1. o o Problem 01-01 HOMEWORK-01 Establish the closed loop block diagram. G c (s)=K p Answer: The oven shown in the figure is heated with a source having thermal flow of Q. Total thermal capacitance in the oven is C, thermal resistance between the oven and outside is R. T o is the outside temperature. The temperature in the oven is T. Heat flow is set by electrical control as Q=K 1 V 1. V 1 is the actuation voltage. K 1 is the control gain. The temperature in the oven is measured as the voltage V 2 with a thermistor and V 2 =K 2 T. K 2 is the sensor gain. Heat transfer between oven and outside in difference of 1 Celsius is 0.5 kJ/s. To increase the temperature of substances up 1 Celsius in a isolated room, the necessity of heat is 2 kJ. Heat flow is Q=30 kJ/s as the voltage of 4 V is applied. Output voltage of 4V corresponds to the temperature of 80 o C.

2. Hot water reservoir Elektro-pnoumatic transducer Controller unit Heat exchanger Fan Air input, T Ai Heated air, T Ao Temperature sensor, T s Problem 01-02 (Kuo, p.215) T w : Water temperature Answer: Fill the missing transfer functions in the given closed loop diagram.

3. The reservoir shown in the figure is filled with a source having fluid flow of Q 1. The reservoir capacity is C=A/ρg, where A is the cross-section of the reservoir, ρ is the density and g is the gravity. The output fluid flow is Q 2. The pressure loss in the output is ∆p 2 =RQ 2. The water level in the reservoir is h 1. V 1 is the input voltage and V 2 is the output voltage. The open loop transfer function is given below. Q d is the disturbance. Establish the closed loop block diagram. Problem 01-03 Answer: Transfer function from Q=Q 1 +Q d to h 1 :

4. Problem 01-04 Answer: θ L is the angular displacement of the load of J L for the system shown in the figure. Transfer function equation is given below. θ r is the reference input. K p is the control gain. Establish the closed loop block diagram.