On–Off Shaping Commands for Asymmetrically Delayed Second-Order Actuators

Abstract

On–off shaping commands are proposed for residual oscillation reduction in undamped flexible systems with asymmetrically delayed second-order actuators, which is a common issue in industrial applications. Asymmetrically delayed second-order actuators could produce large residual oscillations in undamped flexible systems during rest-to-rest operations. Therefore, an exact solution for the on–off shaping commands is developed with a phasor vector approach and step response functions of a second-order system. In addition, a method to obtain robust on–off shaping commands is presented with parameter optimization formulation to compensate for modeling uncertainties under asymmetrically delayed second-order actuators. The control performance of both approaches is analyzed with respect to the command design parameters, residual oscillations, and sensitivity, and it is compared with conventional input shapers. The proposed on–off input shaping commands are numerically evaluated with an undamped single-mode system, and they were experimentally validated with a minibridge crane.