This paper deals with the problem of robust model predictive control of an uncertain linearized model of a building envelope and HVAC system. Uncertainty of the model is due to the imperfect predictions of internal and external heat gains of the building. The Open-Loop prediction formulation of the Robust Model Predictive Control (OL-RMPC) is known to be unnecessarily over-conservative in practice. Therefore, we adopt a Closed-Loop prediction formulation of Robust Model Predictive Control (CL-RMPC) which exploits an uncertainty feedback parameterization of the control sequence and results in a tractable formulation of the problem. To improve on the efficiency of CL-RMPC we propose a new uncertainty feedback parameterization of the control input, which leads to a number of decision variables linear in time horizon as opposed to quadratic as in previous approaches. To assess our approach we compare three different robust optimal control strategies: nominal MPC which does not have a priori information of the uncertainty, OL-RMPC and CL-RMPC. We show results from a quantitative analysis of performance of these controllers at different prediction error values of the disturbance. Simulations show that CL-RMPC provides a higher level of comfort with respect to OL-RMPC while consuming 36% less energy. Moreover, CL-RMPC maintains perfect comfort level for up to 75% error in the disturbance prediction. Finally, the newly proposed parameterization maintains the performance of CL-RMPC while reducing the simulation time by an average of 30%.

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