Oscillation Control of a Double-Pendulum Overhead Crane Using Positive and Negative Input Shaping Techniques

A double-pendulum overhead crane system exhibits significant nonlinearity and is classified as an under-actuated system, making control more complex. This study focuses on designing a robust shaper to effectively mitigate oscillations in such systems. Two robust shapers, which are Zero Vibration Derivative (ZVD) and Negative Equal-Magnitude (NEM), are considered. These are obtained by convolving two input shapers that are designed based on the hook and payload oscillation frequencies. Matlab simulations are utilized to evaluate the performance of the shapers, using a nonlinear dynamic model of the crane to assess their effectiveness. Simulation results show that the ZVD shaper has a better performance in oscillation reduction, with 81% and 76% reductions for the hook and payload oscillations, respectively. In addition, the ZVD provides the lowest mean average error by achieving 87% and 83% reductions in the hook and payload as compared to the case with an unshaped input. However, the NEM shaper provides less delay in the trolley response.