Application of singular perturbation theory in modeling and control of flexible robot arm

This paper presents dynamic modeling and control for a two-link flexible robot arm. The effort has been made in this paper to explain singular perturbation theory and its application to flexible robot arm. Flexible manipulators have two types of motion, rigid and flexible. Using singular perturbation theory, the system is decomposed into a slow subsystem and a fast subsystem associated with rigid motion and flexible motion respectively under the assumption that the flexible dynamics are faster than the rigid dynamics. Singular perturbation approach is used to drive the slow and fast subsystems with two different time scale subsystems for reduced order modeling. Separate controllers are designed for both slow and fast subsystems. Proportional-derivative (PD) control is used for slow subsystem which tracks the desired trajectory and also ensures the robustness in the controlled system and linear?quadratic regulator (LQR) is designed for fast subsystem which damps out the vibration of the flexible arm. The model and control of manipulator have been simulated in MATLAB. The dynamic model validation and performance of the system with and without controller are presented.