User`s guide

place
11-170
11place
Purpose Pole placement design
Syntax K = place(A,B,p)
[K,prec,message] = place(A,B,p)
Description Given the single- or multi-input system
and a vector
p of desired self-conjugate closed-loop pole locations, place
computes a gain matrix 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 t he ordering).
K = place(A,B,p) computes a feedback gain matrix K that achieves the
desired closed-loop pole locations
p, assuming all the i nputs of the plant are
control inputs. The length of
p must match the row size of A. place works for
multi-input systems and is based on the algorithm from [1]. This algorithm
uses the extra degrees of freedom to find a solution that minimizes the
sensitivity of the closed-loop poles to perturbations in or .
[K,prec,message] = place(A,B,p) also returns prec, an estimate of how
closely the eigenvalues of match the specified locations
p (prec
measures the number of accurate decimal digits in the actual closed-loop
poles). If some nonzero closed-loop pole is more than 10% off from the desired
location,
message contains a warning message .
You can also use
place forestimatorgainselectionby transposingthe A matrix
and substituting
C' for B.
l = place(A',C',p).'
Example Consider a state-space system (a,b,c,d) with two inputs, three outputs, and
three states. You can compute the feedback gain matrix needed to place the
closed-loop poles at
p = [1.1 23 5.0] by
p = [1 1.23 5.0];
K = place(a,b,p)
x
·
Ax Bu+=
uKx
–=
ABK
–
A
B
ABK
–