Specifications

lqrd
16-122
16lqrd
Purpose Design discrete LQ regulator for continuous plant
Syntax [Kd,S,e] = lqrd(A,B,Q,R,Ts)
[Kd,S,e] = lqrd(A,B,Q,R,N,Ts)
Description lqrd designs a discrete full-state-feedback regulator that has response
characteristicssimilar to a continuousstate-feedback regulator designed using
lqr. This command is useful to designagainmatrix for digitalimplementation
after a satisfactory continuous state-feedback gain has been designed.
[Kd,S,e] = lqrd(A,B,Q,R,Ts) calculates the discrete state-feedback law
that minimizes a discrete cost function equivalent to the continuous cost
function
The matrices
A and B specify the continuous plant dynamics
and
Ts specifiesthesampletimeof thediscreteregulator.Alsoreturnedare the
solution
S of the discrete Riccati equation for the discretized problem and the
discrete closed-loop eigenvalues
e = eig(Ad-Bd*Kd).
[Kd,S,e] = lqrd(A,B,Q,R,N,Ts) solves the more general problem with a
cross-coupling term in the cost function.
Algorithm The equivalent discrete gain matrix Kd is determined by discretizing the
continuous plant and weighting matrices using the sample time
Ts and the
zero-order hold approximation.
With the notation
un
[]
K
d
xn
[]
–=
Jx
T
Qx u
T
Ru+
()
td
0
∞
ò
=
x
·
Ax Bu+=
Jx
T
Qx u
T
Ru 2x
T
Nu++
()
td
0
∞
ò
=