Model reference command shaping for vibration control of multimode flexible systems with application to a double-pendulum overhead crane

This paper proposes a Model Reference Command Shaping (MRCS) approach for an effective vibration and oscillation control of multimode flexible systems. The proposed MRCS is designed based on a reference model and avoids the need for measurement or estimation of several modes of frequency and damping ratio as in the case of other input shaping and command shaping approaches. To test the effectiveness and robustness, the designed MRCS is implemented for oscillation control of a double-pendulum overhead crane. Simulations on a nonlinear crane model and experiments using a laboratory overhead crane are carried out under two cases, without and with payload hoisting. Without a prior knowledge of the system frequency and damping ratio, the MRCS is shown to provide the highest reductions in the overall hook and payload oscillations when compared to the multimode Zero Vibration and Zero Vibration Derivative shapers designed based on the Average Travel Length approach. In addition, the MRCS is more robust towards changes in the frequency during payload hoisting and changes in the payload mass. It is envisaged that the proposed method can be useful in designing effective vibration control of multimode flexible systems.