The following reactions are carried out in an isothermal continuous stirred tank reactor.
AB
BC
rkcHkoimwkmolmin
B is the desired product and concentration of B is controlled using a PI controller. The feed stream of 1 m/min containing 0.5 kmol/min of A at steady-state operation passes through the reactor. The reactor has a volume of 1 m^3 and the volume of the reaction mixture does not change with time.
a. Derive the transfer function between the inlet concentration of A and the outlet concentration of B, and find the steady-state value of the outlet concentration of B when the inlet concentration is increased to 0.9 kmol/m^3.
b. The transfer functions of the measuring device and control valve are given below. Using the Routh-Hurwitz criterion, determine the ultimate gain of the controller if the integral time is 0.1.
Gs = 1