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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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