The conventional unity magnitude zero vibration (UM-ZV) command shaping technique is an effective means for eliminating vibration in linear mechanical systems with on-off actuators. This paper discusses how the UM-ZV command shaping technique is affected by a common nonlinearity: nonsymmetrical accelerating and braking dynamics. Two approaches for creating new types of UM-ZV shaped commands are presented: a closed-form analytic solution and a numerical optimization approach. Both methods reduce residual vibration of the nonlinear system more effectively than the conventional UM-ZV shaped commands. Simulations and experiments on a bridge crane confirm the effectiveness of the new commands.
Command Shaping Under Nonsymmetrical Acceleration and Braking Dynamics
Bradley, T. H., Danielson, J., Lawrence, J., and Singhose, W. (August 13, 2008). "Command Shaping Under Nonsymmetrical Acceleration and Braking Dynamics." ASME. J. Vib. Acoust. October 2008; 130(5): 054503. https://doi.org/10.1115/1.2948385
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