Recent Developments of Electrical Drives - Part 17. The book stating the recent developments of electrical drives, can be useful for engineers and researchers investigating and designing electrical and electronic devices as well as for students and young researchers dealing with electrical and electronic engineering, computer sciences (advanced computer modelling, sophisticated control systems with artificial intelligence tools applied, optimal design bye use of classical and genetic algorithms employed), applied mathematics and all the topics where electromagnetic, thermal, mechanical phenomena occur | II-1. High-Frequency Position Estimators 151 By using 36 the high-frequency current vector observed from the estimated system qd is given by ldi 0r 0r Dit i0 I1 e - 6r cos it 42 - l By removing the offset I0 in 40 or in the modulus of the current in 42 and by using the inverse tangent function the argument of the exponential function in 40 or in 42 is calculated. From this result the rotor angle can be estimated. It follows from I1 in 39 that the higher the value of AL the higher the resolution of a position estimation which is already concluded for an estimator that uses PWM generated pulses. Estimation errors As mentioned before in most position estimators the magnetizing current direction is approximated by the d-axis direction. However for high loads the controller forces an important stator current along the q-axis. This means that the magnetizing current direction deviates from the d-axis. Consequently the model in 22 or 24 introduces an estimation error. Compensating this error is done in 5 6 by measuring the error during the selfcommissioning of the drive. The error can also be predicted by simulating the drive modeled with 10 with an estimator that uses a high-frequency voltage pulse train and that is based on 22 . The simulation results as a function of are presented in Fig. 5. The error on 6r is zero if the magnetizing current is aligned with one of the magnetic axes. The higher the deviation of i_m from the d-axis the higher the estimation error an increased error is shown if saturation becomes more important. However as permanent demagnetization of the magnets has to be avoided and the stator current has to be limited the results are meaningful for small deviations of from n 2 only. Figure 5. Estimation error on the rotor angle of an IPMSM as a function of for various magnetic states in the case of an approximated magnetizing current. 152 De Belie et al. Figure 6. Estimation error on the rotor angle of an IPMSM as a function of ft in the case of .
