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HVAC here stands for Heating, Ventilation and Air Conditioning. Thus, a HVAC control system applies regulation to e.g. a heating. Usually, a sensing device is used to compare the actual state (e.g. temperature) with a target state. Then, the control system draws a conclusion what action has to be taken (e.g. start blower).
Central controllers and most terminal unit controllers are programmable, meaning the direct digital control program code may be customized for the intended use. The program features include time schedules, setpoints, controllers, logic, timers, trend logs, and alarms. The unit controllers typically have analog and digital inputs that allow measurement of the variable (temperature, humidity, or pressure) and analog and digital outputs for control of the transport medium (hot/cold water and/or steam). Digital inputs are typically (dry) contacts from a control device, and analog inputs are typically a voltage or current measurement from a variable (temperature, humidity, velocity, or pressure) sensing device. Digital outputs are typically relay contacts used to start and stop equipment, and analog outputs are typically voltage or current signals to control the movement of the medium (air/water/steam) control devices such as valves, dampers, and motors.
Groups of DDC controllers, networked or not, form a layer of system themselves. This "subsystem" is vital to the performance and basic operation of the overall HVAC system. The DDC system is the "brain" of the HVAC system. It dictates the position of every damper and valve in a system. It determines which fans, pumps and chiller run and at what speed or capacity. With this configurable intelligency in this "brain", we are moving to the concept of building automation. 
More complex HVAC systems can interface to Building Automation System (BAS) to allow the building owners to have more control over the heating or cooling units. The building owner can monitor the system and respond to alarms generated by the system from local or remote locations. The system can be scheduled for occupancy or the configuration can be changed from the BAS. Sometimes the BAS is directly controlling the HVAC components. Depending on the BAS different interfaces can be used.
It was only natural that the first HVAC controllers would be pneumatic, as the engineers probably understood fluid control. Thus mechanical engineers could use their experience with the properties of steam and air to control the flow of heated or cooled air. There are still pneumatic HVAC systems in operation in some buildings, such as schools and offices, which can be a century old.
After the control of air flow and temperature was standardized, the use of electromechanical relays in ladder logic to switch dampers became standardized. Eventually, the relays became electronic switches, as transistors eventually could handle greater current loads. By 1985, pneumatic control could no longer compete with this new technology.
By the year 2000, computerized controllers were common. Today, some of these controllers can even be accessed by web browsers, which need no longer be in the same building as the HVAC equipment. This allows some economies of scale, as single operations center can easily monitor thousands of buildings.