{"id":1892,"date":"2024-07-19T14:00:27","date_gmt":"2024-07-19T08:30:27","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=1892"},"modified":"2025-07-16T15:14:52","modified_gmt":"2025-07-16T09:44:52","slug":"comparison-of-lead-and-lag-compensators","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ec\/control-systems\/comparison-of-lead-and-lag-compensators","title":{"rendered":"Comparison of lead and lag compensators"},"content":{"rendered":"<table class=\"table table-striped table-bordered table-condensed\" style=\"margin: 0 auto; width: 99%;\">\n<tbody>\n<tr>\n<th width=\"295\">Phase Lead Compensator<\/th>\n<th width=\"295\">Phase Lag Compensator<\/th>\n<\/tr>\n<tr>\n<td width=\"295\">\n<ol style=\"list-style-type: lower-roman;\">\n<li>It improves the transient response<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>It makes the system dynamic response faster.<\/li>\n<li>No significant reduction in steady state error.<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-roman;\" start=\"2\">\n<li>It reduces the rise time.<\/li>\n<li>It increases the bandwidth.<\/li>\n<li>It increases the margin of stability i.e. system becomes more stable.<\/li>\n<li>High frequency noise in the output signal increases or SNR decreases.<\/li>\n<li>It can&#8217;t be applied when phase angle of uncompensated system is increasing rapidly near crossover frequency<\/li>\n<\/ol>\n<\/td>\n<td width=\"295\">\n<ol style=\"list-style-type: lower-roman;\">\n<li>It improves the steady state response.<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li style=\"list-style-type: none;\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>It makes the system dynamic response slower.<\/li>\n<li>It reduces the steady state error.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-roman;\" start=\"2\">\n<li>It increases the rise time.<\/li>\n<li>It decreases the bandwidth.<\/li>\n<li>It reduces the stability margin i.e. system becomes less stable.<\/li>\n<li>High frequency noise in the output signal decreases or SNR increases.<\/li>\n<li>It can&#8217;t be applied if uncompensated system&#8217;s phase angle in low frequency region is not sufficient to provide requisite phase margin.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul style=\"text-align: justify;\">\n<li>Proportional (<em>P<\/em>) Controller<\/li>\n<li>Integral (<em>I<\/em> ) Controller<\/li>\n<li>Derivative (<em>D<\/em>) Controller<\/li>\n<li>Proportional Integral (<em>P<\/em>&#8211;<em>I<\/em> ) Controller<\/li>\n<li>Proportional Derivative (<em>P<\/em>&#8211;<em>D<\/em>) Controller<\/li>\n<li>Proportional Integral Derivative (<em>P<\/em>-I-<em>D<\/em>) Controller<\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\">Proportional (P) Controller<\/h2>\n<p style=\"text-align: justify;\">In proportional controller, the actuating signal for the control action in a control system is proportional to the error signal (which is the input to the controller), therefore the system is called proportional control system.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1895 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/proportional-controller.jpg\" alt=\"Proportional Controller\" width=\"419\" height=\"135\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-controller.jpg 419w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-controller-300x97.jpg 300w\" sizes=\"auto, (max-width: 419px) 100vw, 419px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Integral (I) Controller (Reset Mode)<\/h3>\n<p style=\"text-align: justify;\">In integral controller, the actuating signal for the control action in a control system is proportional to the integral (or integration) of the error signal (which is the input to this controller), therefore the system is called integral control system.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1896 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/reset-mode.jpg\" alt=\"Reset Mode\" width=\"421\" height=\"150\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reset-mode.jpg 421w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reset-mode-300x107.jpg 300w\" sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Derivative (D) Controller (Rate Mode)<\/h3>\n<p style=\"text-align: justify;\">In derivative controller, the actuating signal for the control action in a control system is proportional to the<br \/>\nderivative (or differentiation) of the error signal (which is the input to the controller), therefore the system is called<br \/>\nderivative control system.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1897 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/rate-mode.jpg\" alt=\"Rate Mode\" width=\"422\" height=\"171\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/rate-mode.jpg 422w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/rate-mode-300x122.jpg 300w\" sizes=\"auto, (max-width: 422px) 100vw, 422px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Proportional Integral (P-I) Controller<\/h3>\n<p style=\"text-align: justify;\">It is composite of proportional and integral controllers<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1899 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/proportional-integral-.jpg\" alt=\" Proportional Integral \" width=\"336\" height=\"93\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-integral-.jpg 336w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-integral--300x83.jpg 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Proportional Derivative (P-D) Controller<\/h3>\n<p style=\"text-align: justify;\">It is composite of proportional and derivative controllers<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1900 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/proportional-derivative.jpg\" alt=\" Proportional Derivative\" width=\"330\" height=\"73\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-derivative.jpg 330w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-derivative-300x66.jpg 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Proportional Integral Derivative (P-I-D) Controller<\/h3>\n<p style=\"text-align: justify;\">It is composite of proportional, integral and derivative controllers.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1901 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/proportional-integral-derivative.jpg\" alt=\"Proportional Integral Derivative\" width=\"358\" height=\"91\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-integral-derivative.jpg 358w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/proportional-integral-derivative-300x76.jpg 300w\" sizes=\"auto, (max-width: 358px) 100vw, 358px\" \/><\/p>\n<h2 style=\"text-align: justify;\">State variables analysis<\/h2>\n<h3 style=\"text-align: justify;\">State model of Linear systems:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1902 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/state-model-.jpg\" alt=\"State model \" width=\"596\" height=\"344\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/state-model-.jpg 596w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/state-model--300x173.jpg 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1903 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/output-matrix-.jpg\" alt=\"Output matrix \" width=\"484\" height=\"150\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/output-matrix-.jpg 484w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/output-matrix--300x93.jpg 300w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/h3>\n<h4 style=\"text-align: justify;\">1. Controllable Canonical Form (CCF)<\/h4>\n<p style=\"text-align: justify;\">This form of state-space representation has got the name due to the fact that all of the states are feedback to the input.<br \/>\nConsider the linear system defined by,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1904 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/controllable-canonical.jpg\" alt=\"Controllable Canonical\" width=\"648\" height=\"340\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/controllable-canonical.jpg 648w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/controllable-canonical-300x157.jpg 300w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/controllable-canonical-390x205.jpg 390w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/p>\n<h4 style=\"text-align: justify;\">2. Observable Canonical Form (OCF)<\/h4>\n<p style=\"text-align: justify;\">In this form the feedback is from the output to the state variables and thus named as observable canonical or observer canonical form.<br \/>\nConsider the transfer function system,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1905 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/observable-canonical-form.jpg\" alt=\"Observable Canonical Form\" width=\"538\" height=\"291\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/observable-canonical-form.jpg 538w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/observable-canonical-form-300x162.jpg 300w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/control-systems\/bode-plots\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/control-systems\/performance-of-open-loop-and-closed-control-systems\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-a-control-system\/\" target=\"_blank\" rel=\"noopener\"><strong>What is a Control System?<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Phase Lead Compensator Phase Lag Compensator It improves the transient response It makes the system dynamic response faster. No significant<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[422,6],"tags":[509,508,504,505,506,507],"class_list":["post-1892","post","type-post","status-publish","format-standard","hentry","category-control-systems","category-ec","tag-controllable-canonical-form","tag-observable-canonical-form","tag-proportional-controller","tag-rate-mode","tag-reset-mode","tag-state-model"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=1892"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1892\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=1892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=1892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=1892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}