Consider the batch reactor system studied by Aziz et al.,3. The two reactions, A + B → C and A + C → D, are carried out in a jacketed batch reactor, where C is the desired product and D is a waste product. The manipulated variable is the temperature of the coolant in the cooling jacket. There are two inequality constraints; input bounds on the coolant temperature and an upper limit on the maximum reactor temperature. Using the model parameters specified by Aziz et al., evaluate the following control strategies for a set-point change from 20 °C to 92 °C.

(a) PID controller

(b) batch unit

(c) batch unit with preload

(d) dual-mode controller