Deflection Reduction Shaping Commands with Asymmetric First-Order Actuators

Abstract

In this paper, two approaches for generating deflection reduction shaping commands are proposed to reduce the transient and residual deflections of flexible systems subject to asymmetric first-order actuators. The commands are limited-state in that they consist of two positive actuations of different magnitudes and one negative actuation, similar to on-off-on commands. Standard on–off commands that are commonly used in robots, cranes, and spacecrafts can degrade the control performance of conventional input-shaped commands and cause detrimental damage resulting from large transient deflections of flexible structures due to asymmetric first-order actuators. Therefore, to cope with the performance degradation resulting from the effects of first-order actuators, an approximated closed-form solution and a numerically optimized approach for deflection reduction shaping commands are presented with an exponential function, final impulse magnitude modification of an input shaper is determined by a transient deflection constraint and a phasor vector approach. The performance assessment showed that the approximated analytical approach has an advantage in real-time control applications. The characteristics of the proposed deflection reduction shaping commands are analyzed with respect to system parameters, deflection reduction ratios, and actuator time constants. The proposed command shaping techniques are numerically evaluated using a pendulum system and are experimentally validated on a mini-bridge crane.