It is desired to control the exit temperature T₂ of tie heat exchanger shown in Fig. E. by adjusting the steam flow rate w_s. Unmeasured disturbances occur in inlet temperature T₁. The dynamic behavior of the heat exchanger can be approximated by the transfer function. Where the time constant has units of seconds and the primes denote deviation variables. The control valve and temperature transmitter have negligible dynamics and steady-state gains of K_v = 0.2 lb/s/mA and K_m = 0.25 mA/^oF. Design a minimal prototype controller (i.e., Dahlia?s controller with ? = 0) that is physically realizable and based on a unit step change in the set point. Assume that a zero-order hold is used and that the sampling period is ?t =2s.

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LC 42 23