Auto-Selection of the Sampling Period for a Class of Pole-Placement Controllers

For a class of discrete-time pole-placement controllers that utilize a single non-zero pole, the effect of varying the control sampling period, both on the optimal location of the closed-loop pole and on the size of the feasible pole location region, has been considered. With both deterministic and stochastic optimality measures, fast sampling yields an optimal pole location close to 1 with a very narrow feasible operating region. Conversely, slow sampling yields an optimal pole location at 0 with a much wider feasible operating region; however, the closed-loop response characteristics for slow sampling are much poorer. Sampling at a rate which yields an optimal closed-loop pole in the range 0.2-0.7 is seen to avoid the excessive system sensitivity (as when located closer to 1) and a somewhat degraded system response (when located at 0). These results suggest the basis of an ad hoc design technique for on-line selection of the sampling period which is demonstrated using a nonlinear model of a fixed-bed chemical reactor.