By Bodgan Wilamowski, J. David Irwin

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Extra resources for Control and Mechatronics (The Industrial Electronics Handbook)

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The LC intersects the Poincaré plane at point Pk called Fixed Point (FP). It plays a crucial role in nonlinear dynamics. Instead of investigating the behavior of the LC, the FP is studied. 2 Poincaré Map Function (PMF) After moving the trajectory from the LC by a small deviation, the discrete Poinearé Map Function (PMF) relates the coordinates of intersection point Pn to those of the previous point Pn−1. All points are the intersection points in the Poincaré plane generated by the trajectory. 6 Stable limit cycle and the Poincaré plane (N = 3).

The DCC consists of a Sample&Hold (S&H) unit, a reference frame transformation transforming the three-phase current i–s from SRF to RRF with – – d–q coordinates, a proportional-integral (PI) digital controller with complex parameters K0 and K1 – including a saturation function – s (y ) to avoid overmodulation in VSC, and a SVM algorithm. Suffix m denotes the discrete-time index, and the z−1 blocks delay their input signals with one sampling period Ts. The SVM has to generate a switching sequence with proper timing of state changes in VSC over a fixed modulation period that equals to Ts.

233–244, 2000. ) is the sixth of the period of vector e–s, m = 1, 2… The bifurcation parameter is the ratio ro/r i . A beautiful period-doubling cascade can be seen. 1307. 1281, the period is doubled. The response remains periodic with second-order subharmonic oscillation. 1281 and fourth-order subharmonic appears. After a series of period doubling at successively closer border values of ro/r i, the system trajectory finally becomes chaotic. 37b presents the Lyapunov exponent for the region of the period-doubling cascade showing that at the bifurcation points, the Lyapunov exponent becomes zero.

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