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Viewpoints of analyzing control system behavior

- Routh-Hurwitz
- Root locus
- Bode diagram (plots)
- Nyquist plots
- Nicols plots
- Time domain

automatique by meiling Chen

＋

－

H(s)

L.T.I system

Magnitude:

Phase:

Steady state response

Magnitude:

Phase:

automatique by meiling Chen

automatique by meiling Chen

g1=zpk([],[0 –2 -10],[1])

bode(g1)

g1

g2

g2

n=[-3 -9]

m=[1 –1 –1 –15 0]

g2=tf(n,m)

bode(g1,g2)

g1

automatique by meiling Chen

A transfer function is called minimum phase when all the poles and zeros are LHP and non-minimum-phase when there are RHP poles or zeros.

Minimum phase system

Stable

The gain margin (GM) is the distance on the bode magnitude plot from the amplitude at the phase crossover frequency up to the 0 dB point. GM=-(dB of GH measured at the phase crossover frequency)

The phase margin (PM) is the distance from -180 up to the phase at the gain crossover frequency. PM=180+phase of GH measured at the gain crossover frequency

automatique by meiling Chen

Closed-loop transfer function :

Open loop Stability poles of in LHP

Im

Closed-loop Stability

poles of in left side of (-1,0)

RHP

Re

automatique by meiling Chen

phase crossover frequency:

G.M.>0

Stable system

P.M.>0

automatique by meiling Chen

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