Page 207 - Servo Motors and Industrial Control Theory

204 Appendix B

control strategy so that the eigenvalues are moved to over damped position of
s1 = −10 and s2 = −20. Note that the state space matrix is of order two and there
are only two eigenvalues and they must be moved to the mentioned position
which means that the dominant root has a time constant of 0.1 s. This is fast
enough for the air craft so that it does not fall over and it is slow enough for the
force F be adjusted to control the angular position. It should be noted that all
the parameters are selected arbitrary and may not represent a real system.

L
F
L G
F
Controlled angle teta

T

33. Design a full order observer for problem 32 so that feedback control strategy
can be implemented. Assume that the angular position of the space craft is mea-
sured and it is required to predict both the angular position and angular velocity
of the space craft by an observer. Discuss how the observer based feedback
control strategy may be implemented. Discuss how fast the observer must be
implemented by a computer so that the observed state variables may be used for
control purposes.
34. A major source of instability is often the transport lag (dead time) presents in
the system. It often appears in the feedback sensors. A typical diagram of such
phenomena is shown graphically below which shows a transport lag.

K
T

–K

where T is the transport lag and K is the gain of the transducer which often can
be taken as unity. The input-output of a transducer with a transport lag can be
shown as,

X Y
e –Ts