The self-tuning controller is extended to include rational transfer function (as opposed to polynomial) terms in the associated cost function. Two interpretations of the self-tuning controller are examined in some detail: a model reference adaptive control, and a self-tuning least-squares predictor in conjunction with conventional compensation. The former version is shown to give not only prespecified set point response, but also a closed-loop disturbance with largely prespecified spectral density. The latter version is compared with the method of O.J.M. Smith, and is shown to be less sensitive to uncertainty in some system parameters. Examples are given which illustrate the continuous-time performance of these discrete-time control laws.

Based on a minimum i.t.a.e. criterion, optimal control algorithm parameter surfaces are presented for 2nd-order computer-controlled systems. They illustrate the variation in proportional, integral and derivative parameters with sampling period, time delay and system time constant.