Autotuning for delay systems in meromorphic functions — A second order case

The paper brings 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 asymmetrical limit cycle data. Then a stable second order 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. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. A second order identification 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 an optimization method. The developed approach is illustrated by examples in the Matlab + Simulink environment.