Nonlinear Modeling and Partial Linearizing Control of a Slewing Timoshenko-Beam

The modeling and control of a horizontally slewing inextensible Timoshenko beam, taking into account the centrifugal stiffening effect and a tip payload, are considered. Partial differential equations of motion and orthogonality conditions for the constrained modes are derived. A finite dimensional dynamic model simplified by using the orthogonality conditions is obtained. To achieve the joint angle trajectory tracking with simultaneous suppression of elastic vibrations, a nonlinear controller is designed using input-output linearization and elastic-mode stabilization. A sufficient condition for asymptotic stability of the closed-loop system is established. Numerical examples with the role of slenderness ratio of the slewing beam highlighted are presented to demonstrate the effectiveness of the proposed control strategy.