By Jacek Kabziński
This contributed quantity is written through key experts operating in multidisciplinary fields in electric engineering, linking regulate concept, energy electronics, synthetic neural networks, embedded controllers and sign processing. The authors of every bankruptcy file the state-of-the-art of many of the issues addressed and current result of their very own learn, laboratory experiments and profitable purposes. The offered options pay attention to 3 major parts of interest:
· movement keep watch over in advanced electromechanical platforms, together with sensorless control;
· fault analysis and fault tolerant keep an eye on of electrical drives;
· new regulate algorithms for strength electronics converters.
The chapters and the full e-book own robust monograph attributes. very important useful and theoretical difficulties are deeply and competently offered at the historical past of an exhaustive state-of the paintings evaluation. Many effects are thoroughly new and have been by no means released ahead of. famous keep an eye on equipment like box orientated keep watch over (FOC) or direct torque keep watch over (DTC) are referred as a place to begin for ameliorations or are used for comparability. between various keep an eye on theories used to unravel specific difficulties are: nonlinear regulate, powerful regulate, adaptive keep an eye on, Lyapunov ideas, observer layout, version predictive regulate, neural regulate, sliding mode keep an eye on, sign filtration and processing, fault analysis, and fault tolerant control.
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Extra resources for Advanced Control of Electrical Drives and Power Electronic Converters
Therefore, instead of (38), the Lyapunov function: V2 ¼ V1 þ À Á 1 T À1 l e C A e 1; tan Ke2v þ A 2K 2 1 K¼ p 2D2ev ð44Þ will be used, where V1 deﬁned in (32) is a BLF and Dev is a constraint imposed on the tracking error ev . The Lyapunov function derivative may be represented as: À À ÁÁ ~_ 1 e T CÀ1 A V_ 2 ¼ V_ 1 þ lev 1 þ tan2 Ke2v e_ v þ A 1 ð45Þ and plugging in (36) and (20) results in: À À ÁÁ À À ÁÁ V_ 2 ¼ Àkx e2x 1 þ tan2 ke2x þ ev ex 1 þ tan2 ke2x À À ÁÁÀ Á e T CÀ1 A ~_ 1 : þ ev 1 þ tan2 Ke2v Ài þ AT1 n1 þ A 1 ð46Þ Once again, the control variable i will be designed to compensate the unnecessary components in (46) and to introduce the stabilizing component, so: i¼ ^ T n1 A 1 À Á 1 þ tan2 ke2x À Á þ kv ev ; þ ex 1 þ tan2 Ke2v ð47Þ where kv [ 0 is a design parameter.
As it can be seen in the last chart of Fig. 6 the third harmonic of the stator current appearing in the second plane has a different angle in relation to the fundamental in consecutive time intervals. The angle depends on the machine torque. For the very low torque only the magnetizing current components appear in the phase current. For high values of the torque the active current is great and the third harmonic generated in second plane is synchronized with such the angle that the maximum value of the phase current is increased.
The tracking errors ex ; ev converge to zero asymptotically. Sketch of the proof: 1. V2 ð0Þ is bounded and as V_ 2 0, hence V2 ðtÞ\V2 ð0Þ along the considered trajectory. Lemma 1 yields that jex ðtÞj\Dex and jev ðtÞj\DÀev . Another constraint Á V2 ð0Þ and thus for the tracking error may be obtained noticing that 2k1 tan ke2x qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ À 2Á l 2 ð0ÞÞ . Similarly, and so V2 ð0Þ jex j Dex 2atanð2kV 2K tan Kev p qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 ð0Þ=lÞ . Using analogical reasoning, it can be derived that jev j Dev 2atanð2KV p Adaptive Position Tracking with Hard Constraints … 39 rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2V2 ð0Þ , where kmin ðÃÞ denotes the smallest eigenvalue of the symkmin ðCÀ1 Þ metric matrix Ã.
Advanced Control of Electrical Drives and Power Electronic Converters by Jacek Kabziński