Stability study of a PID controlled cyclic-rate sampled-data chemical reactor system

The study of the stability boundary of a cyclicrate sampled-data, stirred-tank chemical reactor system using a parameter plane method is presented. 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 related stability equations and PID gains as adjustable parameters, the stable region in the parameter plane to maintain the chemical reactor system's stability is determined. The effects on stability boundary of changes in the basic sampling period T, the number of intersamples taken by the cyclic-rate sampler S_c (between kT and (k + 1)T, where k is any positive integer), and the time instants of intersamples are also examined. The advantage of this approach is that the effects of the PID gains on the stability (and performance) of the control system are easily seen in the parameters planes. This can assist control engineers with the design work by providing information on controller gains which meet stability and performance requirements.