Autotuning principles for delayed systems

Abstract

The paper brings a combination of a biased-relay feedback experiment and an algebraic control design method for time-delay systems. The combination results in a new principle of autotuning for a wide class of single input-output dynamic systems. The estimation of the controlled process is based on asymmetrical limit cycle data. Then, a stable transfer function with a dead-time term is identified. The controller is computed through solutions of Diophantine equations in the ring of stable and proper retarded quasipolynomial meromorphic functions (RMS). Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. The controller design in this ring yields a Smith-like feedback controller with the realistic PID structure. The methodology offers a scalar tuning parameter m0 > 0 which can be adjusted by a suitable principle or further optimization. The first and second order timedelay transfer functions can sufficiently estimate systems of quite high orders. The developed principles are illustrated by examples in the Matlab + Simulink environment.