Gain-scheduled Control of a Crane Using the Sum-of-squares Technique

This paper discusses nonconservative design of a gain-scheduled controller for a crane, whose dynamics has nonlinear dependence on uncertain parameters. In particular, the design problem is formulated into a robust semidefinite programming problem and is solved through a sum-of-squares approach. Since the sum-of-squares approach is asymptotically exact, a nonconservative design is possible. Although this approach has a theoretical drawback that computational complexity grows up as the conservatism is reduced, it works practically well to the present problem. The efficacy of the designed controller is shown by simulation and also by a laboratory experiment.