Autotuning for delay systems using meromorphic functions

The paper presents an autotuning method for time delay systems. The novelty in principles is a new combination of biased-relay feedback identification and an algebraic control design method for time-delay systems. The estimation of the controlled process is based on an asymmetrical limit cycle data experiment. Then, a stable transfer function with a dead-time term is identified. The controller is designed through solutions of Diophantine equations in the ring of stable and proper retarded quasipolynomial meromorphic functions. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. First and second order identification gives Smith-like feedback controllers with the realistic PI and PID structure. The design principle also offers a scalar tuning parameter m0 > 0 which can be adjusted by a suitable principle or an optimization method. The developed approach is illustrated by examples in the Matlab + Simulink environment.