Adaptive discrete PID-controllers for single-input plants

Optimal algorithms are derived for adjustment of a discrete PID-controller with an implicit reference model from the data of linear plant identification in sequential identification by a least squares procedure. The notions of complete, weak, and partial adaptability of a discrete adaptive controller are introduced for a discrete linear plant with pure delay. Criterial are obtained for complete, weak, and partial adaptability in terms of adaptability matrix properties. Results obtained in simulation of the controller for a typical second order plant are reported.