumatic member Problem 01-02 (Kuo, p.195) Hot water source Electro-pneumatic member Controller Heat exchanger Aspirator Air inlet, TAi Heated air, TAo Temperature sensor, Ts Tw: Water temperature Sensor Heat Exchanger Fill the missing blocks for the closed loop control diagram of the air heating system: Answer:

Transfer function from Q=Q1+Qd to h1 C (Q1+Qd) The water tank shown in the figure is filled with a source having the flow rate Q1. 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 Q2 . The pressure drop at the outlet is ∆p2=RQ2 and the water level in the tank is h1 . The open loop control diagram is given below as the V1 is input and V2 is the output. V1 is the input voltage (command signal) and V2 is the measured voltage (sensor output). Qd is the uncontrolled input (disturbance). Obtain the closed loop control diagram of the fluid-level control system. Problem 01-03 h1 Area A Pa (Disturbance) (atmospheric pressure) (pressure difference) Answer: Transfer function from Q=Q1+Qd to h1 C (Q1+Qd) (input flow) (level measurement) (error signal) (command signal) (controller) (water tank) (disturbance, rain etc.) (actuator/vane) (sensor) (water level) (sensor output) (reference signal)