Name
Abstract | ||
|---|---|---|
In this paper we prove the general result that, given a linear system. (x) over dot = Ax + u where A is hyperbolic, u is piecewise linear and L-periodic, with integral(L)(0)u(t)dt = 0, then there exists a unique L-periodic solution x = x(p)(t) such that integral(L)(0)x(p)(t)dt = 0. We then consider a DC/DC buck (step-down) converter controlled by the ZAD (zero-average dynamics) strategy. The ZAD strategy sets the duty cycle, d (the length of time the input voltage is applied across an inductance), by ensuring that, on average, a function of the state variables is always zero. The two control parameters are v(ref), a reference voltage that the circuit is required to follow, and k(s), a time constant which controls the approach to the zero average. We show how to calculate d exactly for a periodic system response, without knowledge of the state space solutions. In particular, we show that for a T-periodic response d is independent of ks. We calculate period doubling and corner collision bifurcations, the latter occurring when the duty cycle saturates and is unable to switch. We also show the presence of a codimension two nonsmooth bifurcation in this system when a corner collision bifurcation and a saddle node bifurcation collide. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1142/S0218127409022907 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS |
Keywords | DocType | Volume |
Averaging method, nonsmooth bifurcation, DC/DC converters, control theory | Journal | 19 |
Issue | ISSN | Citations |
1 | 0218-1274 | 3 |
PageRank | References | Authors |
0.59 | 3 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| E. Fossas | 1 | 17 | 4.80 |
| S. J. Hogan | 2 | 17 | 3.74 |
| T. M. Seara | 3 | 9 | 1.60 |