Time-proportional control, a form of pulse-width modulation, is a mathematical technique that allows a feedback controller to use an on/off or discrete actuator as if it were a continuous actuator capable of generating control efforts anywhere between 0% and 100%. The trick is to turn the actuator on and off for periods proportional to the desired control effort.
　　Consider a home cooling systemwww.cechina.cn, for example. Most thermostats use a “bang-bang” control algorithm that compares the actual room temperature with the setpoint specified by the room’s occupants, then turns the air conditioner fully on or fully off if the temperature is more than a few degrees too high or too low. This technique causes the room temperature to fluctuate around the setpoint, but in most homeswww.cechina.cn, that’s good enough.

控制工程网版权所有, a time-proportional controller can emulate the effects of a continuous actuator. In teh top examplewww.cechina.cn," src="http://www.cechina.cn/upload/article/319ecdf9-4bd4-438d-a600-1db482ae9e67/1.gif">

　　By cycling a discrete actuator on and off控制工程网版权所有, a time-proportional controller can emulate the effects of a continuous actuator.  In teh top examplewww.cechina.cn, the controller is attempting to achieve a 50% control effort by keeping the actuator in the "on" position 50% of the time.  In the bottom examplewww.cechina.cn, the controller is trying to achieve a 75% control effort by turning the actuator on for 3 duty cycles then off for 1.
　　The thermostat could achieve tighter control with a continuous actuator such as a motorized damper that would continuously allow a measured amount of chilled air into the room. Those are common in commercial HVAC applications but are typically too expensive for home use.
　　But with time-proportional control, a home thermostat wouldn’t need a continuous actuator to emulate its effects. It could use the air conditioner’s on/off switch to regulate not the amount of cool air being dumped into the room but the duration of each blast. To achieve an X% control effort, the thermostat would simply turn the air conditioner on for X units of time then off for 100 minus X units of time.
　　If those units are small compared to the time it takes to cool the room (a few minutes or so)