Research on Modeling and Dynamics of Flexible Manipulators

Flexible manipulators are distributed systems described by partial-differential equations; therefore their dynamic behavior is of infinite degrees of freedom. From the perspective of control theory, it is impossible to design an infinite dimensional controller. The controlled plant must have a finite dimension thereby requiring less significant terms in the model to be omitted. This causes model uncertainties since those terms generally are time-variable, and system dependent. The boundary conditions set by tip-load, hub inertia, friction, rotatory inertia, and shear force also impact beam dynamics, which make the model implementation more complicated for the purpose of real-time control. A pick-and-place manipulator-like system is considered. The model derivation proceeds step-by-step from calculation of energies through to a dynamic equation and constraints. The representative, formulae are given. An extensive analysis of the resonant frequencies and modal shapes for the governing equations are developed. The modal frequencies and coefficients of modal shape are presented to verify the dynamics and model