<P> The proportional control concept is more complex than an on - off control system like a bi-metallic domestic thermostat, but simpler than a proportional - integral - derivative (PID) control system used in something like an automobile cruise control . On - off control will work where the overall system has a relatively long response time, but can result in instability if the system being controlled has a rapid response time . Proportional control overcomes this by modulating the output to the controlling device, such as a control valve at a level which avoids instability, but applies correction as fast as practicable by applying the optimum quantity of proportional gain . </P> <P> A drawback of proportional control is that it cannot eliminate the residual SP - PV error, as it requires an error to generate a proportional output . To overcome this the PI controller was devised, which uses a proportional term (P) to remove the gross error, and an integral term (I) to eliminate the residual offset error by integrating the error over time to produce an "I" component for the controller output . </P> <P> In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the setpoint and the process variable . In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain . </P> <P> This can be mathematically expressed as, </P>

When controller output is proportional to the amount of error (or deviation) the controller is