This paper presents the design of battery charging control system suitable for different battery types. A PI controller-based battery current control system is designed with the aim of achieving robust control system behavior over a wide range of battery internal resistance variations. In order to enhance the battery current control system performance, an adaptation mechanism comprising a Kalman filter-based battery internal resistance estimator has been designed and tested. The current control system is commanded by a superimposed battery voltage controller aimed at bringing the battery terminal voltage to the fully-charged state while also limiting the maximum battery charging current. The effectiveness of the proposed battery charging cascade control system has been verified experimentally on the battery test setup for a VRLA battery and LiFePO4 cell.