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As most residents spend more than 90% of their time in buildings, acceptable and reasonable control of both indoor thermal comfort and air quality is imperative to ensure occupants' health status and work productivity. However, current control strategies generally take either thermal comfort or indoor air quality as a single loop, rather than the concurrent control of two. To analyze their mutual influence, this study investigated the performance of three multi-control approaches, i.e., proportional integral derivative (PID) control of thermal comfort and a fixed outdoor air ratio, PID control of thermal comfort and design outdoor air rate, and PID control of thermal comfort and occupancy-based demand-controlled ventilation. As a pilot study, three typical control methods were implemented to a multi-zone building via OpenModelica modeling. The results indicate that indoor air temperature can be well-maintained under three control methods, however, the CO2 concentration under the fixed outdoor air ratio was over 1000 ppm, leading to poor indoor air quality. The control strategy with the design outdoor air rate could not properly ensure the CO2 concentration, due to the over-ventilated or under-ventilated phenomena, subsequently resulting in unnecessary energy waste. The occupancy-based demand controlled ventilation could maintain the CO2 concentration under the set-point with an intermediate power energy utilization. [ABSTRACT FROM AUTHOR]