{"id":131383,"date":"2025-06-27T12:20:15","date_gmt":"2025-06-27T17:20:15","guid":{"rendered":"https:\/\/www.controleng.com\/?p=131383"},"modified":"2025-07-22T10:25:39","modified_gmt":"2025-07-22T15:25:39","slug":"pid-spotlight-part-17-heuristic-tuning-of-integrating-processes","status":"publish","type":"post","link":"https:\/\/www.controleng.com\/pid-spotlight-part-17-heuristic-tuning-of-integrating-processes\/","title":{"rendered":"PID spotlight, part 17: Heuristic tuning of integrating processes"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Heuristic PID&nbsp;controller&nbsp;tuning insights<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;controller&nbsp;performance goals determine how&nbsp;controller&nbsp;gain and integral are set.<\/li>\n\n\n\n<li>Use pattern recognition and simple rules to adjust&nbsp;controller&nbsp;tuning.<\/li>\n\n\n\n<li>Combine heuristics with open- and closed-loop tuning methods to speed loop tuning when possible.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Heuristic (guided trial and error) tuning of integrating processes is complicated. Not&nbsp;because&nbsp;it is difficult, but&nbsp;because we are tuning for&nbsp;a&nbsp;primary&nbsp;purpose and also have to work within secondary constraints. This means that there are not necessarily hard guidelines for what&nbsp;good&nbsp;looks like, and&nbsp;that two identical processes&nbsp;in&nbsp;different&nbsp;services&nbsp;may require very&nbsp;different&nbsp;tuning based on their&nbsp;role&nbsp;in&nbsp;the&nbsp;overall&nbsp;process.<\/p>\n\n\n\n<p>Figure&nbsp;1&nbsp;is&nbsp;a&nbsp;tuning map for&nbsp;an&nbsp;integrating process with&nbsp;a process gain (K<sub>p<\/sub>) of 0.2%\/minute, three lags (T<sub>1<\/sub>, T<sub>2<\/sub>, T<sub>3<\/sub>) of 30 seconds&nbsp;each, and no deadtime (D<sub>t<\/sub>). This&nbsp;will&nbsp;help explain the problem we can have when tuning the most common integrating process,&nbsp;a&nbsp;level.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"732\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map-1024x732.jpg\" alt=\"Figure 1: Integrating process PI controller tuning map. Kp = 0.2%\/minute, T1, T2, T3 = 30 seconds, Dt = 0 seconds. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131384\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map-1024x732.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map-300x214.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map-768x549.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map-1536x1098.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig1-Integrating-Process-PI-Controller-Tuning-Map.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 1: Integrating process PI controller tuning map. Kp = 0.2%\/minute, T1, T2, T3 = 30 seconds, Dt = 0 seconds. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>For this process&nbsp;Figure&nbsp;1&nbsp;shows us the window within which we can set the&nbsp;controller&nbsp;gain and integral for this integrating process.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To the left and above the&nbsp;black&nbsp;line&nbsp;titled&nbsp;\u201cstability limit\u201d this process is unstable.&nbsp;<\/li>\n\n\n\n<li>The&nbsp;blue line&nbsp;titled&nbsp;\u201cmin contain gain\u201d is the minimum combination of&nbsp;controller&nbsp;gain and integral that&nbsp;will&nbsp;contain&nbsp;a 50%&nbsp;change&nbsp;in&nbsp;input&nbsp;(or&nbsp;output) flow when the vessel is 50%&nbsp;full. This is&nbsp;an&nbsp;arbitrary&nbsp;convention; if you have specific process knowledge you can set&nbsp;your&nbsp;own minimum.&nbsp;<\/li>\n\n\n\n<li>The green&nbsp;line&nbsp;titled&nbsp;\u201cmin gain w\/ integral\u201d is the minimum&nbsp;controller&nbsp;gain that&nbsp;will&nbsp;suppress integral driven oscillations.&nbsp;In&nbsp;<a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-11-how-a-pid-controller-works-with-an-integrating-process\/\">PID spotlight, part 11<\/a>, we learned that&nbsp;controller&nbsp;gain is required to prevent uncontrolled process swings driven by&nbsp;controller&nbsp;integral action; the faster the integral the larger the&nbsp;controller&nbsp;gain required to prevent instability.&nbsp;In&nbsp;this particular process once the integral gets below&nbsp;6.0 minutes\/repeat oscillations begin regardless of the controller gain setting. At this&nbsp;point&nbsp;oscillations are going to&nbsp;occur&nbsp;and get worse as integral is made faster.<\/li>\n<\/ul>\n\n\n\n<p>The window above the blue and green&nbsp;lines&nbsp;and below and to the right of the&nbsp;black&nbsp;line&nbsp;is the limit of possible tuning for this&nbsp;controller.<\/p>\n\n\n\n<p>Finally, the&nbsp;black&nbsp;dashed&nbsp;line&nbsp;titled&nbsp;\u201c100%&nbsp;gain&nbsp;margin\u201d is&nbsp;one-half&nbsp;the maximum stable&nbsp;controller&nbsp;gain (the&nbsp;black&nbsp;line). Above this&nbsp;line&nbsp;there&nbsp;will&nbsp;be&nbsp;controller&nbsp;gain driven oscillations, therefore normally&nbsp;controller&nbsp;gains should not much exceed this&nbsp;line.<\/p>\n\n\n\n<p>For levels there are three possible performance goals.&nbsp;In&nbsp;order of frequency these are surge&nbsp;control, disturbance rejection and setpoint tracking tuning. We can see that&nbsp;each&nbsp;exists&nbsp;in&nbsp;its&nbsp;own area of the tuning window, and that the window of acceptable tuning for surge&nbsp;control&nbsp;and setpoint tracking tuning can be very wide. Tuning for&nbsp;each performance goal can be summarized as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Surge&nbsp;control: <\/strong>Minimum&nbsp;controller&nbsp;gain and slowest integral consistent with keeping the process variable within acceptable limits.<\/li>\n\n\n\n<li><strong>Disturbance rejection: <\/strong>Maximum&nbsp;controller&nbsp;gain and fastest integral with minimum oscillation.<\/li>\n\n\n\n<li><strong>Setpoint tracking: <\/strong>Maximum&nbsp;controller&nbsp;gain without oscillation and slowest integral with acceptable recovery from disturbances.<\/li>\n<\/ul>\n\n\n\n<p>I&nbsp;will&nbsp;add&nbsp;a&nbsp;final caveat: If you are trying to balance multiple goals the best tuning constants may be somewhere&nbsp;between all three zones.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Heuristic tuning: Too much or little, too fast or slow?<\/h2>\n\n\n\n<p>To recap <a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-9-heuristic-tuning-for-a-self-limiting-process\">PID spotlight, part&nbsp;9<\/a>, heuristic tuning is nothing&nbsp;more than&nbsp;pattern recognition to answer these questions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Is there too much&nbsp;controller&nbsp;gain&nbsp;or&nbsp;too little?<\/li>\n\n\n\n<li>Is the integral too fast&nbsp;or&nbsp;too slow?<\/li>\n\n\n\n<li>Is there too much&nbsp;derivative?<\/li>\n<\/ul>\n\n\n\n<p>As discussed&nbsp;in&nbsp;<a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-12-what-does-good-and-bad-level-controller-tuning-look-like\/]\">PID spotlight, part 12<\/a>, the visual cues used to answer these questions are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If&nbsp;a controller&nbsp;has too much&nbsp;controller&nbsp;gain, integral or&nbsp;derivative&nbsp;it swings.&nbsp;If it has too much&nbsp;controller&nbsp;gain the process variable (PV) and&nbsp;controller&nbsp;output&nbsp;(OP) peaks&nbsp;line up&nbsp;(or are very close).&nbsp;If the integral is too fast the OP peaks trail the PV peaks.&nbsp;\n<ul class=\"wp-block-list\">\n<li>If it has too much&nbsp;derivative&nbsp;the OP peaks lead the PV peaks, and the amplitude of the OP swings are usually larger than the PV swings.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Too little&nbsp;controller&nbsp;gain&nbsp;will&nbsp;look like the integral is set too fast; the process&nbsp;will&nbsp;oscillate and the OP peak&nbsp;will&nbsp;trail the PV peak. Slowing down integral&nbsp;will&nbsp;not fix the tuning problem. It&nbsp;will&nbsp;likely make&nbsp;control&nbsp;worse. As&nbsp;a&nbsp;general rule if the&nbsp;controller&nbsp;gain (K) is&nbsp;less&nbsp;than&nbsp;1.0 raise it to at least&nbsp;1.0.<\/li>\n\n\n\n<li>Integral set too slow&nbsp;will&nbsp;not show up&nbsp;in&nbsp;a&nbsp;setpoint step test. Integrating processes&nbsp;will&nbsp;follow setpoint (SP) changes very&nbsp;well&nbsp;on gain only&nbsp;control. To check integral action, use&nbsp;an&nbsp;induced disturbance test.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Heuristic tuning methodology: Two types<\/h2>\n\n\n\n<p>There are two heuristic tuning methodologies depending on the purpose of the&nbsp;controller. If the purpose of the&nbsp;controller is setpoint response we&nbsp;will&nbsp;use the same methodology that was used for self-limiting processes:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Verify the process is stable and the process variable is on setpoint.<\/li>\n\n\n\n<li>Change the&nbsp;controller&nbsp;setpoint (the&nbsp;controller&nbsp;is&nbsp;in&nbsp;auto).<\/li>\n\n\n\n<li>Observe the process response; what pattern does it match?<\/li>\n\n\n\n<li>Execute&nbsp;the rules for the identified pattern.<\/li>\n\n\n\n<li>Repeat as necessary.<\/li>\n<\/ol>\n\n\n\n<p>However, if we are tuning for surge&nbsp;control&nbsp;or disturbance reduction we need to induce&nbsp;a&nbsp;disturbance&nbsp;into&nbsp;the process. The methodology to do this is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Verify the process is stable and the process variable is on setpoint.<\/li>\n\n\n\n<li>Place the&nbsp;controller&nbsp;in&nbsp;manual.<\/li>\n\n\n\n<li>Change the&nbsp;controller&nbsp;output.<\/li>\n\n\n\n<li>Immediately place the&nbsp;controller&nbsp;back&nbsp;in&nbsp;auto.<\/li>\n\n\n\n<li>Observe the process response; what pattern does it match?<\/li>\n\n\n\n<li>Execute&nbsp;the rules for the identified pattern.<\/li>\n\n\n\n<li>Repeat as necessary.<\/li>\n<\/ol>\n\n\n\n<p>This methodology is required&nbsp;because&nbsp;of the very&nbsp;different&nbsp;way integrating processes respond to setpoint changes and disturbances. It is also assumed that the process&nbsp;will&nbsp;respond about the same way to changes&nbsp;in&nbsp;the&nbsp;input&nbsp;and&nbsp;output flows.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"729\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-1024x729.jpg\" alt=\"Figure 2: Induced disturbance test method, integrating process. Tuning constants are K = 3.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131386\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-1024x729.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-300x214.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-768x547.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-1536x1093.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_MAG2_F1_APC-PID-EB17-Fig2-Induced-Disturbance-Test-Integrating-Process-2048x1458.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 2: Induced disturbance test method, integrating process. Tuning constants are K = 3.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Figure&nbsp;2&nbsp;shows the response of&nbsp;an&nbsp;integrating process to&nbsp;an&nbsp;induced disturbance at the&nbsp;five-minute&nbsp;mark,&nbsp;a&nbsp;natural disturbance at the 30-minute mark, and&nbsp;a&nbsp;setpoint change (SP) at the 60-minute mark. The process variable (PV) response to the induced and natural response is similar but not identical. This is&nbsp;because&nbsp;the process responds immediately to&nbsp;an&nbsp;input&nbsp;flow change, but the response to the&nbsp;output&nbsp;flow is delayed by the three 30-second lags.<\/p>\n\n\n\n<p> Regardless, the two&nbsp;responses&nbsp;appear to be similar enough that we should be able to draw proper conclusions from the response to&nbsp;an&nbsp;induced disturbance. The response to the setpoint change is considerably&nbsp;different, highlighting the need to induce&nbsp;a&nbsp;disturbance when&nbsp;the&nbsp;controller&nbsp;purpose is specifically intended to manage disturbances.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Three rules for too much&nbsp;controller&nbsp;gain<\/h2>\n\n\n\n<p>It is very unusual to run&nbsp;into&nbsp;a&nbsp;level&nbsp;controller&nbsp;with too much&nbsp;controller&nbsp;gain. Typical levels have very large fill time\/deadtime&nbsp;ratios. If you should happen to run&nbsp;into&nbsp;a&nbsp;case where the PV and OP peaks&nbsp;line up&nbsp;you should check for excessive deadtime. The rules are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cut&nbsp;the&nbsp;controller&nbsp;gain by 30%&nbsp;(anywhere&nbsp;between&nbsp;25-50% will&nbsp;do).\n<ul class=\"wp-block-list\">\n<li>Repeat until swinging is reduced to&nbsp;an&nbsp;acceptable level.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>If the tuning logs show the&nbsp;controller&nbsp;gain was recently&nbsp;raised&nbsp;split the difference.<\/li>\n\n\n\n<li>If the swing is quarter amplitude dampening or more (each&nbsp;peak is 25%&nbsp;the size of or larger than the previous peak) use closed-loop tuning rules to estimate new tuning constants.<\/li>\n<\/ul>\n\n\n\n<p>If you end up with&nbsp;a&nbsp;controller&nbsp;gain below&nbsp;1.0 you should take&nbsp;a&nbsp;closer look at the process. Does the process make sense? The&nbsp;controller&nbsp;may no longer be capable of keeping the process within limits.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Two rules for integral set too fast<\/h2>\n\n\n\n<p>This is the most common problem with level controllers. Inexperienced&nbsp;controller&nbsp;tuners (a&nbsp;much-younger me) may not understand that integrating processes are&nbsp;different&nbsp;and use self-limiting process tuning methods inappropriately. This may result&nbsp;in&nbsp;tuning that is&nbsp;short&nbsp;on&nbsp;controller&nbsp;gain and with the integral set too fast. When you run across&nbsp;a&nbsp;process where the OP peaks trail the PV peaks the rules are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Increase the integral by 50%&nbsp;(anywhere&nbsp;between&nbsp;25%&nbsp;and 75% will&nbsp;do).\n<ul class=\"wp-block-list\">\n<li>Repeat until swinging is reduced to&nbsp;an&nbsp;acceptable level.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>If the tuning logs show the integral was recently sped up split the difference.<\/li>\n<\/ul>\n\n\n\n<p>Depending on the&nbsp;controller&nbsp;purpose you may want to consider raising&nbsp;controller&nbsp;gain at the same time.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Two rules for too little&nbsp;controller&nbsp;gain<\/h2>\n\n\n\n<p>This can&nbsp;occur&nbsp;through&nbsp;a&nbsp;misguided&nbsp;attempt at surge&nbsp;control&nbsp;tuning or&nbsp;an&nbsp;attempt to stop&nbsp;an&nbsp;integral induced swing by cutting&nbsp;controller&nbsp;gain (the standard fix for&nbsp;a&nbsp;swinging&nbsp;controller&nbsp;most young&nbsp;control&nbsp;professionals are taught). Should you run across&nbsp;a&nbsp;process with&nbsp;a&nbsp;very slow oscillation and&nbsp;a&nbsp;controller&nbsp;gain&nbsp;less&nbsp;than&nbsp;1.0 the rules are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Set the&nbsp;controller&nbsp;gain using the open loop testing rules for&nbsp;controller&nbsp;gain. Be forewarned that this could go unstable if the process has&nbsp;a&nbsp;low fill time\/deadtime ratio. If this is&nbsp;a disturbance rejection&nbsp;controller&nbsp;(unlikely if the&nbsp;controller&nbsp;gain is&nbsp;less&nbsp;than&nbsp;1.0) continue to increase until&nbsp;a&nbsp;slight swing occurs, and&nbsp;then reduce the gain.<\/li>\n\n\n\n<li>If the tuning logs show&nbsp;controller&nbsp;gain was recently lowered split the difference.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Two rules for integral set too slow<\/h2>\n\n\n\n<p>If the purpose of the&nbsp;controller&nbsp;is setpoint&nbsp;following&nbsp;or surge&nbsp;control&nbsp;integral should be set to restore the PV to SP within some reasonable amount of time. There are no hard and fast rules&nbsp;here, although generally the integral constant should be somewhere&nbsp;between&nbsp;10 and 50 minutes\/repeat.<\/p>\n\n\n\n<p>If, however, disturbance rejection tuning is required:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Decrease the integral by 25%&nbsp;to 50%.\n<ul class=\"wp-block-list\">\n<li>Repeat until&nbsp;a&nbsp;little swinging is detected, then increase if necessary.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>If the tuning logs show the integral was recently slowed down split the difference.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Three rules for too much&nbsp;derivative<\/h2>\n\n\n\n<p>Level controllers should not require&nbsp;derivative, therefore&nbsp;derivative&nbsp;should be set to&nbsp;zero. However other integrating processes may&nbsp;benefit&nbsp;from&nbsp;derivative&nbsp;if the process appears to have multiple lags. The&nbsp;general&nbsp;process is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Set&nbsp;derivative&nbsp;to&nbsp;zero.<\/li>\n\n\n\n<li>Verify and fix, if necessary, the&nbsp;controller&nbsp;gain and integral.<\/li>\n\n\n\n<li>Increase&nbsp;derivative&nbsp;stepwise until desired performance is achieved or swinging starts to&nbsp;occur.<\/li>\n<\/ul>\n\n\n\n<p>Unlike self-limiting processes setting&nbsp;derivative&nbsp;to one-fourth of the integral may not work. Start with&nbsp;a&nbsp;smaller value.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Example&nbsp;1: Disturbance rejection<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"725\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-1024x725.jpg\" alt=\"Figure 3: Heuristic tuning integrating process \u2013 what we found. Tuning constants are K = 4.0, Ti = 4.0 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131388\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-1024x725.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-300x212.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-768x544.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-1536x1088.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig3-Heuristic-Example-1-What-We-Found-2048x1450.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 3: Heuristic tuning integrating process \u2013 what we found. Tuning constants are K = 4.0, Ti = 4.0 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Figure&nbsp;3&nbsp;is&nbsp;a&nbsp;test of&nbsp;a&nbsp;process that should be tuned for disturbance rejection. The tuning is aggressive, causing the process to swing five&nbsp;times&nbsp;before settling after&nbsp;a&nbsp;disturbance. Our first assessment is while the&nbsp;controller&nbsp;output&nbsp;(OP) peak trails the process variable (PV) peak this looks more like&nbsp;a&nbsp;controller&nbsp;tuned with too much&nbsp;controller&nbsp;gain (our best guess is both are too aggressive but&nbsp;controller&nbsp;gain is the bigger problem). The amplitude damping is 32%&nbsp;(1.01\/3.10 \u2013 peak&nbsp;2&nbsp;deviation divided by peak&nbsp;1&nbsp;deviation from SP), which is&nbsp;greater&nbsp;than quarter amplitude dampening and means we can use closed-loop tuning methods to estimate new tuning constants.<\/p>\n\n\n\n<p>Since&nbsp;we do not have&nbsp;<a><u>a<\/u><\/a>&nbsp;continuous&nbsp;oscillation, we know that the current&nbsp;controller&nbsp;gain is&nbsp;less&nbsp;than the ultimate&nbsp;controller gain, and the current oscillation period is longer than the natural period. We can borrow from&nbsp;a&nbsp;closed-loop quarter amplitude damping tuning method&nbsp;a&nbsp;couple of&nbsp;equations to estimate the ultimate&nbsp;controller&nbsp;gain (K<sub>u<\/sub>) and natural period (P<sub>n<\/sub>).<\/p>\n\n\n\n<p><em>K<sub>u<\/sub>&nbsp;=&nbsp;1.5&nbsp;*&nbsp;K<sub>q<\/sub><\/em><\/p>\n\n\n\n<p><em>P<sub>n<\/sub>&nbsp;= 0.7&nbsp;*&nbsp;P<sub>q<\/sub><\/em><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<p>K<sub>q<\/sub>&nbsp;is the quarter amplitude damping&nbsp;controller&nbsp;gain<\/p>\n\n\n\n<p>P<sub>q<\/sub>&nbsp;is the quarter amplitude damping period<\/p>\n\n\n\n<p>G. K. McMillan,&nbsp;Tuning and&nbsp;Control&nbsp;Loop Performance, eq.&nbsp;1.17g,&nbsp;1.17h, p.34<\/p>\n\n\n\n<p>We\u2019re cheating&nbsp;a&nbsp;little&nbsp;bit&nbsp;here, and if the amplitude damping was 50%&nbsp;or&nbsp;greater&nbsp;we would use the&nbsp;controller&nbsp;gain and period directly. Our goal is to be quick with reasonable accuracy.&nbsp;In&nbsp;this case we calculate the approximate ultimate&nbsp;controller&nbsp;gain and natural period to be:<\/p>\n\n\n\n<p><em>K<sub>u<\/sub>&nbsp;=&nbsp;1.5&nbsp;*&nbsp;4.0 =&nbsp;6.0<\/em><\/p>\n\n\n\n<p><em>P<sub>n<\/sub>&nbsp;= 0.7&nbsp;*&nbsp;8.61 =&nbsp;6.03 minutes<\/em><\/p>\n\n\n\n<p>We can use the second series of equations of the closed-loop simplified integrating process PI tuning calculations from <a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-16-closed-loop-tuning-of-an-integrating-process\/\">PID spotlight part 16<\/a> to calculate estimated tuning constants.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"216\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1-1024x216.jpg\" alt=\"Table 1: Simplified integrating process PI tuning constant calculations for proportional-integral (PI) controllers. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131391\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1-1024x216.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1-300x63.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1-768x162.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1-1536x324.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table1-Closed-Loop-Simplified-Integrating-Process-PI-Tuning-Example-1.jpg 1932w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Table 1: Simplified integrating process PI tuning constant calculations for proportional-integral (PI) controllers. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>The new tuning constants are:<\/p>\n\n\n\n<p>K =&nbsp;1.8<\/p>\n\n\n\n<p>T<sub>i<\/sub>&nbsp;=&nbsp;9.38 minutes\/repeat<\/p>\n\n\n\n<p>These calculations tend to confirm our belief that both&nbsp;controller&nbsp;gain and integral are too aggressive.&nbsp;Controller&nbsp;gain is considerably smaller and integral is slowed down quite&nbsp;a&nbsp;bit.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"735\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-1024x735.jpg\" alt=\"Figure 4: Heuristic tuning integrating process \u2013 first tuning attempt. Tuning constants are K = 1.8, Ti = 9.38 minutes\/repeat, Td = 0 Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131392\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-1024x735.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-300x215.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-768x551.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-1536x1103.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig4-Heuristic-Example-1-First-Attempt-2048x1471.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 4: Heuristic tuning integrating process \u2013 first tuning attempt. Tuning constants are K = 1.8, Ti = 9.38 minutes\/repeat, Td = 0. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>In&nbsp;Figure&nbsp;4&nbsp;we see that the new tuning constants are not quite as fast as possible based on the non-symmetrical response of the PV. The response to&nbsp;a&nbsp;natural disturbance is not quite identical, but is certainly close enough that we can have confidence that the tuning process&nbsp;will&nbsp;yield useful results.&nbsp;<\/p>\n\n\n\n<p>The easiest thing to do at this&nbsp;point&nbsp;is split the difference&nbsp;between&nbsp;the original and new tuning constants. The new estimated tuning constants are:<\/p>\n\n\n\n<p>K =&nbsp;2.9<\/p>\n\n\n\n<p>T<sub>i<\/sub>&nbsp;=&nbsp;6.69 minutes\/repeat<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"732\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-1024x732.jpg\" alt=\"Figure 5: Heuristic tuning integrating process \u2013 second tuning attempt. Tuning constants are K = 2.9, Ti = 6.69 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131393\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-1024x732.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-300x215.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-768x549.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-1536x1099.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig5-Heuristic-Example-1-Second-Attempt-2048x1465.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 5: Heuristic tuning integrating process \u2013 second tuning attempt. Tuning constants are K = 2.9, Ti = 6.69 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>The process variable (PV) response&nbsp;in&nbsp;Figure&nbsp;5&nbsp;looks symmetrical but there are some mild secondary oscillations. The PV peaks earlier and at&nbsp;a&nbsp;lower value with these new tuning constants. If this were&nbsp;a&nbsp;noisy&nbsp;signal, we probably wouldn\u2019t notice the oscillations. <\/p>\n\n\n\n<p>Generally, at this&nbsp;point&nbsp;I would call it&nbsp;good&nbsp;and&nbsp;note&nbsp;the constants&nbsp;in&nbsp;the loop tuning log. But&nbsp;since we know there are multiple lags this may be&nbsp;a&nbsp;controller&nbsp;that might&nbsp;benefit&nbsp;from&nbsp;a&nbsp;little&nbsp;derivative. Integrating processes are not like self-limiting processes; you&nbsp;cannot&nbsp;set the&nbsp;derivative&nbsp;to one-fourth the integral and&nbsp;expect&nbsp;it to work. Instead, we should add&nbsp;a&nbsp;little&nbsp;bit&nbsp;of&nbsp;derivative&nbsp;at&nbsp;a&nbsp;time.&nbsp;In&nbsp;this case we&nbsp;will&nbsp;start with 0.25 minutes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"745\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-1024x745.jpg\" alt=\"Figure 6: Heuristic tuning integrating process \u2013 third tuning attempt. Tuning constants are K = 2.9, Ti = 6.69 minutes\/repeat, Td = 0.25 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131394\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-1024x745.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-300x218.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-768x558.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-1536x1117.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig6-Heuristic-Example-1-Third-Attempt-2048x1489.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 6: Heuristic tuning integrating process \u2013 third tuning attempt. Tuning constants are K = 2.9, Ti = 6.69 minutes\/repeat, Td = 0.25 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Figure&nbsp;6&nbsp;shows what happens when the&nbsp;derivative&nbsp;(T<sub>d<\/sub>) is set at 0.25 minutes.&nbsp;Derivative&nbsp;penalizes PV movement, which means we should get&nbsp;a&nbsp;faster response when the PV starts moving resulting&nbsp;in&nbsp;a&nbsp;lower deviation from setpoint (SP). Adding&nbsp;derivative&nbsp;did indeed lower deviation from SP to&nbsp;3.59 from&nbsp;3.88, or&nbsp;about&nbsp;7.5%. However,&nbsp;because&nbsp;derivative penalizes PV movement the PV\u2019s return to SP is slowed down. If we were to continue to raise&nbsp;derivative&nbsp;the PV deviation from SP would continue to decrease (to&nbsp;2.92 at T<sub>d<\/sub>&nbsp;=&nbsp;1.0), but the time for the PV to return to SP would continue to increase (to 15 minutes from about&nbsp;8 minutes&nbsp;without&nbsp;derivative). This helps highlight the&nbsp;tradeoffs&nbsp;that are part of tuning integrating processes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Example&nbsp;2: Test of&nbsp;a&nbsp;controller&nbsp;mistuned for surge&nbsp;control<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"725\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-1024x725.jpg\" alt=\"Figure 7: Heuristic tuning integrating process \u2013 as found. Tuning constants are K = 0.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131395\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-1024x725.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-300x212.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-768x543.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-1536x1087.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-mh-Fig7-Heuristic-Example-2-What-We-Found-2048x1449.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 7: Heuristic tuning integrating process \u2013 as found. Tuning constants are K = 0.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Figure&nbsp;7&nbsp;is the test of&nbsp;a&nbsp;controller&nbsp;mistuned for surge&nbsp;control. The visual cue, the&nbsp;controller output&nbsp;(OP) peaking some&nbsp;9 minutes&nbsp;after the process variable (PV), indicates that the integral is tuned too fast. The normal response would be to&nbsp;slow down&nbsp;the integral, but with&nbsp;a&nbsp;controller&nbsp;gain below&nbsp;1.0 we should strongly consider increasing the&nbsp;controller&nbsp;gain. We may still&nbsp;slow down&nbsp;the integral but the odds are if we do so the&nbsp;controller&nbsp;will&nbsp;not be capable of keeping the level inside the vessel should&nbsp;a&nbsp;large disturbance&nbsp;occur.<\/p>\n\n\n\n<p>Before we retune this&nbsp;controller, we should decide what kind of performance we need from this&nbsp;controller. This is to be tuned for surge&nbsp;control, which means we need to pick how far we are willing to allow the PV to drift from setpoint (SP) and how fast we want to get the PV back on SP. I\u2019m going to pick&nbsp;an&nbsp;arbitrary 30%&nbsp;PV drift from SP target and 60 minutes to return the PV to SP.<\/p>\n\n\n\n<p>Because&nbsp;we were able to do&nbsp;an&nbsp;induced disturbance test, we can calculate the process deadtime and make&nbsp;an&nbsp;estimate of the process fill time from the process reaction curve.&nbsp;Note&nbsp;that the fill time estimate&nbsp;will&nbsp;be long&nbsp;because&nbsp;the&nbsp;controller is taking active measures to correct the process (the process gain&nbsp;will&nbsp;be low).&nbsp;In&nbsp;a&nbsp;worst-case scenario, the&nbsp;controller gain calculation could be oscillatory.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"734\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up-1024x734.jpg\" alt=\"Figure 8: Heuristic tuning integrating process \u2013 as found (initial response). Tuning constants are K = 0.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131397\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up-1024x734.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up-300x215.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up-768x551.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up-1536x1101.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig8-Heuristic-Example-2-What-We-Found-Close-Up.jpg 2042w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 8: Heuristic tuning integrating process \u2013 as found (initial response). Tuning constants are K = 0.5, Ti = 10 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Figure&nbsp;8&nbsp;is&nbsp;a&nbsp;closeup&nbsp;of the initial process response. The standard open-loop tuning&nbsp;data&nbsp;collection method is used. A&nbsp;line&nbsp;is drawn through the steepest part of the response curve. Where it passes through the initial process variable (PV) determines the end of the deadtime.&nbsp;In&nbsp;this case&nbsp;since&nbsp;we are looking for the fill time, we pick the&nbsp;point&nbsp;on our&nbsp;line&nbsp;where the change&nbsp;in&nbsp;PV equals the change&nbsp;in&nbsp;controller&nbsp;output&nbsp;(OP).<\/p>\n\n\n\n<p>Now that we have&nbsp;an&nbsp;estimate of the process deadtime and fill time we can calculate&nbsp;a&nbsp;controller&nbsp;gain using the open loop simplified integrating process PI tuning calculations from Table&nbsp;1&nbsp;in <a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-14-how-open-loop-tuning-works-in-an-integrating-process\/\">PID spotlight, part 14<\/a>.&nbsp;Note&nbsp;that our estimated fill time (5.25 minutes) is longer than the actual fill time (5 minutes) by&nbsp;5%&nbsp;(as&nbsp;expected). This shouldn\u2019t significantly&nbsp;affect&nbsp;our calculations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"362\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1-1024x362.jpg\" alt=\"Table 2: Simplified integrating process PI tuning constant calculations for proportional-integral (PI) controllers. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131553\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1-1024x362.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1-300x106.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1-768x272.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1-1536x544.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table2-Open-Loop-Simplified-Integrating-Process-PI-Tuning-1.jpg 1950w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Table 2: Simplified integrating process PI tuning constant calculations for proportional-integral (PI) controllers. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>Based on&nbsp;a&nbsp;fill time of&nbsp;5.25 minutes and deadtime of&nbsp;1.5 minutes and our 30%&nbsp;deviation from setpoint allowance our tuning constant calculations are:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"330\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1-1024x330.jpg\" alt=\"Table 3: Calculating simplified integrating process PI tuning constants for a process with a fill time (Tfill) of 0.5 minutes\/%, three lags (T1, T2, T3) of 30 seconds and no deadtime (Dt). Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131399\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1-1024x330.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1-300x97.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1-768x247.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1-1536x495.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Table3-Open-Loop-Simplified-Integrating-Process-PI-Tuning-Example-2-1.jpg 2012w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Table 3: Calculating simplified integrating process PI tuning constants for a process with a fill time (Tfill) of 0.5 minutes\/%, three lags (T1, T2, T3) of 30 seconds and no deadtime (Dt). Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>The new tuning constants are:<\/p>\n\n\n\n<p><em>K =&nbsp;1.67<\/em><\/p>\n\n\n\n<p><em>T<sub>i<\/sub>&nbsp;=&nbsp;9.14 minutes\/repeat<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"758\" src=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt-1024x758.jpg\" alt=\"Figure 9: Heuristic tuning integrating process \u2013 first tuning attempt. Tuning constants are K = 1.67, Ti = 9.14 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer\" class=\"wp-image-131400\" srcset=\"https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt-1024x758.jpg 1024w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt-300x222.jpg 300w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt-768x568.jpg 768w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt-1536x1137.jpg 1536w, https:\/\/www.controleng.com\/wp-content\/uploads\/2025\/06\/CTL2506_WEB_F1_APC-PID-EB17-Fig9-Heuristic-Example-2-First-Attempt.jpg 2040w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 9: Heuristic tuning integrating process \u2013 first tuning attempt. Tuning constants are K = 1.67, Ti = 9.14 minutes\/repeat, Td = 0 minutes. Courtesy: Ed Bullerdiek, retired control engineer<\/figcaption><\/figure>\n\n\n\n<p>In&nbsp;Figure&nbsp;9&nbsp;we see that the PV deviation from SP is&nbsp;a&nbsp;little&nbsp;bit&nbsp;short&nbsp;of the targeted 60%&nbsp;of disturbance size (30\/50) at&nbsp;5.52%, but this is not unexpected given the presence of integral. The real issue is how fast the PV is returned to SP,&nbsp;~25 minutes rather than the 60 minutes we specified. Doubling the integral to 18&nbsp;will&nbsp;get us close (not shown).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Using shortcuts for level&nbsp;controller&nbsp;performance&nbsp;in&nbsp;the real world<\/h2>\n\n\n\n<p>I have used shortcuts&nbsp;here&nbsp;because&nbsp;they&nbsp;were available (and you should know&nbsp;they&nbsp;may be available). Unfortunately, unless you are actively working to optimize level&nbsp;controller&nbsp;performance you&nbsp;will&nbsp;likely only be called when&nbsp;a&nbsp;controller&nbsp;is performing poorly. You&nbsp;may&nbsp;walk up&nbsp;to&nbsp;a&nbsp;controller&nbsp;that is already swinging, however, using&nbsp;a&nbsp;shortcut requires that the process be at steady&nbsp;state&nbsp;so that you can&nbsp;execute&nbsp;a&nbsp;test.<\/p>\n\n\n\n<p>When you&nbsp;cannot&nbsp;execute&nbsp;a&nbsp;test, you&nbsp;will&nbsp;be restricted to visual identification of the problem followed by increasing\/decreasing gain and\/or slowing down\/speeding up integral. This may extend the time to resolve the problem. Because&nbsp;levels are slow, you should make&nbsp;a&nbsp;tuning change then walk away and do something else for&nbsp;couple of&nbsp;hours. Once you\u2019ve stopped the&nbsp;continuous&nbsp;swing then you can work on optimizing&nbsp;controller&nbsp;performance.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Heuristic tuning tips<\/h2>\n\n\n\n<p>Heuristic tuning is generally safe&nbsp;since,&nbsp;except&nbsp;for the few seconds the&nbsp;controller&nbsp;will&nbsp;be&nbsp;in&nbsp;manual to&nbsp;execute&nbsp;an&nbsp;induced disturbance test (should you use this test method), the&nbsp;controller&nbsp;remains&nbsp;in&nbsp;auto. Regardless, work with the operator to determine the largest setpoint or&nbsp;controller&nbsp;output&nbsp;step the operator is comfortable with. Larger steps are preferred&nbsp;because&nbsp;noise and&nbsp;control&nbsp;valve problems&nbsp;will&nbsp;have&nbsp;less&nbsp;impact on the results. If you&nbsp;suspect&nbsp;that there are valve problems, you should make multiple steps of&nbsp;different&nbsp;sizes both up and down. If the process response is not the same, you likely have problems tuning&nbsp;cannot&nbsp;solve.<\/p>\n\n\n\n<p>You should keep&nbsp;a&nbsp;loop-tuning log. There are&nbsp;a&nbsp;number of&nbsp;good&nbsp;reasons to keep&nbsp;a&nbsp;log; one is if you are using heuristic methods, you can use the log to guide&nbsp;your&nbsp;tuning efforts. Specifically, if you (for example) recently&nbsp;raised&nbsp;controller&nbsp;gain, and now it appears you went too far you can split the difference&nbsp;between&nbsp;the&nbsp;last&nbsp;setting and the current setting.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Heuristic tuning limits<\/h2>\n\n\n\n<p>Most integrating processes that we work with&nbsp;will&nbsp;be slow, and it is necessary for the response to play&nbsp;out&nbsp;fully to make accurate problem determinations. Of course, you can make rapid tuning changes if you&nbsp;walk up&nbsp;to&nbsp;<a><u>a<\/u><\/a>&nbsp;process that is performing poorly, and you can make&nbsp;an&nbsp;immediate problem diagnosis (this is why I like heuristics). Once you make that first change, exercise patience.<\/p>\n\n\n\n<p>Heuristics can require multiple steps. If&nbsp;a&nbsp;control&nbsp;loop\u2019s tuning is&nbsp;far off&nbsp;the mark it may be better to use open-loop tuning to get&nbsp;a&nbsp;first approximation and then use heuristics to finalize the tuning constants. However, if you are&nbsp;in&nbsp;a&nbsp;reasonably well-tuned facility and you find you must retune&nbsp;a&nbsp;control&nbsp;loop, it is very likely that the existing tuning constants are close to optimum. It&nbsp;will&nbsp;be far quicker to use heuristics, especially if there is&nbsp;a&nbsp;recent SP change&nbsp;in&nbsp;the trends, to estimate new tuning constants.<\/p>\n\n\n\n<p>An induced disturbance test assumes that the process responds the same to&nbsp;input&nbsp;and&nbsp;output&nbsp;changes. If this is not substantially true, then the test results may not be valid.<\/p>\n\n\n\n<p>A&nbsp;bad&nbsp;control&nbsp;valve&nbsp;will&nbsp;warp loop-tuning results. One of the more common problems with&nbsp;bad&nbsp;valves is hysteresis&nbsp;will induce&nbsp;a&nbsp;limit cycle swing. If you are not aware of the&nbsp;unique&nbsp;signature&nbsp;a&nbsp;bad&nbsp;valve creates, you may mistake this for&nbsp;a controller&nbsp;with too much&nbsp;controller&nbsp;gain or integral. Nothing you do&nbsp;will&nbsp;fix the swing, but&nbsp;your&nbsp;tuning efforts could slow the loop down to the&nbsp;point&nbsp;where it does not work.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Next steps:&nbsp;Bad&nbsp;valves and the mechanics of&nbsp;controller&nbsp;tuning<\/h2>\n\n\n\n<p>This concludes the discussion of tuning integrating processes. From&nbsp;here&nbsp;we&nbsp;will&nbsp;discuss some of the practical aspects of&nbsp;controller&nbsp;tuning beginning with how to spot&nbsp;bad&nbsp;control&nbsp;valves, how&nbsp;they&nbsp;affect&nbsp;controller&nbsp;tuning (it isn\u2019t&nbsp;good) and what we can do about it (not much). Then we&nbsp;will&nbsp;discuss the mechanics of&nbsp;controller&nbsp;tuning. We&nbsp;will&nbsp;discuss how to&nbsp;figure&nbsp;out&nbsp;whether tuning is the real problem or if tuning&nbsp;will&nbsp;just&nbsp;cover up&nbsp;other problems. We&nbsp;will&nbsp;also discuss how to work with operators and how to avoid unsafe acts.<\/p>\n\n\n\n<p><strong>Ed Bullerdiek<\/strong>&nbsp;is&nbsp;a&nbsp;retired&nbsp;control engineer&nbsp;with 37&nbsp;years&nbsp;of process&nbsp;control&nbsp;experience&nbsp;in&nbsp;petroleum refining and oil production.&nbsp;Send comments and questions to freerangecontrol@ameritech.net.&nbsp;Edited by Mark T. Hoske,&nbsp;editor-in-chief,<em>Control&nbsp;Engineering,&nbsp;<\/em>WTWH Media<em>,<\/em>&nbsp;mhoske@wtwhmedia.com.<\/p>\n\n\n\n<p><strong>CONSIDER THIS<\/strong><\/p>\n\n\n\n<p>Open-loop, closed-loop and heuristic tuning methods are&nbsp;complimentary. How&nbsp;will&nbsp;having&nbsp;a&nbsp;working knowledge of the concepts behind all three methods speed and improve&nbsp;your&nbsp;tuning efforts?<\/p>\n\n\n\n<p><strong>ONLINE<\/strong><\/p>\n\n\n\n<p>PID series from Ed Bullerdiek, retired&nbsp;control engineer<\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/three-reasons-to-tune-control-loops-safety-profit-energy-efficiency\">Part&nbsp;1: Three reasons to tune&nbsp;control&nbsp;loops: Safety, profit, energy efficiency<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-2-know-these-13-terms-interactions\">PID spotlight, part&nbsp;2: Know these 13 terms, interactions<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-3-how-to-select-one-of-four-process-responses\">PID spotlight, part&nbsp;3: How to select one of four process&nbsp;responses<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-4-how-to-balance-pid-control-for-a-self-limiting-process\">PID spotlight, part&nbsp;4: How to balance PID&nbsp;control&nbsp;for&nbsp;<u>a<\/u>&nbsp;self-limiting process<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-5-what-does-good-and-bad-controller-tuning-look-like\">PID spotlight, part&nbsp;5: What does&nbsp;good&nbsp;and&nbsp;bad&nbsp;controller&nbsp;tuning look like?<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-6-deadtime-how-to-boost-controller-performance-anyway\">PID spotlight, part&nbsp;6: Deadtime? How to boost&nbsp;controller&nbsp;performance anyway<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-7-open-loop-tuning-of-a-self-limiting-process\">PID spotlight, part&nbsp;7: Open-loop tuning of&nbsp;a&nbsp;self-limiting process&nbsp;<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-8-closed-loop-tuning-for-self-limiting-processes\">PID spotlight, part&nbsp;8: Closed-loop tuning for self-limiting processes<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-9-heuristic-tuning-for-a-self-limiting-process\">PID spotlight, part&nbsp;9: Heuristic tuning for&nbsp;a&nbsp;self-limiting process (part A on heuristic tuning)<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-controller-tuning-insights\">PID spotlight, part 10: Heuristic tuning&nbsp;in&nbsp;a&nbsp;self-limiting process<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-11-how-a-pid-controller-works-with-an-integrating-process\">PID spotlight, part 11: How&nbsp;a&nbsp;PID&nbsp;controller&nbsp;works with&nbsp;an&nbsp;integrating process<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/articles\/pid-spotlight-part-12-what-does-good-and-bad-level-controller-tuning-look-like\/\">PID spotlight, part 12: What does&nbsp;good&nbsp;and&nbsp;bad&nbsp;controller&nbsp;tuning look like?<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-13-deadtime-whats-the-best-that-i-can-do\/\">PID spotlight, part 13: Deadtime: what\u2019s the best that I can do?<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-14-how-open-loop-tuning-works-in-an-integrating-process\/\">PID spotlight, part 14: How open loop tuning works&nbsp;in&nbsp;an&nbsp;integrating process<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-15-open-loop-tuning-of-near-integrating-process\/\">PID spotlight, part 15: Open loop tuning of near integrating processes<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/pid-spotlight-part-16-closed-loop-tuning-of-an-integrating-process\/\">PID spotlight, part 16: Closed loop tuning of&nbsp;an&nbsp;integrating process&nbsp;<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/webcasts\/how-to-automate-the-mechanics-of-loop-tuning\">Aug.&nbsp;1&nbsp;RCEP&nbsp;webcast&nbsp;available for one year: How to automate series: The mechanics of loop tuning<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.controleng.com\/control-systems\/pid-apc\">More on PID and advanced process&nbsp;control&nbsp;from&nbsp;<em>Control&nbsp;Engineering<\/em>.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>You are asked to tune an integrating process that is swinging nearly continuously. You\u2019ve done all the checks to prove that it really is a tuning problem. Open loop testing is out of the question; how do you fix it? Using heuristics can help.<\/p>\n","protected":false},"author":4742,"featured_media":131402,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"pgc_sgb_lightbox_settings":"","footnotes":""},"categories":[104038],"tags":[109509,109510,109340,109503,109502,109501,109508,109507,109506,109505,109504],"tracking-metrics":[],"display-location":[109353],"class_list":{"2":"type-post"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>PID spotlight, part 17: Heuristic tuning of integrating processes - Control Engineering<\/title>\n<meta name=\"description\" content=\"You are asked to tune an integrating process that is swinging nearly continuously. 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