User`s guide

lqr
11-121
11lqr
Purpose Design linear-quadratic ( LQ) state-feedback regulator for continuous plant
Syntax [K,S,e] = lqr(A,B,Q,R)
[K,S,e] = lqr(A,B,Q,R,N)
Description [K,S,e] = lqr(A,B,Q,R,N) calculates theoptimal gainmatrix K suchthatthe
state-feedback law
minimizes the quadratic cost function
for the continuous-time state-space model
The default value
N=0 is assumed when N is omitted.
In addition to the state-feedback gain
K, lqr returns the solution S of the
associated Riccati equation
and the closed-loop eigenvalues
e = eig(A–B*K). Note that is derived from
by
Limitations The problem data must satisfy:
• The pair is stabilizable.
• and .
• has no unobservable mode on the imaginary
axis .
uKx
–=
Ju() x
T
Qx u
T
Ru 2x
T
Nu++()td
0
∞
∫
=
x
·
Ax Bu+=
A
T
SSA SBN+()R
1
–
B
T
SN
T
+()– Q++0=
K
S
KR
1
–
B
T
SN
T
+()=
AB
,()
R0
> QNR
1
–
N
T
– 0≥
QNR
1
–
N
T
– ABR
1
–
N
T
–,()