Designing of a command shaper using multi-objective particle swarm algorithm for vibration control of a single-link flexible manipulator system

A new command shaping method is proposed using gain and delay units to shape the reference input in order to reduce vibration of a single-link flexible manipulator system. The values of gain and delay elements can be derived analytically with a priori knowledge of natural frequencies and associated damping ratios of the system, which may not be available for complex flexible systems. Moreover, command shaping in principle causes delay in system's response while it reduces system vibration and in this manner the amount of vibration reduction and the rise time conflict one another. Assuming that, no prior information is available about the system, a new multi-objective particle swarm optimisation (MOPSO) algorithm is applied to optimise the gain values and the amount of delay in order to provide a wide range of solutions that trade-off these conflicting objectives so as to satisfy design goals.