动力机械和机身手册2(178)

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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)
= -20 1o91o a
(5.141)
(5.142)
(5.143)
The gain margin expressed in decibels is positive if a <1 (Fig. 5.21a) and is
negative if a > 1 as shown in Fig, 5.21b. A positive gain marg:in (in decibels)
means that the system is stable, and a negative gain margin (in decibels) means
that the system is unstable. For a stable minimum phase system, the value of the
　
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