104
Now consider one method of selecting feedback gains which will make
the linearized system behave as though it were time-invariant. First
make the definition
Kl(t) := [K1#1(t), Klf2(t)] (6-16)
where Kj^it) corresponds to feedback of the joint positions and K-Lj2(t)
corresponds to feedback of the joint velocities. Using (6-11) through
(6-13) it is possible to write the linearized system matrix as
F*(t) G*(t)Kx(t) -G*(t)K2(t)
-BH,
A
(6-17)
I
Fj(t) J1(*)K1^1(t)
F2(t)
NxN
1,-X*,
J "(0 )K1>2(t)
J(9 )K2(t)
We desire a feedback law which will make the right-hand side of
(6-17) take the following form
0 *NxN 0
m2 m3
-BOA
(6-18)
where e R^xN, M2 e RNxN, and M3 e R^xr^ are constant matrices (note
that A e R^NxrN). can ke that the eigenvalues of (6-18) can be
assigned arbitrarily by proper choice of Mj, M2 and M3. This is, in