Controlling Nonlinear Behavior in Current Mode Controlled Boost Converter Based on the Monodromy Matrix

Recently it has been observed that power electronic converters working under current mode control exhibit codimensional-2 bifurcations through the interaction of their slow-scale and fast-scale dynamics. In this paper, the authors further probe this phenomenon with the use of the saltation matrix instead of the Poincaré map. Using this method, the authors are able to study and analyze more exotic bifurcation phenomena that occur in cascade current mode controlled boost converter. Finally, we propose two control strategies that guarantee the stable period-one operation. Numerical and analytical results validate our analysis. 1. Introduction Power electronic circuits are normally designed to operate in a periodic steady state. The region in the parameter space where this behaviour can be obtained is delimited by various instability conditions. The nature of these instabilities has been recently understood in terms of nonlinear dynamics. In this approach, the periodic orbit is sampled in synchronism with the clock signal (called the Poincaré section), thus obtaining a discrete-time model or a map [1, 2]. The fixed point of the map signifies the periodic orbit, and its stability is given by the eigenvalues of the Jacobian matrix, computed at the fixed point. There are two basic ways in which such a periodic orbit may lose stability.(1)When an eigenvalue becomes equal to ？1, the bifurcation is called a period-doubling bifurcation, which results in a period-2 orbit. This instability is not visible in an averaged model, and so it is also called a “fast-scale” instability [3–5].(2)When a pair of complex conjugate eigenvalues assume a magnitude of 1, this bifurcation is called a Neimark-Sacker bifurcation, which results in the onset of a slow sinusoidal oscillation in the state variables. The orbit rests on the surface of a torus. This instability can be predicted using the averaged model, and so it is also called the “slow-scale” instability [6, 7]. In [8, 9], Chen, Tse, and others showed that dynamical behavior resulting from these two types of bifurcations can interact, giving rise to interesting dynamics. In our earlier papers [10, 11], we further investigated this phenomena using the technique developed in [12–15]. In these papers, we reported creation of a two-loop torus through a Neimark-Sacker bifurcation occurring on a period-2 orbit. There are complex interactions between periodic orbits, tori, and a saturation behavior, in which unstable tori play an important role. We have detected the unstable tori and have demonstrated that the sudden departure