Page 762 - Mechatronics with Experiments

748 MECHATRONICS
2. Consider two independely driven rotary motion axes: axis 1 and axis 2. Our objective is to make
axis 2 follow axis 1 as if they are connected with a mechanical gear ratio. Let the gear ratio be z.a)
Draw the command motion generation block diagram for axis 2 for the case where the master motion
it follows is the commanded motion of axis 1. b) Do the same, however this time the master motion
it follows is the actual position of the axis 1. c) Further consider the case that axis 1 is the drive for
an unwind roll and axis 2 is the drive for a rewind roll for a web application. Axis 2 needs to modify
the gear ratio as a function of the sensed tension. Draw the block diagram and write the pseudo-code
to accomplish this.
3. Consider the registration application shown in Figure 10.12. The rotating axis moves at a constant
gear ratio relative to the speed of the web which is measured by an encoder. The objective is to make
sure the rotating tool axis (print head or knife head) has to be at a certain position within one
revolution when the registration mark passes under the registration sensor. When the registration
mark sensor turns ON, we capture the position of the rotary axis and compare it with the desired
position. Then, the rotating axis makes a corrective index motion on top of the gear ratio motion.
Assume that the web is moving at 2000 ft∕min. and a cycle is repeated every 1.0 ft. It is desired that
the accuracy of the positioning and operation done by the rotating tool axis relative to the web must
be with in ±1∕1000 in. a) Determine the minimum psoition sensor resolution on the rotating axis. b)
What happens to the accuracy if the registration mark sensor has 1.0 ms variation in its accuracy of
responding to the mark? c) What is the maximum allowed variation in the registration mark sensor’s
response time? d) If the position capture is done under software polling and the application software
may have 5 ms variation when it may sample the position of the rotating axis relative to the instant
the registration mark sensor comes on, what would be the positioning error? e) What is the viable
position capturing method in such applications?
4. Consider an xy table. Our objective is to design a programmable motion control system such that
the xy table makes various contour moves. Assume the table x and y axes have already established a
home position. a) Design a pseudo-code so that xy table draws a line with a given slope and length.
b) Design a pseudo-code so the xy table draws a circle with a given center coordinates and diameter.
5. Consider the tension control system shown in Figures 1.7, 10.14 and 10.15. The example on
page 7 shows a web control method that changes the speed command to one of the motorized rolls
in proportion to the tension error. Assume that Figure 10.13 is a more complete and updated version
of Figure 1.7 where the analog op-amp controller circuit is replaced with a digital controller. In
addition, the wind-off roll is also a motorized drive, and there is a line position sensor (encoder).
Update the control system using the electronic gearing method to control the wind-up roll. Assume
the wind-off roll is running at a constant speed. The control algorithm should use the line speed
encoder in Figure 10.13 as the master position to follow with a gear ratio, where the gear ratio is
modified based on tension error through a PI type controller (Figure 10.14). Show the benefits of the
electronic gearing based control method over the traditional direct speed control based on tension
sensor method.