Parameter plane control design for a two-tank chemical reactor system

In this paper, we consider control of a stirred-tank chemical reactor system with a transportation lag using a parameter plane method. Due to wide acceptance of proportional- plus-integral-plus-derivative (PID) control in the chemical process industries, a PID controller is used for this chemical reactor system. Based on two stability equations and using the PID gains as the adjustable parameters, the stability boundary and boundaries with a specified gain margin (G.M.), phase margin (P.M.), damping ratio and damping factor are shown in the first quadrant of parameter planes. The set of all possible gains to maintain the chemical reactor system's stability, and at the same time, to make the system having a prespecified amount of G.M., P.M., damping ratio and damping factor is found. The performance for some representative PID gains chosen in the parameter planes are checked by their Nyquist plots and Bode diagrams. The advantage of using this approach is that the effects of parameters on the stability and performance of the control system can be easily seen in the parameter space, and this can help control engineers to ease the design work by properly adjusting the parameters to obtain the desired system performance.