Elastic manipulators are commonly used in industrial applications. Therefore, understanding their dynamics is one of the most important engineering challenges. Vibration is a crucial phenomenon due to the elastic nature of the manipulators. The accurate positioning and trajectory tracking of elastic manipulators is achieved through vibration control. In this study, boundary control of an axially exponentially graded flexible manipulator with exponential convergence was investigated. The manipulator was modeled using Euler–Bernoulli beam theory. Boundary control inputs were applied at the boundaries of the manipulator. A proportional-derivative boundary controller was designed, and exponential convergence was achieved. A Lyapunov function was designed for the stability of the system. Equations were solved using the finite difference discretization method. Angle tracking and boundary control inputs were obtained.
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