Lyapunov-based piezoelectric control of flexible cartesian robot manipulators

A Lyapunov-based control strategy is proposed for regulating problem of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam arm with a translational base support. The arm cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. A piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamilton´s principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the base and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. The feasibility of the controller is validated through numerical simulations.