An explicit self-tuning controller is described that incorporates closed-loop pole location as the principal design criterion for the objective function of Clarke and Gawthrop. The algorithm includes several minor extensions to improve robustness : a variable dead-time compensator to deal with unknown or time-varying delay, and a method of treating steady-state offset that avoids retaining an integrator in the loop continuously. A new technique has been developed and included in the algorithm that enables the controller to be auto-tuning in the sense that the closed-loop pole(s) and sampling period can be determined on-line so as to optimize the system set-point step response, leaving the system designer to specify only internal model orders and noise characteristics on which to initiate retuning. The resulting controller is quite robust and can easily handle unstable, non-minimum phase systems in a single-loop configuration, as is demonstrated by several simulations including a non-linear model of a fixed-bed autothermal reactor operating over such a large range that auto-tuning of the poles is a necessity.