Adaptive boundary iterative learning vibration control using disturbance observers for a rigid–flexible manipulator system with distributed disturbances and input constraints

In this article, an adaptive boundary iterative learning vibration control is developed for a class of the rigid–flexible manipulator system under distributed disturbances and input constraints. With the help of the virtual work principle, the dynamics of the rigid–flexible manipulator are modeled and described by coupled ordinary differential equations and partial differential equations. Based on the original infinite dimension system model, three compounded adaptive boundary iterative learning vibration control laws are constructed with disturbance observers and adaptive vibration laws, aiming to track the desired joint angular positions and achieve vibration suppression simultaneously. Three disturbance observers are proposed to determine the upper bounded approximation of the unknown external disturbances. Hyperbolic tangent and saturation functions are incorporated into adaptive vibration laws to handle input constraints. It is proved by Lyapunov–Krasovskii-like composite energy functions that elastic vibrations and tracking errors can asymptotically converge to zero along the iteration axis. Finally, the efficacy of the developed adaptive boundary iterative learning vibration control approach is illustrated by the simulation results under distributed disturbances and input constraints.