Main purpose of the study presented in this paper is to demonstrate the boundary controllers design by singular perturbation approach for trajectory tracking of two-link flexible arm. Applying the two-time scale control theory on the nonlinear PDE model, a control scheme is elaborated which makes hubs’ angles track a desired trajectory while damping out the links vibration. In the proposed controller, fast (flexible) subsystem controller will damp out the vibration of the flexible links by a Lyapunov-type design and the other slow (rigid) subsystem Inverse Dynamic controller dominates the trajectory tracking. These two controllers constitute the composite control scheme. The method does not require any information about the vibration of the links along the links for the proposed fast control law as well as discretizing the PDE of arm vibration to set of ODEs. Therefore, the method excludes the effect of both observation and control spillover instability. The simulation results confirm that the proposed boundary controllers are quite effective in performance.
Multi-time Scale Control of Dual-Stage Nanopositioning Systems
