User`s guide

lqrd
11-123
11lqrd
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
characteristics similar to a continuous state-feedbackregulatorde signedusing
lqr. This command is useful to design a gain matrix fordigital implementation
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 specifiesthesamplet ime ofthediscreteregulator.Alsoreturnedare the
solution
S of the discrete Riccati equation for the di scretized 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 discret izing the
continuous pla nt and weighting mat rices using the sample time
Ts and the
zero-order hold approximation.
un
[]
K
d
xn
[]–=
Jx
T
Qx u
T
Ru+()td
0
∞
∫
=
x
·
Ax Bu+=
Jx
T
Qx u
T
Ru 2x
T
Nu++()td
0
∞
∫
=