The control of a multirate sampled-data, stirred-tank chemical reactor system using a parameter plane method is considered. Due to wide acceptance of proportional-plus-integral-plus-derivative (PID) control in the chemical process industries, a PID controller with a “slow-fast”multirate scheme is used for the chemical reactor system. Based on two related stability equations and using the PID
... [Show full abstract] gains as the adjustable parameters, the set of all possible PID gains to maintain the chemical reactor system's stability, and at the same time, to make the system having a specified gain margin, phase margin, damping ratio, and damping factor is determined. The effects of changing the integer N (which is the ratio of the sampling rates between a slow- and a fasl-samplcr)and (he basic sampling period Ton the set of PID gains satisfying the specifications are examined. The results for single-rate and multirate cases are also studied.