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A method of autotuning using an asymmetric relay with hysteresis feedback test is proposed and developed. Then, three parameters for aperiodic first or second order transfer functions can be obtained. After the identification relay experiment, controller parameters are computed through linear diophantine equation in the ring of proper and stable rational functions. This algebraic approach for a traditional 1-DOF feedback structure generates a class of PI or PID controllers. The pole placement principle in the methodology brings a scalar positive "tuning knob" for additional controller tuning. A Matlab-Simulink program implementation was developed for simulation and verification of the studied approach. Two illustrative examples support simplicity and efficiency of the proposed methodology.

The contribution is focused on analysis and synthesis of delay systems in a ring of RQ-meromorphic functions. Controller design is based on solution of Diophantine equations in this ring that leads to Smith predictor like structure. Tuning of the controllers is based on pole-placement method as a desired multiple root of the characteristic closed loop equation. A stable second order transfer function is used as an example to validate the methodology. Furthermore, a biased relay experiment is combined with the proposed control design to bring an autotuning method. Matlab-Simulink examples are given to illustrate the developed approach.

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