On the PD Control of Rotating Flexible Arms Driven by Stepper Motor

In this work, a dynamic model of a flexible-arm attached to a hub with flexible-joint and flexible torsional support is presented. The Lagrangian approach in conjunction with the finile element method is employed in deriving the equations of motion, within the assumption of small deformation theory. The control strategy adopts the approach of applying encounter torque supplied by a small DC motor fixed to a bed, which is recessed to the hub by the torsional spring. The control torque will be applied to the arm root to control the dynamics of the flexible arm and produce minimum tip deflection with precise positioning. Comparisons between rigid arm control and flexible arm are conducted. The control torque of the equivalent linear system is applied on the nonlinear model. Simulation results of the nonlinear and the linearized controlled models are compared and the results are discussed to show the efficiency of the proposed control strategy.