This important paper presents an approach for finite-time control of a distributed-parameter system: a flexible beam connected to a translational mass. A quasi-tracking variable is introduced, and a terminal sliding controller is developed to achieve finite-time convergence of the quasi-tracking variable to a properly predefined trajectory.
It is shown that the error between the end point of the beam and the predefined trajectory, though not decaying to zero, is always bounded by a small time-varying bound. Moreover, a method to reduce the error bound is given. The problem of observation (control) spillovers, which exists in the conventional truncated-model-based controller design, is essentially avoided. Satisfactory simulation results are provided to demonstrate the effectiveness of the presented approach.