Finite-Time Settling Control of a Flexible Arm

This paper considers the position control of a flexible beam attached to a rotating rigid hub. The control torque is applied at the hub through a motor. A state-space model describing the motion of the flexible beam is developed and is employed in the design of the control law. The finite-time settling control strategy that combines feedback and feedforward is applied to the beam problem. The feedback part is separately designed to resolve the issues of asymptotic stability and robustness to uncertainties. The feedforward part simultaneously suppresses the rigid-body mode and a finite set of flexible modes at the end of manoeuvre and, therefore, it is the part responsible for the finite-time settling of the beam to its final configuration. It is shown that if the finite-time settling control is compared with previously developed control strategies under the same input bound constraint, it leads to a better suppression of vibrations at the end of manoeuvre, provided that a sufficient number of flexible modes are incorporated in the computation of the feedforward control law. A robustness test is carried out to show the viability of the control strategy supported by computer simulations.