3-Phase BLDC Motor Sensorless Control Using MC56F8013

Tuning7.5.5.6 PI AlgorithmThe PI algorithm in continuous time domain:1ut () = K e()t + ---- e( τ) dτT I∫τ0(7-1)et () = wt ()–yt ()(7-2)The transfer function is shown below:Fp ( ) = K 1 +1----T I1⋅ --p= ----------up ( )ep ( )(7-3)The PI algorithm in discrete time domain in fractional arithmetic:Tu f ( k) = K sc ⋅ e f ( k) + u If( k – 1) + K Isc ⋅ ---- ⋅e f ( k)T I(7-4)ek ( ) = wk ( )–yk ( )(7-5)whereu f ( k) = uk ( ) ⁄ u maxw f ( k) = wk ( ) ⁄ w maxy f ( k) = yk ( ) ⁄ y maxe f ( k) = ek ( ) ⁄ e max(7-6)(7-7)(7-8)(7-9)K sc K e max= ⋅ ----------u maxe maxK Isc = K ⋅ ----T ⋅ ----------T I u max(7-10)(7-11)3-Phase BLDC Motor Sensorless Control using MC56F8013, Rev. 088 Freescale Semiconductor