Reference shaping of periodic trajectory for systems having constraints

This paper is concerned with off-line reference shaping for closed-loop systems with state/input constraints. We propose a method to generate reference signals which achieve better tracking property for given periodic trajectories subject to system constraints. In order to take account of both transient and steady state tracking performance, the new reference signals consist of two parts. This plays a key role to deal with periodic trajectory tracking. The steady state reference signals are produced first so as to minimize tracking errors in the steady state subject to given system constraints. Then, the transient reference signals are obtained in a similar way with the additional constraint that the transient states are connected to the steady states smoothly. By combining these signals, we obtain the shaped references. Its effectiveness is demonstrated through detailed simulations. Furthermore, an experimental validation is performed.