The complex dynamics of a pendulum controlled by a Proportional-Derivative (PD) compensator are analyzed. A classification of equilibrium points and the characterization of their bifurcations is also presented. It is shown that the controlled pendulum may exhibit a chaotic behavior when the desired position is periodic and the proportional gain and total dissipation are small enough.

1.
Hale, J., and Koc¸ak, H., 1991, Dynamics and Bifurcations, Springer-Verlag.
2.
Lichtenberg, A. J., and Lieberman, M. A., 1992, Regular and Chaotic Dynamics, 2nd. Ed., Springer-Verlag.
3.
Marsden, J. E., 1994, “Geometric Mechanics, Stability, and Control,” Trends and Perspectives in Applied Mathematics, L. Sirovich, ed., Springer-Verlag.
4.
Perko, L., 1991, Differential Equations and Dynamical Systems, Springer-Verlag.
5.
Takegaki
M.
, and
Arimoto
S.
,
1981
. “
A New Feedback Method for Dynamic Control of Manipulators
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
103
, pp.
119
125
.
6.
Wiggins, S., 1988. Global Bifurcations and Chaos. Analytical Methods, Springer-Verlag.
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