This is a boundary control problem of a hybrid ODE-PDE system. The system consists of an actuator, a flexible link fixed to the actuator, and a tip mass at the free end of the link. In most literature, two control inputs are used for the simultaneous position and vibration control of the said system: One is the actuator's torque and the other is a force at the tip mass. The application of a control force at the tip mass of a manipulator does not seem to be a practical solution. Can we use only the actuator's torque to simultaneously control the position and vibration of the beam and the tip mass?

I would be grateful to anyone for sharing any theorem or paper addressing this issue (in support or against).

Thank you!

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