ABSTRACT
This chapter presents the study of the high-mode dynamics in single-link flexible manipulators. The theoretical analyses indicate that high modes still have some impacts on the system dynamics under some specific conditions. A control method was proposed to reduce vibrations of the infinite modes. Robustness analyses show that the method has more insensitivity in frequency. Numerous simulations and experiments verify that the method is effective to control vibrations of the single-link flexible manipulator with infinite modes, and is robust for a large range of modeling errors and working conditions.
This chapter also presents the dynamic modeling of the uncoupled and coupled Duffing oscillator dynamics in flexible link manipulators. The theoretical analyses indicate that flexible link manipulators exhibit Duffing oscillator dynamics. The nonlinear frequency of the flexible manipulator increases with an increase of vibration amplitudes for large mass ratios, and decreases with increasing vibration amplitudes for small mass ratios. Corresponding control methods were proposed to control Duffing oscillator dynamics in flexible single-link manipulators. Robustness analyses show that the control methods have more insensitivity to modeling errors in the system parameter. Numerical simulations and experiments confirmed that the developed model is appropriate for the dynamic modeling of the flexible manipulator and control methods are robust for a large range of modeling errors and working conditions.
