User`s guide

lqrd
11-124
With the notation
the discretized plant has equations
and the weighting matrices for the e quivalent discrete cost function are
The integrals are computed using matrix exponential formulas due to Van
Loan (see [2]). The plant is discretized using
c2d and the gain matrix is
computed from the discretized data using
dlqr.
Limitations The discretized problem data should meet the requirements for dlqr.
See Also c2d Discretization of LTI model
dlqr State-feedback LQ regulator for discrete plant
kalmd Discrete Kalman estimator for continuous plant
lqr State-feedback LQ regulator for continuous plant
References [1] Franklin,G.F., J.D. Powell, andM.L . Wo rkman,DigitalControlofDynamic
Systems, Second Edition, Addison-Wesley, 1980, pp. 439–440
[2] Van Loan, C.F., “Computing Integrals Involving the Matrix Exponential,”
IEEE Trans. Automatic Control, AC-15, October 1970.
Φτ() e
Aτ
,= A
d
ΦT
s
()=
Γτ() e
Aη
Bη,d
0
τ
∫
= B
d
ΓT
s
()=
xn 1
+[]
A
d
xn
[]
B
d
un
[]+=
Q
d
N
d
N
d
T
R
d
Φ
T
τ()0
Γ
T
τ()I
QN
N
T
R
Φτ()Γτ()
0 I
τd
0
T
s
∫
=