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

The modeling and control of a horizontally slewing inextensible Timoshenko-beam including the correct 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. This nonlinear dynamic model places no restrictions on slenderness ratio, slewing angle, and rotational speed provided that the flexure deflections remain small. To achieve a joint angle trajectory tracking with rapid suppression of elastic vibrations, a nonlinear controller is designed using input-output linearization and elastic mode stabilization. The input-output linearization is used to generate a desired joint angle trajectory command. The elastic mode stabilization is designed based on the linear time-invariant part of the partially linearized system. Stability of the closed-loop system is investigated, and a sufficient condition for asymptotic stability is established. This stability condition justifies the existence of joint angle trajectory commands for accurate joint angle trajectory following and simultaneous vibration suppression.