Control-based continuation of dry friction oscillator --- Animation
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Authors
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Jan Sieber, Bernd Krauskopf

(Bristol Centre For Applied Nonlinear Mathematics, Department of
Engineering Mathematics, Queen's Building, University of Bristol,
University Walk, Bristol BS8 1TR, United Kingdom)

Summary
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The animation shows the control-based continuation of the family of
unstable periodic orbits for the idealized setup of the dry friction
oscillator. It is based on data obtained in a computer simulation.

Description of the animation of the experiment
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The mass block is attached to an actuator (on the right) by a
spring. The belt is moving to the right. The motion of the actuator
exerts a feedback control, which is based on the difference between
the measured position and velocity of the block and the control
target. Whenever the motion of the actuator has a small amplitude the
feedback control is non-invasive and the motion of the block
corresponds to a natural (unstable) periodic orbit of the uncontrolled
dry friction oscillator. Transients always remain small during the
whole continuation due to the gradual change of control targets and
parameters and the appropriate choice of the phase condition.

Diagrams in the background 
-------------------------- 

The right diagram shows the current (magnified) time profile of the
motion of the actuator. Whenever a black vertical line occurs the
amplitude of the actuator motion has been accepted as small (below
tolerance=0.005) in the subsequent two periods.

The left diagram shows the one-parameter bifurcation diagram (in the
plane of belt velocity vs. maximal velocity of control target for the
motion of the block) as it is built up gradually. Each large red dot
corresponds to a new control target and parameter value for the belt
velocity.  The small black dots correspond to accepted natural
periodic orbits, which then gradually complete the bifurcation diagram
during the continuation.