Boundary control of a vertical nonlinear flexible manipulator considering disturbance observer and deflection constraint with torque and boundary force feedback signals

Abstract

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to prevent the amount of boundary deflection from violating the constraints and avoiding any simplifications, in the presence of external boundary disturbance, proper control feedbacks and boundary disturbance observer are adopted in order to reach control objectives and to compensate external boundary disturbance effects simultaneously. By choosing proper boundary feedback, system states are proven to be uniform ultimate bounded and converge exponentially toward a small neighbourhood of zero. In order to illustrate the performance of the proposed control approach, numerical simulation results are provided.