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
(6-16)
where K1,1(t) corresponds to feedback of the joint positions and K1,2(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
L -BH
(6-17)
INxN
F2(t) - d-l1 (6**)Ki,2(t)
0
0
-JO )K2(t)
A
We desire a feedback law which will make the right-hand side of (6-17) take the following form
0
Mi
-B
INx
M2
0
(6-18)
where M, c RNxN, M2 E RNxN, and M3 e RNxrN are constant matrices (note that A e RrNxrN). It can be shown that the eigenvalues of (6-18) can be assigned arbitrarily by proper choice of M1, M2 and M3. This is, in
0
Fl1(t) - J-l( *)Kl1,l(t)
-B
Klmt := [Kl,l(t), K1,2(t)]