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ControlDesign[StateObserver]

  

Ackermann

  

calculate the observer gain for single-output systems using Ackermann's formula

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Ackermann(Amat, Cmat, p)

Ackermann(sys, p)

Parameters

Amat

-

Matrix; system matrix of a state-space system

Cmat

-

Matrix or Vector; output matrix of a state-space system

sys

-

System; a DynamicSystems system object of state-space format

p

-

list ; list of desired closed-loop poles (real or complex). Complex poles including those containing symbolic parameters must be given in complex conjugate pairs. All symbolic parameters in the list are assumed to be real.

Description

• 

The Ackermann command calculates the static (Luenberger) observer gain for the single-output systems to put the observer error dynamics poles in the desired location based on the Ackermann's formula. The (Amat,Cmat) pair (or the sys object) must be observable. The closed-loop observer error system matrix is then Ac=AmatL.Cmat (or Ac = sys:-a-L.sys:-c) where L is the calculated observer gain.

Examples

withControlDesign:

AmatMatrix0.9054,39.7500,22.4100,0.1891,0.7366,0.3734,77.0100,41.1600,4.1900,1.0450,0.2815,120.8000,63.6500,4.3650,2.1850,0.4264,2.2290,0.2781,0.0662,0.6509,0.5441,39.1800,21.8400,2.5120,0.8066

Amat:=0.905439.750022.41000.18910.73660.373477.010041.16004.19001.04500.2815120.800063.65004.36502.18500.42642.22900.27810.06620.65090.544139.180021.84002.51200.8066

(1)

CmatMatrix3,9,5,4,6

Cmat:=39546

(2)

p3+2I,1,2.5,32I,4

p:=3+2I,1,2.5,32I,4

(3)

StateObserver:-AckermannAmat,Cmat,p

1.0828719360.45354460460.82428444180.26247443040.3998350201

(4)

References

  

[1] T. Kailath, Linear Systems, Prentice-Hall, 1980.

  

[2] C. T. Chen, Linear System Theory and Design, 3rd Ed., Oxford University Press, 1999.

See Also

ControlDesign

ControlDesign[StateFeedback][Ackermann]

ControlDesign[StateFeedback][PolePlacement]

ControlDesign[StateObserver][PolePlacement]

 


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