Hot and cold liquids are mixed at the junction of two pipes. The temperature of the resulting mixture is to be controlled using a control valve on the hot stream. The dynamics of the mixing process, control valve, and temperature sensor/transmitter are negligible and the steady-state gain is 6mA/mA. Because the temperature sensor is located well downstream of the junction, an Bs time delay occurs. There are no heat losses/gains for the downstream pipe.
(a) Draw a block diagram for the closed-loop system.
(b) Determine the Ziegler-Nichols settings (continuous cycling method) for both PI and PID controllers.
(c) For each controller, simulate the closed-loop responses for a unit step change in set point.
(d) Does the addition of derivative control action provide a significant improvement? Justify your answer.