Page 67 - Servo Motors and Industrial Control Theory -

3.4 State Variable Feedback Control Theory 59

Fig. 3.1 Block diagram form x 1
of state variables feedback U j + U System x
control strategy + 2
x 3

K 1

K 2

K 3

are subtracted from the input signal. Although the control strategy was discussed for
a third order transfer function, the method can be used for more complicated sys-
tems. The eigenvalues of the system matrix with the state variable feedback control
system can be calculated again to ensure the gains are correct.
0 1 0
A:= 0 0 1
−24 −26 −9
v:= eigenvals(A)
− 2
v= −3
−4

The above analysis shows that indeed the eigenvalues have moved to the required
position on the s-plane.
The control strategy mentioned above is shown in block diagram form in Fig. 3.1.
When state variables feedback control system is used, it is important to study the
steady state behavior of the system. For steady state, the derivative terms are set to
zero and the linear equation is solved as

0 0 1 0 x 0
1
0:= 0 0 1 ⋅ x +⋅
0 u
2 i
0 − 24 − 26 − 9 x 1
3
For unit step input,
0 1 0 − 1 0
X:= 0 0 1 ⋅ 0
− 24 − 26 − 9 1
0.042
X = 0
0
y : 0.042=