Dynamic modelling, simulation and input-shaped control of planar two-link flexible manipulators

D.Ing. (Mechanical Engineering)Abstract: Flexible link robots offer potential advantages over conventional rigid robots. However, the major drawback of a lightweight robot is the residual vibrations that need to be accurately modelled and controlled. This research aims to address two main issues: accurate dynamic modelling and residual vibration feed forward control. Most dynamic models for two-link flexible manipulators, using the assumed modes method in conjunction with the Lagrange equation, use approximate boundary conditions at the link end, and truncated orthogonality conditions that only take the masses of flexible links into consideration, while actual mass and inertia, and non-collocated mass at the end of the links are ignored. This project, then, develops an exact, complete and explicit dynamic model using the assumed mode methods with the exact values of the boundary conditions at the link ends. Four companion and equivalent orthogonality condition equations are derived to accurately normalize the mode shapes and diagonalize the stiffness matrix of a two-link flexible manipulator. The proposed model is first used to simulate the response of the two-link flexible manipulator with unshaped bang-bang input torques. Experiments are conducted to verify the proposed model. Next, shaped input torques are developed and applied to the proposed dynamic model. Two types of shaped inputs are developed: Gaussian monopulse shaped and impulse shaped bang-bang input torques. Different shaped input torques with the same amplitudes and durations are applied to the dynamic model, and the results are compared in the time and frequency domains through simulations