Vibration Control of a Two-Link Flexible Manipulator

This work involves mathematical modeling and strain control of a two-link flexible manipulator carrying a payload; the system’s dynamics are derived using the Euler–Lagrange formalism joined with the assumed modes approach. The dominant assumed vibration modes are adopted for Euler–Bernoulli clamped-mass beam, coupled with nonlinear dynamics associated with the rigid rotations of joints to formulate Euler–Lagrange dynamic robot model. The control aim is to obtain accurate trajectory tracking with effective strain elimination. A passivity-based controller is developed relying on the concept of energy shaping of the system. This ensures that the closed-loop system remains passive. The global system stability is proven using the Lyapunov theory and making allowance for passivity property. The proposed controller has been simulated using Matlab/Simulink to demonstrate its effectiveness in suppressing unwanted elastic vibrations.