Performance Comparison of Input-Shaped Model Reference Control on an Uncertain Flexible System

This paper investigates input-shaped model reference control (IS-MRC) applied to an uncertain nonlinear double-pendulum crane. In order to investigate practical implementation issues, a simple single-pendulum is used as the reference model. The proposed controller enhances the robustness to the uncertain difference between the reference model and the plant. Single-and double-pendulum crane dynamics are presented. The natural frequencies of the double-pendulum crane are calculated and utilized to design input shapers. A Lyapunov control law with guaranteed asymptotic stability is derived using only the first mode states of the plant. The state tracking, control effort reduction, and oscillation suppression performances of various IS-MRC designs are tested via numerical simulations and experiments. By analyzing the results, the IS-MRC design that has the largest robustness to the plant uncertainties is demonstrated to provide the best overall performance.