{"id":1977,"date":"2019-12-07T01:38:46","date_gmt":"2019-12-07T01:38:46","guid":{"rendered":"https:\/\/pressbooks.library.ryerson.ca\/controlsystems\/?post_type=chapter&p=1977"},"modified":"2021-01-14T14:19:11","modified_gmt":"2021-01-14T14:19:11","slug":"9-7examples","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/chapter\/9-7examples\/","title":{"raw":"9.7\tExamples","rendered":"9.7\tExamples"},"content":{"raw":"
\r\n

9.7.1 Example<\/h3>\r\nConsider a closed loop unit feedback system operating initially under Proportional Control where the process transfer function G(s) is as follows:\r\n\r\n\"\"\r\n\r\nPart 1. Find the stability range, and assume the operating gain such that the Gain Margin = 2.\r\n\r\nPart 2. Next, replace the gain with a parallel structure of the PID Controller, with the settings for the Derivative Time Constant [latex] \\tau_d =2 [\/latex] seconds and for the Integral Time Constant [latex] \\tau_i =10 [\/latex]seconds. Fine-tune the PID Controller by simulations.\r\n
\r\n

9.7.2 Example<\/h3>\r\n<\/div>\r\nConsider again the system from Example 7.3.17 and Example 8.7.14, only now the P+Rate Feedback and PI+ Rate Feedback are replaced with a series\u00a0<\/strong>configuration of a PID Controller, as shown.\r\n\r\n\"\"\r\n\r\nG(s) process transfer function remains the same as before:\r\n

[latex] G(s)=\\frac{1}{s^2+7s+5} [\/latex]<\/p>\r\nAll gain values are kept exactly the same as you determined them in those two previous examples:\r\n\r\n[latex] K_p=40.78 [\/latex], [latex] K_d=0.0245 [\/latex] and [latex] K_i=0.7 [\/latex].\u00a0 How different will be the PID system closed loop transfer function from the P+Rate and PI+Rate? How different will the system step response be? Will the difference be significant? Briefly justify your answers.\r\n\r\n<\/div>","rendered":"

\n

9.7.1 Example<\/h3>\n

Consider a closed loop unit feedback system operating initially under Proportional Control where the process transfer function G(s) is as follows:<\/p>\n

\"\"<\/p>\n

Part 1. Find the stability range, and assume the operating gain such that the Gain Margin = 2.<\/p>\n

Part 2. Next, replace the gain with a parallel structure of the PID Controller, with the settings for the Derivative Time Constant [latex]\\tau_d =2[\/latex] seconds and for the Integral Time Constant [latex]\\tau_i =10[\/latex]seconds. Fine-tune the PID Controller by simulations.<\/p>\n

\n

9.7.2 Example<\/h3>\n<\/div>\n

Consider again the system from Example 7.3.17 and Example 8.7.14, only now the P+Rate Feedback and PI+ Rate Feedback are replaced with a series\u00a0<\/strong>configuration of a PID Controller, as shown.<\/p>\n

\"\"<\/p>\n

G(s) process transfer function remains the same as before:<\/p>\n

[latex]G(s)=\\frac{1}{s^2+7s+5}[\/latex]<\/p>\n

All gain values are kept exactly the same as you determined them in those two previous examples:<\/p>\n

[latex]K_p=40.78[\/latex], [latex]K_d=0.0245[\/latex] and [latex]K_i=0.7[\/latex].\u00a0 How different will be the PID system closed loop transfer function from the P+Rate and PI+Rate? How different will the system step response be? Will the difference be significant? Briefly justify your answers.<\/p>\n<\/div>\n","protected":false},"author":156,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1977","chapter","type-chapter","status-publish","hentry"],"part":1464,"_links":{"self":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1977","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":3,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1977\/revisions"}],"predecessor-version":[{"id":2684,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/1977\/revisions\/2684"}],"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\/1977\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/media?parent=1977"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapter-type?post=1977"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/contributor?post=1977"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/license?post=1977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}