PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL3(57)

曝光台 注意防骗 网曝天猫店富美金盛家居专营店坑蒙拐骗欺诈消费者

The Nyquist criterion can be used to determine the gain at the crossover point.
This kind of dependence of the system stability on thEeavalue of the gain leads to
 the concepts of gain and phase margins as discussed in the next section.
    The Nyquist stability criterion enables us to define two quantities that are mea-
sures of the level of stability of a given closed-loop system. These quantities are
the so-called gain and phase margin that are widely used in the control system
analyses and design. Generally, the systems with higher values of gain and phase
margins have better capability to withstand changes in the system parameters be-
fore becoming unstable.
     The concepts of gain margin and phase margin are illustrated in Fig. 5.21.
    The gain margin GM is the reciprocal of the magnitude IG( jc.o)l at the phase
crossover frequency. The phase crossover frequency is the frequency toi  at which
the phase angle of the open-loop transfer function G( jco) is -180 deg. The gain
margin is given by
                    1
GM = IG( jcoi)l
(5.140)
    1

 

 

    {
482             PERFORMANCE, STABlL17Y, DYNAMICS, AND CONTROL
                                         
┏━━━━━━━━━━━━━━━┳━━━┓
┃                         Im / ┃1     ┃
┃e Grun Mr.rgin                ┃      ┃
┃                              ┃      ┃
┃                              ┃~-    ┃
┃                              ┃~/ .i ┃
┣━━━━━━━━━━━━━━━╋━━━┫
┃                              ┃      ┃
┗━━━━━━━━━━━━━━━┻━━━┛
                            kn d     L     
┏━━━━━━━━━━━━━━━━┳━━━┓
┃"~                              ┃~-R'  ┃
┣━━━━━━━━━━━━━━━━╋━━━┫
┃}-  ;-,- '~-                    ┃      ┃
┗━━━━━━━━━━━━━━━━┻━━━┛
a) Stable system                                             b) Unstable system
Fig.5 21   G:un and phase margins.
If a -. IG( jtjoi)l (see Fig. 5.21), then
                            .    1
                                 GM - -
                                  a
The gain margin is usually expressed in decibels as
                             GM(db) = 201o91o  1)
　
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