Time-Optimal Control Of High-Speed Flexible-Robot Arm Using PD Algorithms

Abstract

This paper addresses utilization of proportional-plus derivative (PD) control algorithms for time-optimal control of flexible-robots. Flexibility is modeled using one mode of vibration with negligible structural damping. Two novel methods for time-optimal control were derived and closed form equations for tuning the required PD gains were obtained. The resulting controllers were used to control a high-speed flexible-robot for minimum settling time in response to a step angular motion command. Similarly, for the sake of comparison, three other techniques were used to control the same flexible-robot arm. The first used multi-switch bang-bang control technique. The second used PD approach in which the gains are computed through locating the dominant poles as far left as possible in the left hand side of the complex plane. The third approach used multi-switch bang-bang control followed by PD control. Uncertainties were introduced in the model to evaluate robustness of the methods. Results obtained showed that the novel techniques out performed the other ones.