Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

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Direct Torque Control with Space Vector Modulation After differentiating of the above equation one obtains: 2 sy sy Ls sy = Rs + Ψ s + pb Ψ PM dU dI d I dΩm ( ) dt dt dt dt Take into account that from equation (5.61) the y-axis current is equal I sy (5.69) 2M e = 3p Ψ , b s dΩ m 1 = ( M e − M l ) and under assumption that the motor is no loaded equation (5.69) takes dt J form: dU dM L d M p ( ) dt p dt p dt J 2 sy 2 e s 2 e b = Rs + Ψ s + M e 3 b Ψs ΨPM 3 b Ψs (5.70) Using Laplace transformation and after some arrangements the equation (5.70) can be written: 2Ls 2 2R Ψs p s b sU sy = M e ( s + s + ) 3p Ψ 3p Ψ J b PM b s (5.71) Hence, the transfer function between electromagnetic torque be obtained as: G M e M 2 sy() M M M e and y-axis voltage U sy can M () s A s () s = = U s s + B s+ C (5.72) Where: A M 2 3pbΨ PM RsΨ 3 Ψ PM s ΨPM pb = and BM = CM = 2L Ψ L 2JL s s s s Using the motor parameters (see Appendices) we may calculates: A = 198 , B = 115.3 and C = 9065 M M M Continuous s-domain The torque control loop of the block scheme DTC-SVM from Fig. 5.25 is shown in Fig. 5.35, where CM ( s ) is a transfer function of the PI controller given by equation 5.28: 100
Direct Torque Control with Space Vector Modulation M e _ ref U sy C () M s GM () s M e Figure 5.35. Block diagram of torque control loop in s-domain. The transfer function of torque control loop is obtained as: G M _ closed () s M () s C () s G () s e_ ref M M = = (5.73) M e() s 1 + CM() z GM() s Substituting in equation (5.73) transfer function for CM ( s) -Eq.5.28 and GM ( s) - Eq.5.72 we may calculate: KiM AMKpM( s+ ) K pM GM _ closed() s = = 2 s + ( B + K A ) s+ C + K A M pM M M iM M (5.74) Discrete design z −1 Using backward difference method for discretization process ( s = ) the transfer function Tz for discrete PI controller is expressed as: s K pM ( z − ) Tz KpM + K s iM CM( z) = KpM(1 + ) = ( KpM + KiM) T ( z−1) ( z−1) iM (5.75) Where: K iM K pM = Ts - integration gain; s TiM T - sampling time 101
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POLITECHNIKA WARSZAWSKA WARSAW UNIV
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Contents Table of Contents Chapter
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Introduction Chapter 1 INTRODUCTION
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Introduction to surface-mounted mac
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Introduction vector control, which
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Introduction presented and studied.
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Modeling and control modes of PM sy
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Voltage source PWM inverter for PMS
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Page 53 and 54: Voltage source PWM inverter for PMS
Page 55 and 56: Voltage source PWM inverter for PMS
Page 57 and 58: Control methods of PM Synchronous m
Page 69 and 70: Direct Torque Control with Space Ve
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DSP implementation of DTC-SVM contr
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Summary and closing conclusion Chap
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Appendices APPENDICES A1 Rotor and
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Appendices ⎡ ⎤ ⎢ 1 0 ⎥ ⎡K
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Appendices i(t1->t0)+=it1 it1: it1=
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Appendices A7 PWM technique - six s
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List of symbol List of symbols Symb
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References Books and PhD-Thesis 1.
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References 39. J.-I. Itoh, N. Nomur
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References 74. N. Ertugrul, P. Acar
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References 108. D. Świerczyński,
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