Tham khảo tài liệu 'nano - and micro eelectromechanical systems - . lyshevski part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The total kinetic energy of the mechanical system which is a function of the equivalent moment of inertia of the rotor and the payload attached is expressed by GM y Jq 3 Then we have G G GM y Lsqi Lsrqiq2 y Lrq2 y Jq3 The mutual inductance is a periodic function of the angular rotor . . NN displacement and Lsr ỡr  Q The magnetizing reluctance is maximum if the stator and rotor windings are not displaced and Âm Qr is minimum if the coils are displaced by 90 degrees Then L min L Q L where L _ NN and srmi sr r srmax srmax Âm 90o L NsNr srmm Âm 0 The mutual inductance can be approximated as a cosine function of the rotor angular displacement The amplitude of the mutual inductance between NN the stator and rotor windings is found as LM L s r M sr max Âm 90 Then Lsr qr LM cosQr LM cosq3 One obtains an explicit expression for the total kinetic energy as r y Lsqi LMqiq2 cosq3 y Lrq2 y Jq3. The following partial derivatives result - . - Lsqi LMq2 cosq3 fqi fqi 0 LMqi cosq3 Lrq2 fq2 fq 2 LMqiq2 slnq3 Jq3 fq3 fq3 The potential energy of the spring with constant ks is n 2 ksq Therefore ffP 0 Ểr 0 and It k-q-- fqi fq2 fq3 2001 by CRC Press LLC The total heat energy dissipated is expressed as D DE DM where DE is the heat energy dissipated in the stator and rotor windings DM is the heat energy dissipated by mechanical ỳ Bmql rrq2 and 3D Bmq3 3q3 DE 2 rq 2 rrq2 system DM 2 BmqM Hence D 2 ifi 2 r One obtains 3D r 3D 3qi s 3q2 Using qi q2 q3 r qi i q2 i q3 Wr s s Qi Us Q2 Ur and Q3 -TL we have three differential equations for a servo-system. In particular L LM cos 0 id - LMi sin 0 id rr us s Ml r Ml r r s s s dt dt dt LrdiD LM cos r - LmÌ sin r il r3r Ur dt dt dt J C dt LMisir sin r Bm tr k r -TL The last equation should be rewritten by making use the rotor angular velocity that is d r M w dt r Finally using the stator and rotor currents angular velocity and position as the state variables the nonlinear differential equations in Cauchy s form are found as dis _ - rsLris - 2LMiswr .