Motion planning and tracking for tip displacement and deflection angle for flexible beams

We present results for motion planning and tracking for flexible beams with Kelvin-Voigt damping, when the goal is to track sinusoidal reference signals for the displacement and deflection angle at the free-end of the beam using only actuation at the base. We present the solution to the motion planning problem for the string model, and a method of leveraging the string solution with PDE backstepping theory to solve the motion planning problem for the shear beam. We then present state-feedback boundary controllers that stabilize their respective systems around the motion planning solution.