The videos below show an experiment where the time delay in a
feedback loop was varied. The experiment involves balancing
an pendulum in the inverted (upright position), by moving the
base of pendulum according to a prescribed control law. The
law is guaranteed to stabilize the system when there is no time
delay, but when there is a time delay instability can arise.
More detail can be found in the associated paper.
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| This video shows the behaviour when there is no time delay in the feedback. The pendulum is maintained in the vertical position, even if there are disturbances in the system. |
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| This shows the behaviour when there is a small time delay in the feedback. For delays less than about 0.062 seconds, pendulum is still maintained in the vertical position. When the system is disturbed, the pendulum oscillates, but the oscillations eventually die down and the pendulum returns to the vertical position. |
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| This shows the behaviour when there is a large enough time delay in the feedback. At a delay of about 0.062 seconds, a bifurcation occurs in the system. The inverted position is no longer stable and the pendulum oscillates with constant amplitude. This indicates that a delay-induced Hopf bifurcation has occurred in the system. |
The experimental without delay was designed and manufactured by Quanser. Details about the experimental setup can be found here.