Adaptive PID controller for systems with time delay

A digital self-tuning controller algorithm for systems with time delay is presented in this paper. The controller parameter design is derived from the ultimate gain and ultimate period of the system. The main part of the paper consists in deriving the simple algebraic expressions for the ultimate values computation. It is performed for a first-order model with time delay on the basis of condition that poles of the closed loop with ultimate gain lie on the stability boundary. This procedure can be implemented on various types of controller design based on the knowledge of the ultimate values, such as the well-known Ziegler-Nichols method.