Force and vibration control of a flexible arm without vibration sensor

This paper proposes a force and vibration controller of the flexible arm without vibration sensor. Since the tip of the flexible arm contacts with a given constraint surface, a constraint condition should be satisfied. By using Hamilton´s principle, we derive dynamic equations of the joint angle, the vibration of the flexible arm, and the constraint force. The derived boundary condition is nonhomogeneous. We introduce a new variable and derive a homogeneous boundary condition. To compensate the spillover instability an optimal controller with low-pass property is constructed. A set of simulations has been carried out. Simulation results confirm that the controller performs remarkably well