Reduced-order observer based output feedback control for a Timoshenko beam

This paper proposes observer based controls for a MIMO Timoshenko beam system with disturbances and references from an exosystem, and by further limiting the references and disturbances, also gives reduced-order controls. At first, we propose state feedback controls to guarantee the output regulation problem of a nominal Timoshenko beam system, which is obtained by specially choosing known disturbances and references. This also makes the PDE observer easily designed based on tracking errors only. Then, exosystem observers and their reduced-order forms are proposed in case of different geometric multiplicities and limited conditions of disturbances, references and system uncertainties. This gives observer based robust controls and reduced-order observer based controls. Robust output regulation is proved for the Timoshenko beam under observer based controls. Simulation examples are provided for a Timoshenko beam system with different references and system uncertainties.