SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

e
e
Rsin( r)
cos( )
R r
(6.15)
The model is nonlinear and cannot be described using Equations (6.8) and (6.9) unless it is
linearized somehow. In [174] the authors rely on the assumption that the mechanical time
constant is significantly less than the electrical time constant. Although this is not true for all
motors, they claim that making the assumption allows the mechanical speed to be considered a
relatively constant value as compared to the electrical quantities. Noting that the derivatives of
the bEMFs are given by Equation (6.16), they can be written in terms of the states, Equation
(6.17).
e
e
Rcos( r)
sin( )
ee
ee
R r
Then the state and output equations may be written, Equations (6.18) and (6.19).
i R/ Ls 1/
L i
s 1/ Ls
d i
R/ Ls 1/ L
i
s 1/ L
v s
dt e e
v
e e
i i
1
i
i
1
e
e The authors implement a reduced-order observer which will not be further described. 42
(6.16)
(6.17)
(6.18)
(6.19)
The observer that will be described in this report is full-order observer based on the linearized
equations above. To see how an observer is used to implement sensorless FOC, recall the block
diagram for FOC, Figure 6.9. The rotor angle must be measured by a suitable position transducer
(resolver or encoder).
42 Their observer achieved convergence within one mechanical revolution of starting, which is impressive.
A plot of the error in rotor angle estimation was not given, but by visually comparing the plots of true
versus estimated rotor position it appears the error is negligible. Finally, results are given that show
negligible position error due to 130% detuning of parameters (R, Ls).
248