Version 4 SHEET 1 2928 1376 WIRE -64 528 -144 528 WIRE 112 528 16 528 WIRE 112 560 112 528 WIRE 112 672 -144 672 WIRE 112 672 112 640 WIRE 416 528 384 528 WIRE 544 528 496 528 WIRE 672 528 624 528 WIRE 672 592 672 528 WIRE 672 720 416 720 WIRE 672 720 672 672 SYMBOL res 32 512 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R SYMATTR Value "" SYMBOL ind 96 544 R0 WINDOW 0 44 28 Left 0 WINDOW 3 -144 89 Left 0 SYMATTR InstName Theta SYMATTR Value n*dphi/dt SYMBOL res 512 512 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R1 SYMATTR Value "" SYMBOL ind 528 544 R270 WINDOW 0 52 106 VTop 0 WINDOW 3 263 -67 VBottom 0 SYMATTR InstName Theta SYMATTR Value "" SYMBOL bi2 672 592 R0 WINDOW 3 4 87 Left 0 SYMATTR InstName B1 SYMATTR Value e=i*omega*dl/dteta TEXT -176 528 Left 0 ;i TEXT -200 624 Left 0 ;u TEXT 216 616 Left 0 ;= TEXT 344 528 Left 0 ;i TEXT 368 664 Left 0 ;u TEXT 528 584 Left 0 ;l(teta)*di/dt TEXT -208 720 Left 0 ;One phase SR electrical model TEXT 328 760 Left 0 ;Induced voltage breakout in linear rate TEXT -200 -280 Left 0 ;Translation Mr MULTON's Bernard paper entitled:\n TEXT -200 -200 Left 0 ;2.1 Electrical model:\n \nIn order we analyze, dimention and simulate such a motor controller, we need refer to an electrical model.\nAs far we supposed magnetic interphase coupling very low, we can define only a single phase model.\nThat model embeds the winding resistance and the the induced voltage tied to the current and inductance variation. see Pic below . TEXT -200 -48 Left 0 ;Electrical equations can be written: TEXT -200 32 Left 0 ;Where PHI is the total flux embeded by all the phase winding turns.\n \nIn linear rate we can write: TEXT -208 168 Left 0 ;Then: TEXT -200 248 Left 0 ;And in permanent rate, at omega = Constant. TEXT -200 344 Left 0 ;We can see the last term is a serial type electromotive force, given it is proportional \nto the current and the rotation speed. In a non saturated machine fed by a constant current\nthe electromotive force has the same shape as the instantaneous torque; by the way\ntorque and electromotive force are both proportional to the inductance derivative. TEXT -216 800 Left 0 ;In saturated rate we can write:\n \nConsidering for example the inductance is function of the position and the current: TEXT -216 984 Left 0 ;Or in a different way: TEXT -216 1064 Left 0 ;The second term is proportional to the incremental inductance and the third is still the electromotive force. TEXT -200 -8 Left 0 ;u = R * i + n * dphi / dt = R * i + dPHI / dt TEXT -200 128 Left 0 ;PHI = l (Theta , i) "l" is lower case L TEXT -200 208 Left 0 ;u = R *i + l (Theta )* di / dt + i * omega * dl / dTheta TEXT -200 296 Left 0 ;u = R * i + l (Theta) * di / dt + i * omega * dl / dTheta TEXT -216 896 Left 0 ;PHI = l (Theta, i) *i TEXT -216 936 Left 0 ;u = R * i + l (Theta , i ) * di / dt + i * ( @ l / @Theta * dTheta / d t + @ l / @ i * d i / d t) TEXT -216 1024 Left 0 ;u = R * i + @PHI / @i * di / dt + @ PHI / @Theta * omega. TEXT 128 488 Left 0 ;Theta = Rotation angle LINE Normal 144 592 80 624 LINE Normal 144 592 144 592 LINE Normal 160 592 144 592 LINE Normal 64 656 64 592 LINE Normal 64 592 64 592 LINE Normal 64 592 64 592 LINE Normal 48 608 64 592 LINE Normal 48 608 48 608 LINE Normal 64 608 64 592 LINE Normal 64 592 64 608 LINE Normal 80 608 64 592 LINE Normal -160 512 -144 528 LINE Normal -160 544 -160 512 LINE Normal -160 544 -160 544 LINE Normal -160 544 -160 544 LINE Normal -144 528 -160 544 LINE Normal 80 608 48 608 LINE Normal 80 608 80 608 LINE Normal -208 672 -208 544 LINE Normal -224 560 -208 544 LINE Normal -192 560 -224 560 LINE Normal -208 544 -192 560 LINE Normal 320 576 320 576 LINE Normal 592 496 592 496 LINE Normal 720 560 720 560 LINE Normal 720 560 720 560 LINE Normal 704 576 704 576 LINE Normal 368 512 384 528 LINE Normal 368 544 368 512 LINE Normal 368 544 368 544 LINE Normal 368 544 368 544 LINE Normal 384 528 368 544 LINE Normal 608 560 608 560 LINE Normal 360 712 360 584 LINE Normal 344 600 360 584 LINE Normal 376 600 344 600 LINE Normal 360 584 376 600 LINE Normal 624 496 544 544 LINE Normal 656 496 624 496 LINE Normal 672 496 672 496 LINE Normal 560 560 624 560 LINE Normal 560 560 560 560 LINE Normal 560 560 560 560 LINE Normal 544 560 560 560 LINE Normal 560 544 544 560 LINE Normal 560 576 560 544 LINE Normal 544 560 560 576 RECTANGLE Normal 1056 -224 -208 -304