Input-shaped model reference control of a nonlinear time-varying double-pendulum crane

This paper investigates the performance of input-shaped model reference control on a time-varying double-pendulum using a linear single-pendulum reference model. The single- and double-pendulum crane dynamics are presented. An input-shaped model reference control scheme is then developed. The robustness of the controller is enhanced to handle both parameter variations and the system order difference between the reference model and the plant. The natural frequencies of the double-pendulum crane are calculated and utilized to design a two-mode specified insensitivity input shaper. A Lyapunov control law using only the first mode states of the plant is derived. The state tracking, oscillation suppression, and control effort reduction performances of the proposed controller is tested via numerical simulations and experiments.