Heating, ventilation and air-conditioning (HVAC) units in buildings form a system-of-subsystems entity that must be accurately integrated and controlled by the building automation system to ensure the occupants' comfort with reduced energy consumption. As control of HVACs involves a standardized hierarchy of high-level set-point control and low-level Proportional-Integral-Derivative (PID) controls, there is a need for overcoming current control fragmentation without disrupting the standard hierarchy. In this work, we propose a model-based approach to achieve these goals. In particular: The set-point control is based on a predictive HVAC thermal model, and aims at optimizing thermal comfort with reduced energy consumption; the standard low-level PID controllers are auto-tuned based on simulations of the HVAC thermal model, and aims at good tracking of the set points. One benefit of such control structure is that the PID dynamics are included in the predictive optimization: in this way, we are able to account for tracking transients, which are particularly useful if the HVAC is switched on and off depending on occupancy patterns. Experimental and simulation validation via a three-room test case at the Delft University of Technology shows the potential for a high degree of comfort while also reducing energy consumption.@en