Feedback Control Systems – I (FBCS - I)
1st sessional test
Duration: 100 minutes Total points: 15
Q1. Figure Q1 shows a ball and beam system. We desire to balance a rolling ball on a tilting
beam, as shown in Figure. The torque generated by the motor is propostional to the input
current, that is ,
. Furthermore, we assume that the inertia of motor is negligible and
there is no friction in the motor. Mass of the ball is and the inertial of beam is . The
motion of ball on the beam is frictionless. Obtain a mathematical model of system. (5 points)
Figure Q1
Q2. For the system described by
( ) ( ) ( )
( ) ( )
a. Obtain a transfer function ( )
( ) of the system. (3 points)
b. Obtain the state-space representation of the system. (3points)
Q3. Simplify the block diagram shown in Figure Q2. (4 points)
Figure Q2
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