Pulse Width Modulation Duty Cycle and Desired Angle-Based Command Shaping for Vibration Suppression of Flexible Manipulators

Abstract This work demonstrates vibration suppression of a single-link flexible manipulator (SLFM) and a two-link flexible manipulator (TLFM) using input shaping. In this, inputs include pulse width modulation (PWM) duty cycle and desired angular position. The shaping of these parameters is done based on the damping ratio of the system. Vibrations due to flexibility in flexible manipulators are suppressed for better end-effector accuracy. Extra damping for the first link is achieved using a belt, and a nonrotating second link is connected to the first link to get modified single flexible link. The modified system requires fewer iterations for vibration suppression. Results are compared with a nonlinear dynamics model developed using the assumed mode method (AMM) and decoupled natural orthogonal complement (DeNOC) matrices. A simple proportional–derivative (PD) controller manages the angular position in simulations. The process of input shaping is explained in detail, showing angular position and tip deflection variations with PWM duty cycle and time. The effect of input shaping on vibration suppression is shown for a two-link flexible manipulator, i.e., when both the links are rotated.