Extraction surface cleaning wherein a cleaning liquid is applied to a surface to be cleaned and extracted to remove the soiled cleaning fluid from the surface, and the surface is heated prior to or concurrent with the application of the cleaning fluid to the surface. First measure the plant in an open-loop control fashion, and using the measured data, describe a state equation of the plant by system identification and order determination methods. A tube member has ends thereof secured to each dam member and extends axially through a passage formed in the rotating shaft. The input gear includes a contact portion that is in contact with a coupling member to receive the driving force and a gear portion. With the apparatus in place upon the roll bars, the main extension bar exerts upward force against the soft top roof of the vehicle, thereby reducing movement of the soft top roof and noise within the interior of the vehicle.