{"id":678,"date":"2019-07-26T01:15:14","date_gmt":"2019-07-26T01:15:14","guid":{"rendered":"https:\/\/pressbooks.library.ryerson.ca\/controlsystems\/?post_type=chapter&p=678"},"modified":"2021-01-12T19:23:05","modified_gmt":"2021-01-12T19:23:05","slug":"4-3-step-response-specifications-definitions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/chapter\/4-3-step-response-specifications-definitions\/","title":{"raw":"4.3 Step response specifications - Definitions","rendered":"4.3 Step response specifications – Definitions"},"content":{"raw":"

4.3.1 Percent Overshoot<\/strong><\/p>\r\n

Maximum Overshoot is defined as:<\/p>\r\n\r\n\r\n\r\n\r\n
[latex]MO = y_{max} - y_{ss}[\/latex]<\/td>\r\nEquation 4\u20111<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Percent Overshoot is defined as:<\/p>\r\n\r\n\r\n\r\n\r\n
[latex]PO = \\frac{y_{max} - y_{ss}}{y_{ss}} \\cdot 100[\/latex]%<\/td>\r\nEquation 4\u20112<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[caption id=\"attachment_681\" align=\"aligncenter\" width=\"944\"]\"Figure Figure 4-2: Definition of Percent Overshoot[\/caption]\r\n

Note that while the constant reference signal (which can be referred to as [latex]r_{ss}[\/latex]) in Figure 4\u20112 is shown as unit (1), in fact, it does not have to be that, and can be any value.<\/p>\r\n\r\n

4.3.2 Settling Time<\/strong><\/h3>\r\n

The Settling Time [latex]T_{settle}[\/latex] is defined, as shown in Figure 4\u20113, as either [latex]T_{settle(\\pm 5 \\%)}[\/latex] - within 5% of the steady state value, or [latex]T_{settle(\\pm 2\\%)}[\/latex] - within 2% of the steady state value.<\/p>\r\n\r\n\r\n[caption id=\"attachment_683\" align=\"aligncenter\" width=\"1001\"]\"Figure Figure 4-3: Definition of Settling Time[\/caption]\r\n

4.3.3 Rise Time<\/strong><\/h3>\r\n

The Rise Time [latex]T_{rise}[\/latex] is defined, as shown in Figure 4\u20114, as either calculated as time from 10% to 90% of the steady state value of the output, [latex]y_{ss}[\/latex], or from 0 to 100% of the steady state value of the output, [latex]y_{ss}[\/latex].<\/p>\r\n\r\n

4.3.4 Steady State Error<\/strong><\/h3>\r\n

The Steady State Error [latex]e_{ss}[\/latex] is defined, as shown in Figure 4\u20115 and Equation 4\u20113:<\/p>\r\n

[latex]e_{ss} = r_{ss} - y_{ss}\\%[\/latex]<\/p>\r\n

[latex]e_{ss\\%} = \\frac{r_{ss} - y_{ss}}{r_{ss}} \\cdot 100\\%[\/latex]<\/p>\r\n\r\n\r\n[caption id=\"attachment_686\" align=\"aligncenter\" width=\"460\"]\"Figure Figure 4-4: Definition of Rise Time[\/caption]\r\n\r\n[caption id=\"attachment_685\" align=\"aligncenter\" width=\"460\"]\"Figure Figure 4-5: Definition of Steady State Error[\/caption]","rendered":"

4.3.1 Percent Overshoot<\/strong><\/p>\n

Maximum Overshoot is defined as:<\/p>\n\n\n\n
[latex]MO = y_{max} - y_{ss}[\/latex]<\/td>\nEquation 4\u20111<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Percent Overshoot is defined as:<\/p>\n\n\n\n
[latex]PO = \\frac{y_{max} - y_{ss}}{y_{ss}} \\cdot 100[\/latex]%<\/td>\nEquation 4\u20112<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\"Figure
Figure 4-2: Definition of Percent Overshoot<\/figcaption><\/figure>\n

Note that while the constant reference signal (which can be referred to as [latex]r_{ss}[\/latex]) in Figure 4\u20112 is shown as unit (1), in fact, it does not have to be that, and can be any value.<\/p>\n

4.3.2 Settling Time<\/strong><\/h3>\n

The Settling Time [latex]T_{settle}[\/latex] is defined, as shown in Figure 4\u20113, as either [latex]T_{settle(\\pm 5 \\%)}[\/latex] – within 5% of the steady state value, or [latex]T_{settle(\\pm 2\\%)}[\/latex] – within 2% of the steady state value.<\/p>\n

\"Figure
Figure 4-3: Definition of Settling Time<\/figcaption><\/figure>\n

4.3.3 Rise Time<\/strong><\/h3>\n

The Rise Time [latex]T_{rise}[\/latex] is defined, as shown in Figure 4\u20114, as either calculated as time from 10% to 90% of the steady state value of the output, [latex]y_{ss}[\/latex], or from 0 to 100% of the steady state value of the output, [latex]y_{ss}[\/latex].<\/p>\n

4.3.4 Steady State Error<\/strong><\/h3>\n

The Steady State Error [latex]e_{ss}[\/latex] is defined, as shown in Figure 4\u20115 and Equation 4\u20113:<\/p>\n

[latex]e_{ss} = r_{ss} - y_{ss}\\%[\/latex]<\/p>\n

[latex]e_{ss\\%} = \\frac{r_{ss} - y_{ss}}{r_{ss}} \\cdot 100\\%[\/latex]<\/p>\n

\"Figure
Figure 4-4: Definition of Rise Time<\/figcaption><\/figure>\n
\"Figure
Figure 4-5: Definition of Steady State Error<\/figcaption><\/figure>\n","protected":false},"author":118,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-678","chapter","type-chapter","status-publish","hentry"],"part":664,"_links":{"self":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/678","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\/118"}],"version-history":[{"count":19,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/678\/revisions"}],"predecessor-version":[{"id":2645,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/678\/revisions\/2645"}],"part":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/parts\/664"}],"metadata":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapters\/678\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/media?parent=678"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/pressbooks\/v2\/chapter-type?post=678"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/contributor?post=678"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.torontomu.ca\/controlsystems\/wp-json\/wp\/v2\/license?post=678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}