Q3. Liquid flows into a tank whose height is due to be controlled. The input flow is regulated by a valve. A flow of 3 m3/sec is produced for 1 mm change in the valve position. The valve has a dead time (delay) of 6 seconds. The tank is such that an input flow of 1 m3/sec produces a height of 2 m and it has a first order response with a time constant of 10 seconds. (a) Draw the block diagram of the closed loop system and calculate all the gains and transfer function with corresponding physical dimensions. 5 marks (b) Use Pade approximation for the time delay, calculate the unity feedback closed loop transfer function when a proportional controller of gain 0.5 is cascaded with the valve. What is the natural frequency, the closed loop damping ratio and the damped natural frequency of the closed loop system. 5 marks (c) The sine wave r(t) = 2 sin(0.3-0.1) is applied to the set point of the closed loop system. What will be the output? EE472/EE972 PLEASE TURN OVER Page 3 of 7 (d) 5 marks You are asked to design a PID type controller for this system, the control design specifications given are zero steady state error, overshoot between 10% to 20%, and the transient response to a step input as fast as possible. From the information in (a) to (c), explain clearly how you select the type of controller P, PI, or PID? Suggest a tuning method to find the gains of the controller you propose to meet the design specifications