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acker - Pole placement design for single-input systems

Syntax

k = acker(A,b,p)

Description

k = acker(A,b,p)

Given the single-input system

and a vector p of desired closed-loop pole locations, acker (A,b,p) uses Ackermann's formula [1] to calculate a gain vector k such that the state feedback places the closed-loop poles at the locations p. In other words, the eigenvalues of match the entries of p (up to ordering). Here A is the state transmitter matrix and b is the input to state transmission vector.

You can also use acker for estimator gain selection by transposing the matrix A and substituting c' for b when y = cx is a single output.

l = acker(a',c',p).'

Limitations

acker is limited to single-input systems and the pair must be controllable.

Note that this method is not numerically reliable and starts to break down rapidly for problems of order greater than 5 or for weakly controllable systems. See place for a more general and reliable alternative.

References

[1] Kailath, T., Linear Systems, Prentice-Hall, 1980, p. 201.

See Also

lqr, place, rlocus

abs

allmargin

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