This paper presents several robust model predictive controllers that improve the temperature performance and minimize energy consumption in an automotive air-conditioning/refrigeration (A/C-R) system with a three-speed and continuously-varying compressor. First, a simplified control-oriented model of the A/C-R system is briefly introduced. Accordingly, a discrete Model Predictive Controller (MPC) is designed based on the proposed model for an A/C-R system with a three-speed compressor. A proper terminal weight is chosen to guarantee its robustness under both regular and frost conditions. A case study is conducted under various heating load conditions. Two hybrid controllers are made, which combine the advantages of both the on/off controller and discrete MPC such that they will be more efficient under any ambient heating condition. In addition, a continuous MPC is developed for systems with continuous variable components. Finally, the experimental and simulation results of the new controllers and the conventional on/off controller are provided and compared to show that the proposed controllers can save up to 23% more energy. (C) 2016 Elsevier Ltd. All rights reserved.