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.