{"id":1045,"date":"2017-06-15T13:09:29","date_gmt":"2017-06-15T13:09:29","guid":{"rendered":"http:\/\/bryceautomation.com\/?p=1045"},"modified":"2017-06-15T13:09:29","modified_gmt":"2017-06-15T13:09:29","slug":"proportional-integral-derivative-pid","status":"publish","type":"post","link":"https:\/\/bryceautomation.com\/index.php\/2017\/06\/15\/proportional-integral-derivative-pid\/","title":{"rendered":"Proportional, Integral, Derivative (PID)"},"content":{"rendered":"<h2>Introduction to Proportional, Integral, and Derivative (PID)<\/h2>\n<p>Proportional, Integral, and Derivative (PID) is a 3-step formula to bring a process to a setpoint, and attempt to hold it there. \u00a0 The example we will use is a heating process. \u00a0 We will bring fluid in a pipe up to a certain temperature and attempt to hold it at the setpoint. \u00a0Other examples would include tank levels, flow control, and motor speeds.<\/p><div id=\"bryce-585441197\" class=\"bryce-afterfirst bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"7728240895\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>\n<h3>Conceptual Example<\/h3>\n<p>Imagine the furnace at your house, which is controlled by a thermostat. \u00a0 This is NOT a PID because it simply turns on at one temperature, and shuts off at another temperature. \u00a0 \u00a0 Your house temperature is unstable using this method. \u00a0 Now, imagine if we had a special controller that controlled the amount of gas to the burners on your furnace.<\/p>\n<p>The PID controller would decide exactly how much gas needs to be provided at all times. \u00a0 This would bring your house temperature up to the setpoint and hold it there. \u00a0If you opened the door in your house, and the temperature started to drop, the PID would open the gas valve a little more. \u00a0 If the sun comes out for the day, the PID would detect that it needs to provide less output to maintain a constant temperature. \u00a0 \u00a0Of course I&#8217;m just using your furnace example to help you understand the controller&#8230;. \u00a0 don&#8217;t try that at home!<\/p>\n<h3>Demonstration example<\/h3>\n<p>Compare that concept to the diagram below. \u00a0 If we open the manual valve, we will need to provide more output to maintain temperature of the fluid in the pipe. \u00a0 When you close the manual valve, we need less output.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1047 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/PIDOverview.png\" alt=\"PID Overview\" width=\"503\" height=\"306\" data-srcset=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/PIDOverview.png 503w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/PIDOverview-300x183.png 300w\" data-sizes=\"(max-width: 503px) 100vw, 503px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 503px; --smush-placeholder-aspect-ratio: 503\/306;\" \/><\/p>\n<h2>Terminology<\/h2>\n<p>First, \u00a0we will cover common terminology that you will need to know in order to understand the controller in this demonstration:<\/p>\n<p><strong>Control Variable:<\/strong> \u00a0This is the output of the PID. \u00a0In the above example, this is the output to the heating control unit.<\/p>\n<p><strong>Process Variable:<\/strong> \u00a0This is the feedback from the system. \u00a0 In the above example, we have a thermocouple, or temperature transmitter. \u00a0 This allows you to see how the output is affecting the temperature.<\/p>\n<p><strong>Setpoint:<\/strong> \u00a0In this demonstration, the setpoint is the temperature that we wish to acheive.<\/p>\n<p><strong>Error:<\/strong> \u00a0Error is the difference between the setpoint and the process variable. \u00a0 This indicates how far away we are from the setpoint. \u00a0 The error can be positive, or negative depending on if our process variable is above or below the setpoint. \u00a0Depending on the process, the error is calculated as the Setpoint minus Process Variable, or Process Variable minus Setpoint.<\/p>\n<h3>Proportional Overview<\/h3>\n<p>Proportional output is based on the amount of error. \u00a0 The more error we have, the more output will be affected. Let&#8217;s consider the following diagram:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1049 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/Proportional.png\" alt=\"Proportional Graph\" width=\"516\" height=\"281\" data-srcset=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/Proportional.png 516w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/Proportional-300x163.png 300w\" data-sizes=\"(max-width: 516px) 100vw, 516px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 516px; --smush-placeholder-aspect-ratio: 516\/281;\" \/><\/p>\n<p>At the left of the graph, you will see that we have a lot of error. \u00a0Our process variable is far from the setpoint. \u00a0 As the process variable approaches the setpoint, the error decreases. \u00a0 This means the output to our heat bands decrease. \u00a0 When the process variable is at the setpoint, we have no error, and therefore no output. \u00a0 However, it takes the heat bands a while to cool off, so we might see the process variable go above the setpoint. \u00a0As the process variable comes back down, we still have no output until we are below the setpoint.<\/p>\n<h3>Problem using Proportional Only<\/h3>\n<p>In a heating system such as this, we will always loose heat from the system. \u00a0 This can be in the form of ambient losses, or losses due to load. \u00a0When we constantly have losses, the process variable will not stay at the setpoint. \u00a0 With proportional output only (in this example), we must have error to provide enough output to make up for the losses.<\/p>\n<p>Notice that our temperature (process variable) settles below the setpoint. \u00a0 When we open the manual valve, the fluid is taking more heat out of the system, so our error is greater. \u00a0This will provide more output to make up for the losses. \u00a0The temperature will naturally settle at a level that provides an exact output to make up for the losses. \u00a0As you can see, the problem with only using <strong>proportional<\/strong> is that we cannot hold the process variable at the setpoint. \u00a0 Otherwise, we would have no output. \u00a0It might work for a tank level if there are no leaks, but not in this heating process.<\/p>\n<p>The tuning variable in the controller determines how much output we have based on each 1% of error.<\/p>\n<h2>Integral Overview<\/h2>\n<p>Next, we will discuss the <strong>Integral<\/strong> component of PID. \u00a0Aside from the tuning variables, Integral is based on two components: \u00a0Error and Time. \u00a0Look at the following diagram:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1050 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/Integral.png\" alt=\"Inject Integral\" width=\"153\" height=\"238\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 153px; --smush-placeholder-aspect-ratio: 153\/238;\" \/><\/p>\n<p>Here, we have our graph divided into 3 sections after integral is added. \u00a0These three sections are time periods. \u00a0Look at the error in the first time period We have quite a bit of error in this first time period, so quite a bit of output is provided. \u00a0Look at the second (middle) time period. \u00a0 Although the same amount of time is passed in this time period, we have less error. \u00a0 Therefore, we ADD less to the output. \u00a0We don&#8217;t decrease the output&#8230; \u00a0 We just have less to add to the output.<\/p>\n<p>During the third time period, we have even less to add. \u00a0 We can say that as our process variable approaches the setpoint, we continuously add to the output, but just have less and less to add during each time period until we approach the setpoint. \u00a0 At the setpoint, we have nothing to add to the output, because there is no error.<\/p>\n<p>The tuning variable for integral determines how often these time periods occur. \u00a0Each time period is called a &#8220;repeat&#8221;. \u00a0These repeats can be closer together (more aggressive), or further apart to make the Integral less aggressive.<\/p>\n<h2>Derivative Overview<\/h2>\n<p>Derivative is based on rate of change of error. \u00a0 This is used for &#8220;Anticipation&#8221;. \u00a0 Derivative is not used very often because it can cause problems if we have a noisy process variable. \u00a0 Derivative also complicates the tuning of your loop because changes in the other parameters affect the rate of change of error, and therefore affect your derivative. \u00a0Let&#8217;s consider the following diagram.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1052 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/Derivative.png\" alt=\"Derivative Graph\" width=\"199\" height=\"185\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 199px; --smush-placeholder-aspect-ratio: 199\/185;\" \/><\/p>\n<p>As soon as the valve is fully opened, our temperature starts to drop fast. \u00a0In the few seconds after the valve is opened, we don&#8217;t have a lot of error. \u00a0This means we do not have a lot of output based on Proportional. \u00a0 Also, not a lot of time has passed yet, so we don&#8217;t have much output based on Integral. \u00a0 We do have a large rate of change of error though. \u00a0 Derivative will provide output based on this rate of change of error. \u00a0Derivative opposes a change in the process variable. \u00a0 \u00a0Please be aware, though, that as the temperature starts to come back up to the setpoint later on, the slope is in the opposite direction. \u00a0 \u00a0This means that as the process variable goes down, our output will be increased. \u00a0 As the process variable comes back up, the output is decreased!<\/p>\n<p>The tuning variable for derivative determines how much our output is affected based on this rate of change of error.<\/p>\n<p>All Actions<\/p>\n<p>Here we have a graph of the appearance of each separate component.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-1054 lazyload\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/AllActions-1.png\" alt=\"All Actions\" width=\"890\" height=\"226\" data-srcset=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/AllActions-1.png 890w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/AllActions-1-300x76.png 300w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/06\/AllActions-1-768x195.png 768w\" data-sizes=\"(max-width: 890px) 100vw, 890px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 890px; --smush-placeholder-aspect-ratio: 890\/226;\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>For more information on ControlLogix, please visit the <a href=\"https:\/\/bryceautomation.com\/index.php\/category\/controllogix\/\">ControlLogix Post <\/a>page!<\/p>\n<p>&nbsp;<\/p>\n<p>&#8212; Ricky Bryce<\/p>\n<div id=\"bryce-1611578066\" class=\"bryce-after-content bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"4667596182\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); 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