By Jacek Kabziński
This contributed quantity is written by way of key experts operating in multidisciplinary fields in electric engineering, linking keep watch over conception, strength electronics, man made neural networks, embedded controllers and sign processing. The authors of every bankruptcy record the state-of-the-art of many of the themes addressed and current result of their very own learn, laboratory experiments and profitable purposes. The offered suggestions pay attention to 3 major parts of interest:
· movement regulate in advanced electromechanical platforms, together with sensorless control;
· fault prognosis and fault tolerant keep watch over of electrical drives;
· new keep watch over algorithms for strength electronics converters.
The chapters and the whole booklet own robust monograph attributes. vital useful and theoretical difficulties are deeply and safely provided at the heritage of an exhaustive state-of the artwork evaluate. Many effects are thoroughly new and have been by no means released ahead of. recognized keep an eye on tools like box orientated regulate (FOC) or direct torque keep an eye on (DTC) are referred as a place to begin for differences or are used for comparability. between a number of keep an eye on theories used to unravel specific difficulties are: nonlinear keep an eye on, powerful keep an eye on, adaptive regulate, Lyapunov innovations, observer layout, version predictive regulate, neural keep watch over, sliding mode keep watch over, 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
The velocity will be the ‘virtual control’ for position tracking. Let us consider the error equation: e_ x ¼ x_ d À v ð14Þ and the desired ‘virtual control’ trajectory vd with the tracking error deﬁned as: ev ¼ vd À v: ð15Þ The desired ‘virtual control’ vd will be designed to guarantee the required convergence of the error ex . Considering the following QLF: 1 V1 ¼ e2x 2 ð16Þ allows one to conclude that the desired ‘virtual control’ vd : vd ¼ x_ d þ kx ex ; ð17Þ where kx [ 0 is a design parameter, will generate the tracking error dynamics: e_ x ¼ x_ d À x_ d À kx ex þ ev ¼ Àkx ex þ ev ð18Þ V_ 1 ¼ Àkx e2x þ ex ev ð19Þ and: and so will assure stability if v ¼ vd : During the second stage of the backstepping procedure the velocity error ev is considered: Adaptive Position Tracking with Hard Constraints … l_ev ¼ l_vd À l_v ¼ l_vd À i þ ATo n ¼ Ài þ AT1 n1 ; 33 ð20Þ where the new variables are deﬁned as: Â Ã AT1 ¼ l; ATo ; nT1 ¼ ½_vd ; nT : ð21Þ The derivative of the reference speed is given by: v_ d ¼ €xd þ kx ðÀkx ex þ ev Þ; ð22Þ so, fortunately, it is available for the control algorithm, and hence ξ1 in (21) is a known function.
The selection of certain vectors for developing models of the induction motor may results in particular beneﬁts. The induction motor model with a main flux vector is especially convenient because this makes it possible to control the saturation of main magnetic path. The application of nonlinear transformation to the stator current and main flux vectors makes it possible to deﬁne following variables: q11ðnÞ ¼ xrðnÞ ; ð44Þ q12ðnÞ ¼ wmaðnÞ isbðnÞ À wmbðnÞ isaðnÞ ; ð45Þ Sensorless Control of Polyphase Induction Machines 15 q21ðnÞ ¼ w2maðnÞ þ w2mbðnÞ ; ð46Þ q22ðnÞ ¼ wmaðnÞ isaðnÞ þ wmbðnÞ isbðnÞ : ð47Þ The differential equation for the multiscalar model variables deﬁned by formulae (44)–(47) are as follows: n dq11ð1Þ 1 X 1 ¼ q À m0 ; J 1 12ðnÞ J ds ð48Þ dq12ðnÞ 1 ¼À q À d8ðnÞ i2sðnÞ q11ðnÞ Tm1ðnÞ 12ðnÞ ds þ d11ðnÞ q22ðnÞ þ d4ðnÞ q21ðnÞ q11ðnÞ þ d12ðnÞ u12ðnÞ : ð49Þ dq21ðnÞ ¼ 2d7ðnÞ q21ðnÞ þ 2d6ðnÞ q22ðnÞ þ 2d10ðnÞ u21ðnÞ : ds ð50Þ dq21ðnÞ 1 ¼À z22ðnÞ þ d2ðnÞ q21ðnÞ þ d6ðnÞ i2s À d11ðnÞ q12ðnÞ q11ðnÞ þ d12ðnÞ u22ðnÞ ; Tm1ðnÞ ds ð51Þ where i2sðnÞ ¼ q21ðnÞ ; ð52Þ wðnÞ ; RsðnÞ LrðnÞ þ RrðnÞ LsðnÞ ð53Þ LrrðnÞ LmðnÞ þ LrsðnÞ LrðnÞ ; wðnÞ ð54Þ LmðnÞ : wðnÞ ð55Þ Tm1ðnÞ ¼ d11ðnÞ ¼ q212ðnÞ þ q222ðnÞ d12ðnÞ ¼ u12ðnÞ ¼ wraðnÞ usbðnÞ À wrbðnÞ usaðnÞ ; ð56Þ u21ðnÞ ¼ wmaðnÞ usaðnÞ þ wmbðnÞ usbðnÞ ; ð57Þ u22ðnÞ ¼ wraðnÞ usaðnÞ þ wrbðnÞ usbðnÞ : ð58Þ The control variables u12ðnÞ and u21ðnÞ are determined in the control system and the voltage vector components for the control of an inverter are calculated as follows: 16 Z.
In particular, the model of the ‘squirrel cage’ induction motor contains one differential equation for the rotor flux without a control variable on the right hand side. It is possible to change the induction model variables using liner transformation. Different vectors may be used in the mathematical model even without a known physical meaning. If the rotor flux vector does not appear in the motor model, the control variable is present on the right hand side of all of the differential equations.