compute the gain-margin and phase-crossover frequency - Maple Help

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DynamicSystems[GainMargin] - compute the gain-margin and phase-crossover frequency

Calling Sequence

GainMargin( sys, opts )

Parameters

sys

-

System; a system object

opts

-

(optional) equation(s) of the form option = value; specify options for the GainMargin command

Description

• 

The GainMargin command returns the gain margin and corresponding phase-crossover frequency of the linear system sys.

• 

This command normally returns a Matrix of lists. Each list consists of the gain-margin and associated crossover-frequency corresponding to the transfer function of each Matrix element. However, if the Matrix of transfer functions is one by one, then the single list is returned directly.

• 

A phase-crossover frequency is a frequency at which the phase of the transfer function equals π radians (180 degrees).

• 

If there is more than one phase-crossover frequency, then the one with the minimum gain-margin is used.

• 

If there is no phase-crossover frequency for a transfer function, then the associated list is [Float(undefined),Float(undefined)].

• 

For a sampled (discrete) system, the z to s transformation z = exp(s*Ts), where Ts is the sample period, is applied to the transfer function(s). The frequency range is limited to the Nyquist frequency.

Examples

withDynamicSystems:

sys:=TransferFunction11+s3:

GainMarginsys

18.06179974,1.732050808

(1)

g:=GainMarginsys,decibels=false

g:=8.000000000,1.732050808

(2)

gain:=g1

gain:=8.000000000

(3)

freq:=g2

freq:=1.732050808

(4)

sys:=TransferFunction1s+13,1s3+4s2+s6:

GainMarginsys

18.06179974,1.73205080820.00000000,1.

(5)

p1:=plotfreq,0,freq,gain,color=blue,thickness=2:

p2:=MagnitudePlotsys:

plots[display]p1,p2

See Also

DynamicSystems, DynamicSystems[BodePlot], DynamicSystems[PhaseMargin]


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