A control method regulates an electronic expansion valve of a chiller to maintain the refrigerant leaving a DX evaporator at a desired or target superheat that is minimally above saturation. The expansion valve is controlled to convey a desired mass flow rate, wherein valve adjustments are based on the actual mass flow rate times a ratio of a desired saturation pressure to the suction pressure of the chiller. The suction temperature helps determine the desired saturation pressure. A temperature-related variable is asymmetrically filtered to provide the expansion valve with appropriate responsiveness depending on whether the chiller is operating in a superheated range, a saturation range, or in a desired range between the two.