Control of Flexible Euler-Bernoulli Beam with Input/Output Delay and Stochastic Disturbances

Abstract

We consider the problem of stability enhancement of an undamped flexible beam with a tip mass in presence of input delay and random disturbances. In absence of delay this problem is classically solved through output feedback based on a suitable approximation of an infinite-dimensional Kalman filter. To cope with the presence of input or output delays we derive and compare two solutions, one based on a predictor from estimates in the past and the other one based on a filter with delayed measurements. An identical delay bound in closed form is derived for both solutions and we show that by an appropriate choice of the control gain it is possible to stabilize the system in presence of arbitrarily large delays. A modular structure is proposed for the case of arbitrary gain and delay bound. Finally, we consider the problem of deriving a finite-dimensional approximation of the predictor.