Pole Placement Self-Tuning Control of Unstable Nonminimum Phase Systems

An explicit self-tuning controller is developed that incorporates closed-loop pole location as the principal design criterion for the method of Clarke and Gawthrop. The algorithm includes a variable dead-time compensator to deal with unknown or time-varying delay, and a new method of treating steady-state offset. A technique has been developed and included in the algorithm that enables the controller to be "nearly self-tuning" in the sense that the closed-loop pole(s) and/or sampling period can be determined on-line so as to optimize the system set-point step response, leaving the system designer only to specify internal model orders and noise characteristics on which to initiate retuning. This controller can easily handle unstable, nonminimum phase systems in a single-loop configuration, as is demonstrated by several simulations including a non-linear model of a fixed-bed autothermal reactor.