The dynamic behavior of the heat exchanger shown in figure can be described by the following transfer functionsThe valve lift x is measured in inches. Other symbols are defined in Figure.(a) Find the Ziegler-Nichols settings for a PT controller.(b) Calculate the corresponding gain and phasemargins.

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Process: 2 °FA6 min T' (0.432s + 1)(0.017s + 1) Control valve: X _0.047 in/psi P 0.083s + 1 lb - 112 min in X' Temperature sensor-transmitter: Pr 0.12 psi/°F T 0.024s + 1 Steam T. X-D- TC Process fluid w, T Condensate Trap