For a crane system in which the trolley stroke and the pendulum length are constrained to move in a specified range，a stabilizing control law that damps the pendulum oscillation quickly has been proposed using the Lyapunov's second method. In deriving the law，the nonlinearities of the system are considered outright. The control system has a structure where the trolley and the load are moved a㏄ording to sinusoidal reference functions generated from the pendulum trajectory.
The results of a numerical experment show that the design method realizes a high performance control system with some robustness with respect to parameter variations in the controlled system.