User`s guide

dlqr
11-59
11dlqr
Purpose Design linear-quadratic (LQ) state-feedback regulator for discrete-time plant
Syntax [K,S,e] = dlqr(a,b,Q,R)
[K,S,e] = dlqr(a,b,Q,R,N)
Description [K,S,e] = dlqr(a,b,Q,R,N) calculates the optimal gain matrix K such that
the state-feedback law
minimizes the quadratic cost function
for the discrete-time state-space mode
l
The default value
N=0 is assumed when N is omitted.
In addition to the state-feedback gain
K, dlqr returns the solution S of the
associated discrete-time 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 unit circle.
See Also dare Solve discrete Riccati equations
lqgreg LQG regulator
un
[]
Kx n
[]–=
Ju() xn[]
T
Qx n[] un[]
T
Ru n[] 2xn[]
T
Nu n[]++()
n1=
∞
∑
=
xn 1
+[]
Ax n
[]
Bu n
[]+=
A
T
SA S– A
T
SB N+()B
T
XB R+()
1
–
B
T
SA N
T
+()– Q+0=
K
S
KB
T
XB R+()
1
–
B
T
SA N
T
+()=
AB
,()
R0
> QNR
1
–
N
T
– 0≥
QNR
1
–
N
T
– ABR
1
–
N
T
–,()