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Generally, conventional controllers for comfort are designed by using on/off control or proportional-integral (PI) control, with little consideration of energy consumption of the system. This paper presents a multi-input-multi-output (MIMO) model predictive control (MPC) for a direct expansion (DX) air conditioning (A/C) system to improve both indoor thermal comfort and air quality, whereas the energy consumption is minimised. The DX A/C system is modelled into a nonlinear system, with a varying speed of compressor and varying speed of supply fan and volume flow rate of supply air being regarded as inputs. We first propose an open loop controller based on an optimisation of energy consumption with the advantage of a unique set of steady states. The MPC controller is proposed to optimise the transient processes reaching the steady state. To facilitate the MPC design, the nonlinear model is linearised around its steady state. MPC is designed for the linearised model. The advantages of the proposed energy-optimised open loop controller and the closed-loop regulation of the MIMO MPC scheme are verified by simulation results. [ABSTRACT FROM AUTHOR]