In this paper, we define a dynamic discrete model of a passive air conditioning unit, without the more typical compression or absorption-refrigeration cycle. The unit is composed of heat exchangers, a positioning system and humid corrugated pads. The aim of the study was to follow the temperature in a greenhouse and to replicate it with a desired and stable relative humidity in a ventilated growth chamber. A control law, based on a quadratic criterion and dynamic programming, taking output error and energy consumption minimisation into account, was used to control the behaviour of the unit in spite of air intake disturbances. The results of the simulation indicate that the air conditioning unit can produce a variable climate in the growth chamber, with a wide range of relative humidity setpoints.