The control of SRM drives depends on the phase current, rotor position and rotor speed signals to obtain closed-loop control of current, torque and speed. Concerning the feedback signals for the control, current and rotor position can be physically measured with good accuracy using the present sensor technology. One note, the rotor position is definitely needed for the commutation control. However, the position sensor has many demerits due to high cost, installation expense and system reliability reduction. Using a position sensor could be a decisive drawback in applications, where cost and reliability play a crucial role. There have been many attempts in the past to eliminate the position sensor by applying indirect position estimation techniques instead of encoders and resolvers. Comprehensive overviews of published works concerning rotor position estimating methods and sensorless control techniques are summarized in [4], [8], [9], [22] and [74]. Nevertheless, the sensorless operation often has a degraded drive performance and requires more complexity of the control, which is the price to be paid for eliminating position sensor.
For the position sensorless operation, an instantaneous torque control as it is used in the presented simulation model should operate on the basis of measured electrical terminal quantities i.e. current and voltage. From the phase voltage vph, the flux-linkage can be indirectly determined by rearranging the voltage equation:
( )
∫
−= v t R t i t dt
t ph ph ph
ph( ) ( ) ( ) ( )
ψ (4.3)
Since the phase current and flux-linkage are available, the position estimation is developed on the current-flux-linkage method. Due to its simplicity, this method can be implemented with a short computation time. A potential error source is the unknown phase resistance Rph in (4.3).
In praxis, its value varies with temperature and losses during operation. Despite this fact, most of the flux-linkage estimations in literature were implemented by assuming a constant phase resistance [76], [89], [99], [109] and [130]. With the assumption that the flux-linkage reaches zero at the end of the phase excitation as the current reaches zero at time t0, (4.3) can be used for online phase resistance estimation [86]:
∫
Implementing this procedure into an analog circuit and a Digital Signal Processor (DSP) platform requires generating a reset signal for the integrators at the end of the stroke excitation by a phase active period signal. At the same instant, the values of voltage and current integral must be sampled and phase resistance is determined by the DSP. It is expected that the variation of Rph can be compensated by this method and the accuracy of the flux-linkage is improved. From the predicted or measured machine characteristics it is possible to determine the rotor position by using current and flux-linkage. Derived from the relationships ψ(i,Θ) and T(i,Θ), a rotor position characteristic as a function current and flux-linkage Θ(i,ψ) can be obtained, which is shown in Fig. 4.9. Using this Θ(i,ψ) curves the rotor position can be indirectly estimated with a sufficient accuracy in a wide operating range.
Fig. 4.9 Machine characteristics: rotor position vs. current for various flux levels Θ (i,ψ) Fig. 4.10 shows the block diagram of the sensorless control strategy using flux-linkage-current method and storing these characteristics in a look-up-table. It was shown by J.P.
Lyons in [126] that the accuracy of the position estimation depends on the output gradient of the Θ(i,ψ) characteristic, especially in the range of aligned and unaligned position. That’s why during commutation a selecting function chooses the phase with the lowest gradient on
the Θ(i,ψ)-plane which will contribute to the absolute rotor position angle from all phases in order to minimize the output error.
Fig. 4.10 Function block diagram of position sensorless SRM control
For small angles near the unaligned position the Θ(i,ψ) curves are bunched very tightly in the lower left-hand corner of the graph in Fig. 4.9. Therefore, under the condition of low current and near the unaligned position, small errors in current or flux input values result in large errors in the angle estimation. Likewise, at large angles near alignment the curves are nearly vertical. Thus, near the aligned position, small errors in current input values can also cause large errors in the angle estimation. In order to overcome these problems, the resolution of the look-up table should be higher near the aligned and unaligned position. Alternatively, the position estimation on any phase should be restricted to the central region of these curves, as proposed in [126].
To determine the sensitivity of the position accuracy the position error was calculated between the ‘true’ position angle computed by means of the mechanical equation Θ=dω/dt and the total estimated angle Θest. It is shown in Fig. 4.11 with the factor 2 for the sake of clarity. In the middle period of the phase excitation the difference between the estimated and
‘true’ position angle is near zero. However there are still noticeable errors at the beginning and the end of excitation. These errors can be reasoned by two main points: The first point is that the gradient of the current in these positions is relatively high, on the other hand the resolution of the Θ(i,ψ) characteristic is insufficient near aligned and unaligned position as explained above. Hence the accuracy of the position estimation is very sensitive to interpolation errors of flux and current between the mesh points in the look-up-table. The second error source is the magnetic coupling between phases during commutation. Since the measured (or calculated) flux-linkage in the static ψ-i-characteristics neglects magnetic coupling effects, mutual coupling in the ‘real’ operation can affect the measured flux-linkage.
However, after a series of simulation experiments it was found that these small estimation
errors have only small effect on the performance of the current and torque control for SRM I under the condition of a sufficient fine resolution in the Θ(i,ψ)-plane.
Fig. 4.11 Absolute estimated position angle constructed of estimated angle from each active phase