Transcript Trajectory Tracking Experiment under Presence of Multiple Delays

Trajectory Tracking Experiment
Of
Multiple Time Delayed System
2007 © ALARM LAB
Summary of the Exercise
The mission is to make the pendulum track a reference path, using time
delayed feedback.
The setup using
• A pendulum that is attached to the shaft of the DC motor.
• An optical encoder detects the angular position of the pendulum
(4096 pulses/rev).
• Feedback errors in angular position and velocity are available time
delays 1 and 2, respectively.
The Motivation:
• To experimentally verify the findings of CTCR Method. Various
delay composition are tested, to show the stability outlook of the
system.
• To show even for the larger time delays, the tracking performance
may be good.
2007 © ALARM LAB
Pendulum Control System
Amplifier
(Driver)
Computer (Controller)
DC Motor(Actuator)
&
Encoder(Feedback)
2007 © ALARM LAB
Pendulum
(System)
STABILITY MAP OF THE SYSTEM
Unstable
Region
Unstable
Region
Unstable
Region
2
Unstable
Region
Unstable
Region
Stable
Region
(sec)
Unstable
Region
Unstable
Region
B
Unstable
Region
A
1 (sec)
**A and B are the test points shown next.
Unstable
Region
Hz
A
Trajectory Tracking of Non-delayed System
Desired Trajectory:
A
Өd=0.1sin(12.56 t)sin(0.377t)
6
4
Error*10
Ө(degree)
2
Actual
Trajectory
0
Reference
Trajectory
-2
-4
0
5
Time
(sec)
Time
10
2007 © ALARM LAB
15
Trajectory Tracking with Delays
B
1  0.595 sec, 2  0.41sec
Desired Trajectory:
B
Өd = 0.1sin(12.56t)sin(0.377t)
6
4
Error*10
2
Ө(degree)
Actual
Trajectory
0
Reference
Trajectory
-2
-4
-6
0
5
Time (sec)
Time
10
15
**Has a smaller error than the non-delayed system!**
2007 © ALARM LAB