Specifications

acker
16-11
16acker
Purpose Pole placement design for single-input systems
Syntax k = acker(A,b,p)
Description 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.Inother
words, the eigenvalues of match the entries of
p (up to ordering). Here
A isthestatetransmitter 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=cxis 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 forproblems of order greater than 5 or for weakly controllable systems.
See
place for a more general and reliable alternative.
See Also lqr Optimal LQ regulator
place Pole placement design
rlocus Root locus design
References [1] Kailath, T., Linear Systems, Prentice-Hall, 1980, p. 201.
x
·
Ax bu+=
ukx–=
Abk–
Ab
,()