Disturbance compensation based on harmonic injection switching for unknown time-delay systems

Disturbance rejection under unknown input time-delay remains a challenging problem in control systems. This paper investigates a novel strategy for systems with both unknown input delay and periodic disturbances to achieve asymptotic compensation. First, a characteristic observer is designed to estimate the key parameters related to delay time and disturbance frequency. It is worth noting that the proposed disturbance compensation method does not rely on precise key parameter values. To address this, switching criteria are specially constructed to help determine whether the estimated values enter a reasonable region. Next, reliable delay characteristics can be used to reconstruct and predict disturbances. Compared with existing approximation approaches, the proposed prediction and compensation method requires neither a known upper bound of the delay nor an accurate delay estimate, while enabling quantitative stability analysis. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed disturbance rejection method.