In this paper, we consider the problem of optimal experiment design for LPV system identification with the local approach when the identified model has to be used for LPV control. This local approach for LPV system identification is characterised by a number of local LTI identification experiments performed at constant values of the scheduling variable. In this paper, we determine these constant values of the scheduling variable as well as the input spectra of the corresponding local LTI identification experiments in an optimal way. The optimal LPV identification experiment is here defined as the experiment with the least input energy while guaranteeing that the identified LPV model is sufficiently accurate to yield a satisfactory LPV controller.