<!DOCTYPE html>
<html class="client-nojs vector-feature-night-mode-disabled vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-sticky-header-enabled" lang="en" dir="ltr"><head>
<meta charset="UTF-8">
<title>Setpoint (control system)</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="canonical" href="https://en.wikipedia.org/wiki/Setpoint_(control_system)"> <link href="./mw/ext.cite.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/ext.math.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.icons.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.search.codex.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/skins.vector.styles.css" rel="stylesheet" type="text/css">
<link href="./mw/user.styles.css" rel="stylesheet" type="text/css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link rel="stylesheet" type="text/css" href="./mw/site.styles.css">
<link rel="stylesheet" type="text/css" href="./mw/noscript.css">
<link rel="stylesheet" type="text/css" href="./footer.css">
<link rel="stylesheet" type="text/css" href="./vector-2022.css">
</head>
<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Setpoint_control_system rootpage-Setpoint_control_system skin-vector-2022 action-view">
<div class="mw-page-container">
<div class="mw-page-container-inner">
<div class="mw-content-container">
<main id="content" class="mw-body">
<header class="mw-body-header vector-page-titlebar">
<h1 id="firstHeading" class="firstHeading mw-first-heading">
<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Setpoint (control system)</span></span>
</h1>
</header>
<a id="top"></a>
<div id="bodyContent" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" aria-labelledby="firstHeading" data-mw-ve-target-container="">
<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr">
<style data-mw-deduplicate="TemplateStyles:r1236090951">
/* start https://en.wikipedia.org/ */
.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}
/* end https://en.wikipedia.org/ */
</style><div role="note" class="hatnote navigation-not-searchable">This article is about setpoints in control theory. For other uses, see <a href="Set_point_(disambiguation)" class="mw-redirect mw-disambig" title="Set point (disambiguation)">Set point</a>.</div>
<p>In <a href="Cybernetics" title="Cybernetics">cybernetics</a> and <a href="Control_theory" title="Control theory">control theory</a>, a <b>setpoint</b> (<b>SP</b>;<sup id="cite_ref-Bequette_1-0" class="reference"><a href="#cite_note-Bequette-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> also <b>set point</b>) is the desired or target value for an essential variable, or <a href="Process_variable" title="Process variable">process value</a> (PV) of a <a href="Control_system" title="Control system">control system</a>,<sup id="cite_ref-Achterbergh_2-0" class="reference"><a href="#cite_note-Achterbergh-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> which may differ from the actual measured value of the variable. Departure of such a variable from its setpoint is one basis for error-controlled regulation using <a href="Negative_feedback" title="Negative feedback">negative feedback</a> for automatic control.<sup id="cite_ref-Ashby_3-0" class="reference"><a href="#cite_note-Ashby-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A setpoint can be any physical quantity or parameter that a control system seeks to regulate, such as temperature, pressure, flow rate, position, speed, or any other measurable attribute.
</p><p>In the context of <a href="Proportional%E2%80%93integral%E2%80%93derivative_controller" title="Proportional–integral–derivative controller">PID controller</a>, the setpoint represents the reference or goal for the controlled process variable. It serves as the benchmark against which the actual <a href="Process_variable" title="Process variable">process variable</a> (PV) is continuously compared. The <a href="Proportional%E2%80%93integral%E2%80%93derivative_controller" title="Proportional–integral–derivative controller">PID controller</a> calculates an error signal by taking the difference between the setpoint and the current value of the <a href="Process_variable" title="Process variable">process variable</a>. Mathematically, this error is expressed as:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e(t)=SP-PV(t),}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>e</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>S</mi>
<mi>P</mi>
<mo>−<!-- − --></mo>
<mi>P</mi>
<mi>V</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle e(t)=SP-PV(t),}</annotation>
</semantics>
</math></span><img src="./9fbb3562ba86333446b6cb4d281451429c7f218f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.744ex; height:2.843ex;" alt="{\displaystyle e(t)=SP-PV(t),}" loading="lazy"></span></dd></dl>
<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e(t)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>e</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle e(t)}</annotation>
</semantics>
</math></span><img src="./98cb518a61ada87bcd636f531d4d9fd2e67876c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.732ex; height:2.843ex;" alt="{\displaystyle e(t)}" loading="lazy"></span> is the error at a given time <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>t</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle t}</annotation>
</semantics>
</math></span><img src="./65658b7b223af9e1acc877d848888ecdb4466560.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SP}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
<mi>P</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle SP}</annotation>
</semantics>
</math></span><img src="./6af938aba900659f559fabe1ae5c79aa074ce796.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.245ex; height:2.176ex;" alt="{\displaystyle SP}" loading="lazy"></span> is the setpoint, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PV(t)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>P</mi>
<mi>V</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle PV(t)}</annotation>
</semantics>
</math></span><img src="./ec80ac98ce03e4c1bc00e9943b3d197c89d37eba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.182ex; height:2.843ex;" alt="{\displaystyle PV(t)}" loading="lazy"></span> is the <a href="Process_variable" title="Process variable">process variable</a> at time <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>t</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle t}</annotation>
</semantics>
</math></span><img src="./65658b7b223af9e1acc877d848888ecdb4466560.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}" loading="lazy"></span>.
</p><p>The PID controller uses this error signal to determine how to adjust the control output to bring the <a href="Process_variable" title="Process variable">process variable</a> as close as possible to the setpoint while maintaining stability and minimizing <a href="Overshoot_(signal)" title="Overshoot (signal)">overshoot</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>
<p><b>Cruise control</b>
</p><p>The <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SP-PV}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
<mi>P</mi>
<mo>−<!-- − --></mo>
<mi>P</mi>
<mi>V</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle SP-PV}</annotation>
</semantics>
</math></span><img src="./1aef6206cec87f30eeced49f7c100e12506b10e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.618ex; height:2.343ex;" alt="{\displaystyle SP-PV}" loading="lazy"></span> error can be used to return a system to its norm. An everyday example is the <a href="Cruise_control" title="Cruise control">cruise control</a> on a road vehicle; where external influences such as gradients cause speed changes (PV), and the driver also alters the desired set speed (SP). The automatic control algorithm restores the actual speed to the desired speed in the optimum way, without delay or overshoot, by altering the power output of the vehicle's engine. In this way the <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SP-PV}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
<mi>P</mi>
<mo>−<!-- − --></mo>
<mi>P</mi>
<mi>V</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle SP-PV}</annotation>
</semantics>
</math></span><img src="./1aef6206cec87f30eeced49f7c100e12506b10e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.618ex; height:2.343ex;" alt="{\displaystyle SP-PV}" loading="lazy"></span> error is used to control the PV so that it equals the SP. A widespread of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SP-PV}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>S</mi>
<mi>P</mi>
<mo>−<!-- − --></mo>
<mi>P</mi>
<mi>V</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle SP-PV}</annotation>
</semantics>
</math></span><img src="./1aef6206cec87f30eeced49f7c100e12506b10e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.618ex; height:2.343ex;" alt="{\displaystyle SP-PV}" loading="lazy"></span> error is classically used in the <a href="PID_controller" class="mw-redirect" title="PID controller">PID controller</a>.
</p><p><b>Industrial applications</b>
</p><p>Special consideration must be given for engineering applications. In industrial systems, physical or process restraints may limit the determined set point. For example, a reactor which operates more efficiently at higher temperatures may be rated to withstand 500°C. However, for safety reasons, the set point for the reactor temperature control loop would be well below this limit, even if this means the reactor is running less efficiently.
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Process_control" class="mw-redirect" title="Process control">Process control</a></li>
<li><a href="Proportional%E2%80%93integral%E2%80%93derivative_controller" title="Proportional–integral–derivative controller">Proportional–integral–derivative controller</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
<style data-mw-deduplicate="TemplateStyles:r1239543626">
/* start https://en.wikipedia.org/ */
.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}
/* end https://en.wikipedia.org/ */
</style><div class="reflist">
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-Bequette-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bequette_1-0">^</a></b></span> <span class="reference-text">
<style data-mw-deduplicate="TemplateStyles:r1238218222">
/* start https://en.wikipedia.org/ */
.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}
/* end https://en.wikipedia.org/ */
</style><cite id="CITEREFB._Wayne_Bequette2003" class="citation book cs1">B. Wayne Bequette (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PdjHYm5e9d4C&pg=PA5"><i>Process Control: Modeling, Design, and Simulation</i></a>. Prentice Hall Professional. p. 5. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780133536409</bdi>.</cite></span>
</li>
<li id="cite_note-Achterbergh-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Achterbergh_2-0">^</a></b></span> <span class="reference-text">
An 'essential variable' is defined as "a variable that has to be kept within assigned limits to achieve a particular goal": <cite id="CITEREFJan_Achterbergh,_Dirk_Vriens2010" class="citation book cs1">Jan Achterbergh, Dirk Vriens (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3hsbxMzi7w0C&q=%22a+variable+that+has+to+be+kept+within+assigned+limits+to+achieve+a+particular+goal%22&pg=PA47">"§2.3 Cybernetics: Effective methods for the control of complex systems"</a>. <i>Organizations: Social Systems Conducting Experiment</i>. Springer Science & Business Media. p. 47. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9783642143168</bdi>.</cite></span>
</li>
<li id="cite_note-Ashby-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ashby_3-0">^</a></b></span> <span class="reference-text">
<cite id="CITEREFW._Ross_Ashby1957" class="citation book cs1">W. Ross Ashby (1957). "Chapter 12: The error-controlled regulator". <a rel="nofollow" class="external text" href="http://pcp.vub.ac.be/books/IntroCyb.pdf"><i>Introduction to cybernetics</i></a> <span class="cs1-format">(PDF)</span>. Chapman & Hall Ltd.; Internet (1999). pp. <span class="nowrap">219–</span>243.</cite> </span>
</li>
</ol></div></div>
<style data-mw-deduplicate="TemplateStyles:r1271159938">
/* start https://en.wikipedia.org/ */
.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}.mw-parser-output :not(p):not(.asbox)+style+.asbox,.mw-parser-output :not(p):not(.asbox)+link+.asbox{margin-top:3em}
/* end https://en.wikipedia.org/ */
</style></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2024-12-23" href="https://en.wikipedia.org/wiki/?title=Setpoint_(control_system)&oldid=1264796256">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
</div>
</div><!--/htdig_noindex--></div>
</div>
</main>
</div>
</div>
</div>
</body></html>