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In a refrigeration process heat is absorbed in an evaporator by evaporating a flow of liquid refrigerant at low pressure and temperature. Controlling the evaporator inlet valve and the compressor in such a way that a high degree of liquid filling in the evaporator is obtained at all compressor capacities ensures a high energy efficiency. The level of liquid filling is indirectly measured by the superheat. Introduction of variable-speed compressors and electronic expansion valves enables the use of more sophisticated control algorithms, giving a higher degree of performance and just as important are capable of adapting to a variety of systems. This study proposes a novel method for superheat and capacity control of refrigeration systems, namely by controlling the superheat by the compressor speed and capacity by the refrigerant flow. A new low-order non-linear model of the evaporator is developed and used in a backstepping design of a non-linear adaptive controller. The stability of the proposed method is validated theoretically by Lyapunov analysis and experimental results show the performance of the system for a wide range of operating points. The method is compared with a conventional method based on a thermostatic superheat controller.