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Rejection of sinusoidal disturbances for known LTI systems in the presence of output delay. (English) Zbl 1388.93034
Summary: This paper focuses on estimation and cancellation of unknown sinusoidal disturbances in a known LTI system with the presence of a known output delay. Parametrizing the disturbance and representing the delay as a transport PDE, the problem is converted to an adaptive control problem for an ODE-PDE cascade. An existing state observer is used to estimate the ODE system states. The exponential stability of the equilibrium of the closed-loop and error system is proved. The perfect estimation of the disturbance and state is shown. Moreover, the convergence of the state to zero as $$t \rightarrow \infty$$ is achieved in the closed loop system. The effectiveness of the controller is demonstrated in a numerical simulation.

##### MSC:
 93B35 Sensitivity (robustness) 93D20 Asymptotic stability in control theory 93C05 Linear systems in control theory 93C73 Perturbations in control/observation systems 93C20 Control/observation systems governed by partial differential equations 93C40 Adaptive control/observation systems 93B07 Observability
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