{"id":1558,"date":"2011-08-20T12:36:31","date_gmt":"2011-08-20T12:36:31","guid":{"rendered":"http:\/\/instrumentacionycontrol.net\/?p=1558"},"modified":"2020-05-27T11:22:10","modified_gmt":"2020-05-27T16:22:10","slug":"closed-loop-controller-tuning-ultimate-gain-method","status":"publish","type":"post","link":"https:\/\/instrumentacionycontrol.net\/en\/sintonizacion-de-controladores-a-lazo-cerrado-metodo-ultima-ganancia\/","title":{"rendered":"Closed-loop controller tuning: Ultimate Gain Method"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Closed loop refers to the operation of the control system with its control devices in \u201c<strong>automatic<\/strong>\u201d, where the flow of information from the sensor element followed by the transmitter, controller, control element, process and returning to the sensor represents a continuous feedback loop (\u201c<strong>closed<\/strong>\u201d).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the total amount of signal amplification provided by the instruments is too much (<strong>revenue<\/strong>), the control loop will begin to self-oscillate. While oscillation is almost always undesirable in control systems, it can be used for exploratory testing of process dynamics if the controller operates purely with proportional action (without integral and derivative actions): providing useful information for effectively calculating the PID controller parameters. Therefore, a closed-loop tuning procedure involves disabling any integral or derivative actions of the controller, then gradually increasing the controller gain until the process variable begins to oscillate. The amount of gain required to generate sustained oscillations (constant amplitude) is called \u201c<strong>last sensitivity<\/strong>\u201d&quot; either &quot;\u201c<strong>last profit<\/strong>\u201d(Su) of the process, while the time (period) between each oscillation peak is called \u201c<strong>last period<\/strong>\u201d&quot;(Pu) of the process.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When performing closed-loop tests, it is important to ensure that the oscillation peaks do not exceed the limits of the instrumentation, either in the measurement or in the final control element. In other words, for the oscillation to accurately reflect the ultimate gain and period, the oscillations must be naturally limited and not artificially limited by the instrumentation, whether by the transmitter or the saturation of the control valve. Therefore, we must avoid this phenomenon at all costs if we want to obtain the best values for ultimate gain and period. The following graph shows PV oscillation but with control valve saturation, which we must avoid:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"457\" height=\"297\" src=\"http:\/\/instrumentacionycontrol.net\/wp-content\/uploads\/2017\/10\/close-loop1.gif\" alt=\"\" class=\"wp-image-1565\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">If the controller has <strong>ONLY <\/strong>With the proportional action configured, the recommendations of Ziegler and Nichols tell us that we should set the controller gain to a value of half the last gain (Ku):<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Kp = 0.5Ku<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kp: controller gain<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ku: Last gain determined by increasing the controller gain until self-sustaining oscillation is achieved.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Generally, a controller gain of half the experimentally determined &quot;last gain&quot; provides a reasonably fast response to setpoint and load changes. Oscillations of the process variable following setpoint and load changes are typically dampened, with each wave peak being approximately one-quarter the amplitude of the previous peak. This is known as quarter-wave damping. While not ideal, it represents a balance between fast response and stability.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The following trend graph of a process shows how the oscillation attenuates in each cycle to a quarter of the previous amplitude, after making a setpoint (SP) change:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"506\" height=\"310\" src=\"http:\/\/instrumentacionycontrol.net\/wp-content\/uploads\/2017\/10\/close-loop2.gif\" alt=\"\" class=\"wp-image-1566\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Some might criticize (myself included) that allowing a quarter-wave amplitude attenuation to occur puts unnecessary stress on the control valve, causing stem wear over time and consuming large amounts of compressed air to operate. Given that all modern controllers have integral action (reset) capabilities, unlike the simple pneumatic controllers of Ziegler and Nichols&#039; day, it is not really necessary to tolerate a prolonged offset and thus prevent valve deterioration with each oscillation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the controller in question has integral (reset) action in addition to proportional action, Ziegler and Nichols&#039; recommendation tells us to set the gain slightly less than half the value of the last gain, and set the integral time constant to a value slightly less than the last period.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Kp = 0.45 Ku<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Ti = Pu \/ 1.2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kp = Controller gain<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ku = \u201cLast gain\u201d determined by increasing the controller until oscillation is achieved.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ti = integral controller time (minutes per repetition)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pu = \u201cLast\u201d period obtained from the oscillations (minutes)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the controller in question has all three control actions present (Full PID), Ziegler and Nichols recommend configuring the controller as follows:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Kp = 0.6 Ku<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Ti = Pu \/ 2<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Td = Pu\/8<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kp = Controller gain<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ku = \u201cLast gain\u201d determined by increasing the controller until oscillation is achieved.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ti = integral controller time (minutes per repetition)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Td = Derivative time of the controller (minutes)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pu = \u201cLast\u201d period obtained from the oscillations (minutes)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An important caveat with any tuning procedure based on ultimate gain is the potential to cause problems in the process while experimentally determining the ultimate gain value. Recall that \u201cultimate\u201d gain is the amount of gain in the controller (proportional action) needed to generate constant oscillation (constant amplitude) in the process variable. To determine this gain value, one must spend time provoking the process with sudden setpoint changes (to induce oscillations) and experiment with increasingly larger gains until constant amplitude oscillations are achieved. Any gain greater than the \u201cultimate gain\u201d will cause oscillations of increasing amplitude (out of control) and can only be brought under control by decreasing the controller gain or switching to manual mode (and thus stopping the entire feedback system). The problem with this is that one never knows for sure when the ultimate gain has been reached until this value is exceeded (generating increasing oscillations). In other words, the system must be pushed to the brink of total instability to determine its ultimate gain value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It&#039;s not just the time we spend trying to achieve this (especially in systems with a long natural oscillation period), as is the case with many temperature and composition control applications, but also the risk of potentially damaging equipment and compromising process quality. To see how impractical this can be, simply tell an Operations Supervisor or the manager of a chemical process that you want to over-tune the main furnace temperature controller or the pressure controller of one of the larger distillation columns to the point of causing oscillations in the process variable, and that to do this you need hours of unstable operation before you find the perfect gain value. Consider yourself lucky if, when you mention what you want to do, there isn&#039;t a security guard to escort you out of the control room! :D:D In fact, one could argue that any process that tolerates this &quot;oscillation abuse&quot; probably doesn&#039;t need to be finely tuned!.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Besides the practical limitations, the rules given by Ziegler and Nichols shed light on a real relationship between the tuning parameters P, I, and D and the operational characteristics of the process. The controller gain should be some fraction of the gain required for the process to oscillate steadily. The integral time constant should be proportional to the process time constant; for example, slow-responding processes should have a slower integral action. The derivative time constant should likewise be proportional to the process time constant, even though this has the opposite meaning from an aggressiveness perspective: a slow process warrants a high derivative time value.<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h2 class=\"wp-block-heading\">Help us grow <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, if you are determined to learn Industrial Automation and advance your professional career, you may be interested in our Premium courses:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2013 Click to see all our courses at <a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\">MyAutomationClass.com <\/a><br>- Course: <a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/aprende-plcs-desde-cero-con-rslogix500-basico-avanzado?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\">\u00ab&quot;Become a PLC expert in 60 days, from basic to pro&quot;\u00bb <\/a><br>- Course: <a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/aprende-controladores-pid-de-manera-practica?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\">\u00ab&quot;PID Controllers Master Class \u2013 100% practical&quot;\u00bb <\/a><br>- Course:<a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/desarrollo-de-proyectos-scadahmi-con-wonderware-intouch?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\"> \u00ab&quot;How to create SCADA\/HMI projects from scratch with InTouch&quot;\u00bb <\/a><br>- Course:<a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/pid-tuning-ultimate-sintonizacion?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\"> \u00ab&quot;PID Tuning Ultimate: The Definitive Course for Tuning&quot;\u00bb <\/a><br>- Course:<a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/modelamiento-practico-de-procesos-10-pasos-impresindibles-para-ser-un-experto?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\"> \u00ab&quot;Practical Process Modeling: Definitive Steps to Becoming an Expert&quot;\u00bb <\/a><br>- Program:<a rel=\"noreferrer noopener\" href=\"https:\/\/myautomationclass.com\/p\/the-ultimate-process-control-training-se-un-maestro-control-pid?utm_source=iycnet&amp;utm_medium=post&amp;utm_campaign=footer_link_post\" target=\"_blank\"> \u00ab&quot;The Ultimate Process Control Formula&quot; (All-inclusive: PID Control, Tuning, and Modeling)<\/a> <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">- Course: <a href=\"https:\/\/myautomationclass.com\/p\/aprende-instrumentacion-industrial-facil\" target=\"_blank\" rel=\"noreferrer noopener\">How to Learn Industrial Instrumentation, Easily (Complete)<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you have any questions, contact us via <a rel=\"noreferrer noopener\" href=\"http:\/\/m.me\/instrumentacionycontrol.net\" target=\"_blank\">Facebook Messenger<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Until next time. COMMENT AND SHARE! I&#039;ll be happy to answer your questions.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>","protected":false},"excerpt":{"rendered":"<p>Lazo cerrado refiere a la operaci\u00f3n del sistema de control con sus dispositivos de control en modo \u201cautom\u00e1tico\u201d, donde el flujo de informaci\u00f3n desde el elemento sensor seguido por el transmisor, controlador, elemento de control, proceso y regresando al sensor representa un lazo realimentado continuo (\u201ccerrado\u201d). Si la cantidad total de amplificaci\u00f3n de la se\u00f1al [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":12306,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[70],"tags":[20869,379,20793,20870,20214],"class_list":["post-1558","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-curso-sintonizacion-controladores","tag-cerrado","tag-controladores","tag-lazo","tag-metodo","tag-sintonizacion","post-wrapper","thrv_wrapper"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Sintonizaci\u00f3n de controladores a lazo cerrado: M\u00e9todo \u00daltima Ganancia<\/title>\n<meta name=\"description\" content=\"Lazo cerrado refiere a la operaci\u00f3n del sistema de control con sus dispositivos de control en modo 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