Equation 11\u20114<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
As shown in Figure 11\u20115, if Phase Margin is found above [latex]-180^{0}[\/latex] line, then it is considered positive, [latex]\\Phi_{m} > 0[\/latex], and is associated with the stable system, where Gain margin is also positive. [latex]\\Phi_{m} = 0^{0}[\/latex] is associated with a marginally stable system, where gain margin is also equal to zero. If Phase Margin is found below [latex]-180^{0}[\/latex] line, then it is considered negative,[latex]\\Phi_{m}< 0[\/latex], and is associated with the unstable system, where Gain margin is also negative.<\/p>\r\n\r\n\r\n[caption id=\"attachment_948\" align=\"aligncenter\" width=\"599\"]![\"\"](\"http:\/\/pressbooks.library.ryerson.ca\/controlsystems\/wp-content\/uploads\/sites\/75\/2019\/10\/11.5.jpg\")
Fig 11-5 Definition of the Phase Margin[\/caption]","rendered":"
A corollary to the Gain Margin can also be defined, describing the so-called Phase Margin. Let the crossover frequency be defined as [latex]\\omega_{cp}[\/latex], the frequency at which the gain plot (in dB) crosses over 0 dB line, then let Phase Margin be defined as:<\/p>\n
| [latex]\\Phi_{m} =180^{0}+\\angle GH(\\omega_{cp})[\/latex]<\/td>\n | \n Equation 11\u20114<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n As shown in Figure 11\u20115, if Phase Margin is found above [latex]-180^{0}[\/latex] line, then it is considered positive, [latex]\\Phi_{m} > 0[\/latex], and is associated with the stable system, where Gain margin is also positive. [latex]\\Phi_{m} = 0^{0}[\/latex] is associated with a marginally stable system, where gain margin is also equal to zero. If Phase Margin is found below [latex]-180^{0}[\/latex] line, then it is considered negative,[latex]\\Phi_{m}< 0[\/latex], and is associated with the unstable system, where Gain margin is also negative.<\/p>\n |