High Performance Control of AC Drives with Matlab / Simulink Models

8.3 Sensorless Control of PMSM

The rotor speed and produced torque can be computed using the Luenbergera back emf observer. Assuming that the dynamics of the mechanical system are much slower than the dynamics of the electric variables, we may assume that the motor back emf does not change during an observer sampling period, so that

(8.49)

(8.50)

The used Luenberger observer for the PMSM back emf in the stationary αβ frame is described as [63,64,67]

(8.51)

(8.52)

(8.53)

(8.54)

where ^ is the estimated value; L_s is the stator inductance, assuming that L_s = L_d; and K_iα, K_iβ, K_eα, K_eβ, are observer gains (when using symetrical motor K_iα = K_iβ = K_i, K_eα = K_eβ = K_e).

The state variables in the observer are stator currents i_α, i_β; however, the back emf signals e_α, e_β are disturbances that should be identified in the observer. The block showing such an operation is illustrated in Figure 8.14 ...