Hot and cold liquids are mixed at the junction of

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.

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