1 research outputs found
Exponential Stabilization for Vibration Cable with a Tip Mass under Boundary Control and Non-Collocated Observation
We study the output feedback exponential stabilization for a vibration cable
with tip mass. With only one measurement, we construct an infinite-dimensional
state observer to trace the state and design an estimated state based
controller to exponentially stabilize the original system. This is an
essentially important improvement for the existence reference [O. Morgul, B.P.
Rao and F. Conrad, IEEE Transactions on Automatic Control, 39(10) (1994),
2140-2145] where two measurements including the high order angular velocity
feedback were adopted. When a control matched nonlinear internal uncertainty
and external disturbance are taken into consideration, we construct an
infinite-dimensional extended state observer (ESO) to estimate the total
disturbance and state simultaneously. By compensating the total disturbance, an
estimated state based controller is designed to exponentially stabilize the
original system while making the closed-loop system bounded. Riesz basis
approach is crucial to the verifications of the exponential stabilities of two
coupled systems of the closed-loop system. Some numerical simulations are
presented to illustrate the effectiveness.Comment: arXiv admin note: text overlap with arXiv:2011.0784