Nonsmooth dynamics of electrical systems

Abstract

In this paper we briefly review the current knowledge on the nonsmooth phenomena in power electronic systems. We describe a method of investigating the stability of nonsmooth limit cycles, and demonstrate its application in investigating the nonsmooth phenomena in the current mode controlled boost converter-which exhibits interesting bifurcations involving tori.

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

“…In sliding, the tangential force is proportional to the normal force, ∥f t ∥= µ k ∥f n ∥, (66). In the constrained sticking mode, the force vector is calculated from Lagrange multipliers as in (65).…”

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

“…This will force n to be non zero and hence change the slope of ℎ. In this case, the switching manifold will be modified as: ℎ (X, 𝑡) = 𝐾 0 + 𝐾 1 X (𝑡) − (1 + 𝑏) 𝑀 (𝑥 1 (𝑡)) − 𝑉 𝑝 = 0, (10) where…”

“…The reason for choosing the spectral radius of the Monodromy matrix at 0.99 is to limit the transient overshoot resulting from higher values of the variable (𝑏) needed for a smaller value of the spectral radius. If the overshoot reaches a high enough value, it might hit the unstable boundary, and the response of the system will be saturated as described in [10,11]. The behavior of the system is very sensitive to the initial conditions.…”

“…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][13][14][15]. In these papers, we reported creation of a two-loop torus through a Neimark-Sacker bifurcation occurring on a period-2 orbit.…”