Page 194 - Servo Motors and Industrial Control Theory -

Appendix B 191

Q

h1
h2

Q0
h1 Electronic
h2 level transducer
Y

Investigate whether the two output variables can be controlled by the single in-
put variable Q . If not study the possibility of adjusting the two variables Q and
i
i
Q . Investigate the possibility of designing two parallel state variable feedback
o
control strategies. This may be set as final year project for students.
14. Consider an upward pendulum which is connected to a motor driven cart. This
system is inherently unstable. As shown below, by an application of a force
on the cart the position of pendulum must be controlled. In this example, it is
assumed that the motor driven cart moves by the force generated by the motor.
It is also assumed that the force is generated quite fast and its dynamics com-
pared the response time of the pendulum is negligible. This upward pendulum
is the model for space craft and missiles that have to move in a defined angle.

m
θ

L

F
M

Write the governing differential equations in terms of (sin (θ) and cos (θ)) and
then assume that the variation of θ is very small and convert the governing
differential equations to linear form. You should drive two second order differ-
ential equations. Assume that the inertia of connecting rod, which connects the