Parameter plane control design for a stirred-tank chemical system with slow-fast multirate sampling

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 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 ensure the system has 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 fast-sampler) and the basic sampling period T on the set of PID gains are examined and the results for single-rate and multirate cases are also studied.