3-Phase BLDC Motor Sensorless Control Using MC56F8013

Mathematical Description of the BLDC MotorThe equations Equation 2-4 can be rewritten taking into account the motor phase resistance and theinductance. The mutual inductance between the two motor phase windings can be neglected because itis very small and has no significant effect for our abstraction level.where;R s, L su VAu VBu VC–––u backEMFau backEMFbu backEMFcCc1di– -- u3 Vx – u backEMFx R s i Sa L Sa= + s--------(2-5)dt∑x = AC∑x = ac1di– -- u3 Vx – u backEMFx R s i Sb L Sb= + s---------dt∑x = AC∑x = ac1di– -- u3 Vx – u backEMFx = R s i Sc + L Scs--------dt∑x = A∑x = aphase resistances and inductancesThe internal torque of the motor itself is defined as:where;T iω,θψ Sxc1T i = --- uω∑backEMFx ⋅ i Sx = -----------∑⋅ idθ Sx(2-6)x = acx = adψ Sxinternal motor torque (no mechanical losses)rotor speed and rotor positionmagnetic flux of phase winding xIt is important to understand how the back-EMF can be sensed and how the motor behavior depends onthe alignment of the Back-EMF to commutation events. This is explained in the next sections.2.3.3 Back-EMF SensingThe back-EMF sensing technique is based on the fact that only two phases of a BLDC motor areenergized at a time (see Figure 2-2). The third phase is a non-fed phase that can be used to sense theback-EMF voltage.Consider the situation when phases A and B are powered and phase C is non-fed. No current passesthrough phase C. Assume the following conditions are met:S Ab, S Bt← PWMswitching11u VA= +−--u2 d, u VB= ± --u 2 di Sa= – i Sb, i Sc= 0,di Sc= 0u backEMFa+ u backEMFb+ u backEMFc= 0(2-7)The branch voltage u VC can be calculated when considering the above conditions:3u VC= --u2 backEMFC(2-8)3-Phase BLDC Motor Sensorless Control using MC56F8013, Rev. 0Freescale Semiconductor 19