An experimental implementation of a new distributed parameter shape control design methodology is presented. The technique is based upon the input/output representation of distributed parameter systems in a spatially- and temporallytransformed frequency space. The analysis is specialized to shape control through the introduction of generalized spatial transforms of the plant response which explicitly parameterize the shape control task. Experiments are summarized wherein a 4Oin pinned-pinned steel beams shape is controlled, in the presence of quasi-static and resonant disturbances, over a bandlimited set of four sinusoidal shape basis functions at a closed-loop temporal bandwidth of 2Hz, using distributed piezoelectric actuators. Temporal compensation is provided by digitally-implemented LQG/LTR compensators. A novel inner-loop damping formulation, based upon the second method of Lyapunov, is developed and implemented to damp the beam resonant response beyond the LQG/LTR control bandwidth.
Shawn Edward Burke,
James E. Hubbard,
"Closed-loop dynamic shape control of a flexible beam", Proc. SPIE 1303, Advances in Optical Structure Systems, (1 October 1990); doi: 10.1117/12.21515; https://doi.org/10.1117/12.21515