Various issues on the closed-loop identification of empirical latent variable dynamic models for model predictive control (MPC) of the trajectories of process variables in batch systems are investigated. The concept of identifiability is explored in the context of batch processes and desirable conditions for the identification experiments to be informative for building latent variable dynamic models are proposed. It is shown that in many situations it is possible to identify the batch process models only from historical batch data without the need for external excitation of the closed-loop system. However, adding one or two batch runs with only slight set-point trajectory changes is an efficient approach to enhance the data for the identification of the batch dynamic models. The issue of model bias in closed-loop identification using nonparametric or highly parametrized modeling approaches is also investigated and it is shown that closed loop data obtained using tightly tuned PID controllers will minimize the bias.