Relay-based autotuning: a second order algebraic design

Abstract

The paper is focused on autotuners tuning a class of PID like controllers. The autotuning principle combines relay feedback identification and an algebraic control design method for stable systems. The estimation of the stable controlled process is performed through asymmetrical limit cycle data. Then a second order transfer function with a double real pole is identified. The controller is derived through parameterized solutions of diophantine equations in the ring of proper and stable rational functions. Controller parameters can be simply tuned by a pole-placement problem as a desired multiple root of the characteristic closed loop equation. This scalar tuning parameter m(0)> 0 can be adjusted by various principles, e.g. by an equalization method. The proposed methodology is illustrated by examples and analysis which demonstrates the restriction of the aperiodicity of estimated transfer function.