{"id":1974,"date":"2019-12-07T01:34:36","date_gmt":"2019-12-07T01:34:36","guid":{"rendered":"https:\/\/pressbooks.library.ryerson.ca\/controlsystems\/?post_type=chapter&#038;p=1974"},"modified":"2019-12-19T01:12:16","modified_gmt":"2019-12-19T01:12:16","slug":"9-6effect-of-pid-controller-modes-on-system-stability","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/chapter\/9-6effect-of-pid-controller-modes-on-system-stability\/","title":{"raw":"9.6\tEffect of PID Controller Modes on System Stability","rendered":"9.6\tEffect of PID Controller Modes on System Stability"},"content":{"raw":"PID Controller modes affect the overall system stability and Gain Margin. In general, if Proportional Mode is our reference, Integral (or Proportional + Integral) Control reduces relative stability of the closed loop system, while Proportional + Derivative Control increases relative stability of the closed loop system. Let's consider again the example from Chapter 9.2, where G(s) was described by Equation 9\u20113. The summary of stability analysis for all four modes of PID Controller for this example is shown in Table 9\u20111. We shall return to this topic later, using Root Locus analysis for discussion.\r\n\r\n[caption id=\"attachment_1975\" align=\"aligncenter\" width=\"698\"]<img src=\"http:\/\/pressbooks.library.ryerson.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28.png\" alt=\"Table 9\u20111: Summary of Stability Analysis for the Example System\" width=\"698\" height=\"327\" class=\"wp-image-1975 size-full\" \/> Table 9\u20111: Summary of Stability Analysis for the Example System[\/caption]","rendered":"<p>PID Controller modes affect the overall system stability and Gain Margin. In general, if Proportional Mode is our reference, Integral (or Proportional + Integral) Control reduces relative stability of the closed loop system, while Proportional + Derivative Control increases relative stability of the closed loop system. Let&#8217;s consider again the example from Chapter 9.2, where G(s) was described by Equation 9\u20113. The summary of stability analysis for all four modes of PID Controller for this example is shown in Table 9\u20111. We shall return to this topic later, using Root Locus analysis for discussion.<\/p>\n<figure id=\"attachment_1975\" aria-describedby=\"caption-attachment-1975\" style=\"width: 698px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/pressbooks.library.ryerson.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28.png\" alt=\"Table 9\u20111: Summary of Stability Analysis for the Example System\" width=\"698\" height=\"327\" class=\"wp-image-1975 size-full\" srcset=\"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28.png 698w, https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28-300x141.png 300w, https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28-65x30.png 65w, https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28-225x105.png 225w, https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/12\/figure_9_6_28-350x164.png 350w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><figcaption id=\"caption-attachment-1975\" class=\"wp-caption-text\">Table 9\u20111: Summary of Stability Analysis for the Example System<\/figcaption><\/figure>\n","protected":false},"author":156,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1974","chapter","type-chapter","status-publish","hentry"],"part":1464,"_links":{"self":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1974","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/users\/156"}],"version-history":[{"count":2,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1974\/revisions"}],"predecessor-version":[{"id":2336,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1974\/revisions\/2336"}],"part":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/parts\/1464"}],"metadata":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1974\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/media?parent=1974"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapter-type?post=1974"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/contributor?post=1974"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/license?post=1974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}