Central air conditioning systems having compensating control function for total heat load in a plurality of rooms

A central air conditioning system includes a compensating control function in which the prescribed target temperature Tfs of the conditioned air supplied from the air conditioning apparatus to a main duct is changed from the original value to a prescribed value of a modified target temperature Tfm to establish the target temperature Tfs when the actual room temperature Ta in each room does not achieve a corresponding desired room temperature Ts even though the damper of the corresponding air volume control unit is positioned at either the fully opened position or the closed position. The temperature of the conditioned air from the air conditioning apparatus is controlled in accordance with the target temperature Tfs, and the target temperature Tfs of the conditioned air is further changed to successive values of the modified target temperature Tfm until the actual room temperature Ta in each room achieves the corresponding desired room temperature Ts.