Robust control for crane considering all varying parameters in the dynamics

In this study, a design method of gain scheduling control based on a parameter dependent Lyapunov function for a crane is proposed. The method takes all varying parameters of crane dynamics into account. The Euler-Lagrange equation of the crane has velocity and acceleration of rope length. Velocity and acceleration of the rope length are not ignored in a dynamics, but the rope length, its velocity and acceleration are treated as time-varying parameters. The mass of the load is treated as uncertain but time-invariant parameter. A dynamics of the crane has rational expressions of scheduling parameters. To obtain affine system for the scheduling parameters, we adopt Linear Fractional Transformation with redundant descriptor representation. A gain scheduling controller based on the parameter dependent Lyapunov function is designed. The time-varying parameters are treated as scheduling parameters. The effectiveness of the proposed method is illustrated by simulations.