An experimental application of the anticontrol of Hopf bifurcations

D. M. ALONSO; E. E. PAOLINI; J. L. MOIOLA

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

World Scientic Publishing Company

Año: 2001 vol. 11 p. 1977 - 1988

0218-1274

The control of nonlinear systems exhibiting bifurcation phenomena has been the subject of active research in recent years. Contrary to regulation or tracking objectives common in classic control, in some applications it is desirable to achieve an oscillatory behavior. Towards this end, bifurcation control aims at designing a controller to modify the bifurcative dynamical behavior of a complex nonlinear system. Among the available methods, the so-called anti-control" of Hopf bifurcations is one approach to design limit cycles in a system via feedback control. In this paper, this technique is applied to obtain oscillations of prescribed amplitude in a simple mechanical system: an underactuated pendulum. Two diferent nonlinear control laws are described and analyzed. Both are designed to modify the coeficients of the linearization matrix of the system via feedback. The rst law modi es those coeficients that correspond to the physical parameters, whereas the second one changes some null coeficients of the linearization matrix. The latter results in a simpler controller that requires the measurement of only one state of the system. The dependence of the amplitudes as function of the feedback gains is obtained analytically by means of local approximations, and over a larger range by numerical continuation of the periodic solutions. Theoretical results are contrasted by both computer simulations and experimental results.