verify whether the system poles are in a desired region - MapleSim Help

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ControlDesign[RegionPoles] - verify whether the system poles are in a desired region

Calling Sequence

RegionPoles(sys, zeta, omegan, opts)

Parameters

sys

-

System; a DynamicSystems system object in continuous-time domain; must be single-input single-output (SISO)

zeta

-

realcons; the specified damping

omegan

-

realcons; the specified natural frequency

opts

-

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

Description

• 

The RegionPoles command verifies whether the system poles are in a desired region. The desired region is specified by zeta and omegan and is defined based on relative stability and damping conditions as follows:

– 

Relative Stability: The desired region is part of the complex left half plane (LHP) with real part less than ζomegan. This is equivalent to the relative stability of the closed-loop system with respect to the line s=jωζomegan (rather than the imaginary axis). Clearly, if zeta or omegan are set to zero, the relative stability reduces to the absolute stability with respect to the imaginary axis.

– 

Damping: The desired region is part of the complex left half plane (LHP) inside the angle +/-arccosζ measured from the negative real axis.

Examples

withControlDesign:

sys:=DynamicSystems:-NewSystems+5s3+12s2+22s+14

sys:=Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1s

(1)

ζ1:=45:omegan1:=2:

RegionPolessys,ζ1,omegan1,output=verify

false

(2)

RegionPolessys,ζ1,omegan1,output=plot

RegionPolessys,ζ1,omegan1,output=verify,condition=damping

true

(3)

RegionPolessys,ζ1,omegan1,output=plot,condition=damping

RegionPolessys,ζ1,omegan1,output=verify,condition=relativestability

false

(4)

RegionPolessys,ζ1,omegan1,output=plot,condition=relativestability

See Also

ControlDesign, ControlDesign[Characterize], ControlDesign[CohenCoon], ControlDesign[FeasibleGains], ControlDesign[GainPhaseMargin], ControlDesign[ZNFreq], ControlDesign[ZNTimeModified]


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