Control and Mechatronics (The Industrial Electronics by Bodgan Wilamowski, J. David Irwin

By Bodgan Wilamowski, J. David Irwin

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9 Example for (a) frequency-locked and (b) quasi-periodic state. © 2011 by Taylor and Francis Group, LLC 1-14 Control and Mechatronics coincides with the starting point 0 as three times 120° is 360°. The process is periodic, the trajectory closes on itself, it is the F-L state. , p/q = 2π as long as the point P makes one rotation around circle R, it completes 2π rotations around circle r. 28). After any further full rotations around circle R, the phase shifts of the intersection points from P0 on the Poincaré plane remain irrational; therefore, they will never coincide with P0, and the trajectory will never close on itself.

Note also that it lies in a bounded region of state space. 1 The System The objective is to highlight the complex behavior of a three-phase DC–AC voltage source vonverter (VSC) controlled by a closed-loop hysteresis AC current controller (HCC) [10]. 36. It consists of a three-phase full-bridge VSC with six bidirectional switches, a simple circuit modeling the AC side, a reference frame transformation, a comparator, and the HCC. All voltage and current vectors used are three-phase space vectors.

CD Rom ISBN: 0-7803-7907-1. © [2003] IEEE. 40) K1 = where – – λ0 and λ1 are the eigenvalues of the Jacobian matrix calculated at the FP in the linear region – – F and G are complex constants – – – – Selecting λ0 and λ1 on the basis of the dynamic requirements, K0 and K1 are determined from the last – – two equations. The eigenvalues λ0 and λ1 must be inside the unit circle to ensure stable operation. 40 even within the unit circle. 5e j45° and λ1 was changed along line B1, by modifying – λ1 = μe j40° where μ is the bifurcation parameter.

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