Chapter 11 — Robots with Flexible Elements

Inverse dynamics control for a flexible link

A single flexible link with rotation at its base is controlled by computing the stable inverse dynamics of the flexible system associated with the desired trajectory for the end-effector. This feedforward command is made more robust by the addition of a suitable PD feedback control at the joint. Because of the non-minimum phase nature of the tip output, the resulting input command is non-causal, starting ahead of the actual output trajectory (pre-shaping the link) and ending after (discharging the link). Comparison is made with a PD joint control using a step reference input and with a full state feedback (utilizing strain gauge signals and their rates) and a nominal trajectory command. The inverse dynamics control demonstrates superiority both in terms of overshoot and residual vibrations. References: 1. D.-S. Kwon: An Inverse Dynamic Tracking Control for a Bracing Flexible Manipulator, Dissertation, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, (1991); 2. D.-S. Kwon, W.J. Book: A time-domain inverse dynamic tracking control of a single-link flexible manipulator, ASME J. Dyn. Syst. Meas. Control 116, 193-200 (1994); doi: 10.1115/1.2899210
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