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This brief presents a model-based predictive control (MPC) approach to building cooling systems with thermal energy storage. We focus on buildings equipped with a water tank used for actively storing cold water produced by a series of chillers. First, simplified models of chillers, cooling towers, thermal storage tanks, and buildings are developed and validated for the purpose of model-based control design. Then an MPC for the chilling system operation is proposed to optimally store the thermal energy in the tank by using predictive knowledge of building loads and weather conditions. This brief addresses real-time implementation and feasibility issues of the MPC scheme by using a simplified hybrid model of the system, a periodic robust invariant set as terminal constraints, and a moving window blocking strategy. The controller is experimentally validated at the University of California, Merced. The experiments show a reduction in the central plant electricity cost and an improvement of its efficiency.