A Relay Feedback Structure for Time-Delay Processes under Disturbances: Stability Analysis using Poincaré map

In this paper, the stability of a relay feedback structure that provides a stable and symmetrical oscillation for process under disturbances is analysed. The relay feedback structure consists of a block which removes static disturbance or drift followed by a relay. The block is composed of a high-pass filter followed by a relay plus an integrator. From an equivalent relay structure, the conditions for the existence and local stability of the limit cycle for the relay feedback structure and a linear time-invariant (LTI) system with time delay are obtained. In addition, the analysis is extended to cases where the time delay is larger than half of the oscillation period. Simulation studies illustrate the results.