What form of control function can drive a discontinuous-mode boost converter to chaos via period-doubling? (English)
Int. J. Circuit Theory Appl. 26, No.3, 281-286 (1998).
From the introduction: The authors establish a condition on the form of a control function that may give rise to period-doubling cascades in the boost regulator operating in discontinuous mode. In [{\it C. K. Tse}, IEEE Trans. Circuit Syst. I, CAS-41, 16-23 (1994)], a closed-form iterative map that describes the dynamics of the boost regulator operating in discontinuous mode has been derived. Using this map, period-doubling cascades have been predicted when the regulator is controlled under a simple proportional feedback, the bifurcation parameter being the feedback gain. Experimental measurement bears witness to the predicted chaos. Although the work op. cit. gives no theoretical insights into the underlying cause of chaos in such systems, it does prompt the important practical question of what form of feedback control may give rise to chaotic behavior. This letter attempts to answer this question in the light of the Schwarzian derivative.