Editing Proportional–integral–derivative controller (section)

===Proportional term===
[[File:PID varyingP.jpg|right|thumb|320px|Response of PV to step change of SP vs time, for three values of ''K''<sub>p</sub> (''K''<sub>i</sub> and ''K''<sub>d</sub> held constant)]]

The proportional term produces an output value that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant ''K''<sub>p</sub>, called the proportional gain constant.

The proportional term is given by
:<math>P_\text{out} = K_\text{p} e(t).</math>

A high proportional gain results in a large change in the output for a given change in the error. If the proportional gain is too high, the system can become unstable (see [[#Loop tuning|the section on loop tuning]]). In contrast, a small gain results in a small output response to a large input error, and a less responsive or less sensitive controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances. Tuning theory and industrial practice indicate that the proportional term should contribute the bulk of the output change.{{Citation needed|date=March 2011}}

====Steady-state error====

The '''steady-state error''' is the difference between the desired final output and the actual one.<ref>{{Cite book| title = Instrument Engineers' Handbook: Process control and optimization | first = Béla G. | last = Lipták | edition = 4th | publisher = CRC Press | year = 2003 | isbn = 0-8493-1081-4 | page = 108}}</ref> Because a non-zero error is required to drive it, a proportional controller generally operates with a steady-state error.{{efn|The only exception is where the target value is the same as the value obtained when the controller output is zero.}} Steady-state error (SSE) is proportional to the process gain and inversely proportional to proportional gain. SSE may be mitigated by adding a compensating [[biasing|bias term]] to the setpoint AND output or corrected dynamically by adding an integral term.