Design of restricted complexity digital regulators using explicit criterion minimisation

Describes a technique for designing digital regulators when their structure is restricted. A new formula is first derived for computing quadratic performance indices, which indicates that, rather than using iterative algorithms or residue calculus which may be difficult to apply for high-order systems, the problem reduces to solving certain Diophantine equations. Furthermore, gradients of the performance indices, which are needed in any algorithm for updating the controller parameters, can also be easily computed using similar equations. Based on this, the authors present a minimisation algorithm for tuning the controller parameters. Design of restricted complexity adaptive regulators used in controlling systems subjected to random noise is also given. Because of the importance of PID controllers, the authors show briefly how the method is applied to their tuning. Several examples for designing the controllers in both the adaptive and nonadaptive cases are given to demonstrate the feasibility of the proposed method and its merits.