Robustness analysis of input-shaped model reference control on a double-pendulum crane

This paper analyzes the robustness of input-shaped model reference control when applied to a double-pendulum crane using a linear single-pendulum crane as the reference model. The single- and double-pendulum crane dynamics are derived and then used to develop the input-shaped model reference control scheme. 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 cranes are calculated and utilized to design a three-mode zero-vibration input shaper. A Lyapunov control law using only the states associated with the first mode is derived. The robustness of the proposed controller in state tracking and oscillation suppression performances are analyzed and verified via numerical simulations and experiments. The controller has good robustness to the parameter estimation errors and the fundamental system order difference between the reference model and the plant.