A New Frequency-Modulation Input-Shaping Strategy Applied on a Double-Pendulum

Abstract In this work, a new frequency modulation technique is used to effectively control oscillations in multi-mode systems using single-mode command-shaping. It is well known that single-mode input shaper can effectively eliminate residual vibration of multi-mode system given that all frequencies within the system are odd-multiples of the shaped command frequency. Using this criterion, a new command shaping strategy specifically designed for multi-mode systems is developed. Our proposed strategy involves convolving a well defined formula with the original double-step command shaper. The resulting command modulates the modal frequencies such that the higher mode frequencies are odd-multiples of the first mode frequency. The equation of motion of the system is solved and the natural frequencies are determined analytically as a function of a controller gain. This gain is used to modify the trolley acceleration. To show the effectiveness of our strategy, two numerical simulation are conducted and validated experimentally on double pendulums.