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Basics of the Electric Servomotor and Drive - Part 4: Brushless PM Motors (conc.)

George Ellis

8/12/2008 2:50 PM EDT

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[Part 1 of this article covers basic magnetics, definitions of the motor control system elements, and an overview of electric servomotors. Part 2 examines the electrical and mechanical characteristics of permanent-magnet brush motors, as well as methods used in their control and their strengths and weaknesses. Part 3 begins a look at brushless permanent magnet motors and methods used in their control.]

15.6.4 DQ Control of Brushless PM Motors
A parallel method for phase control of brushless PM motors is direct-quadrature, or DQ, control. DQ control rearranges the system by placing commutation inside the current loop. This improves some aspects of controller performance because the commutation frequency does not pass through the current controller. Thus, phase lag caused by the current loop does not alter the commutation angle. Rather than regulating measured states (I_A, I_B, and I_C), DQ loops regulate calculated states, namely, the direct and quadrature currents, I_D and I_D.

Direct and quadrature currents produce flux in relationship to the rotor, whereas phase currents produce flux in relationship to the stator. For example, if a motor were rotating at a constant speed and with a constant torque, the phase currents (I_A, I_B, and I_C) would be varying sinusoidally, but I_D and I_D would be constant values. Phase currents are measured with respect to the stator frame of reference; a phase controller sees abundant activity in a motor spinning at high speed. DQ currents are measured with respect to the rotor frame; when DQ currents are measured on a spinning motor, there may be very little activity in the current controllers.

In DQ controllers, measured phase currents are combined to produce the state currents I_D and I_D using trigonometry to translate from the stator frame to the rotor frame:

I_Q = I_Asin(θ_E) + I_B sin(θ_E - 120°) + I_Csin(θ_E - 240°) (15.23)
I_D = I_Acos(θ_E) + I_Bcos(θ_E - 120°) + I_Ccos(θ_E - 240°) (15.24)

The direct and quadrature currents are closely related to the winding and field fluxes that have been discussed throughout this chapter. In fact, I_D generates Φ_T and I_D generates Φ_F-WINDING. Figure 15-24b is redrawn in Figure 15-28 accordingly.

Figure 15-28. Flux generated by DQ currents shown in vector form.

To better comprehend the operation of DQ control, consider the diagram in Figure 15-29, which shows a rotor in two positions, with winding flux (Φ_T) moved so that it is 90° ahead of the field flux (Φ_F) in both positions. Here the torque producing current is equal in both positions and there is no field weakening.

Figure 15-29. Two rotor positions, with the controlled flux vectors remaining constant.

Note that after 20° of rotation, the Φ_T has moved 20° with respect to the stator. However, the position of Φ_T is constant with respect to the magnet position; in both cases it is correctly aligned between the magnet poles. So while the phase currents would vary between these two positions, the quadrature current (generating Φ_T) and the direct current (generating Φ_F-WINDING = 0) would not vary.

The DQ control system is shown in Figure 15-30. The torque command (T_C) is explicitly divided down by the estimated K_T (K*_T), although this step is implicit in most drives. The quadrature current loop is closed before commutation. The direct current

Figure 15-30. Brushless DQ controller with I_D regulation.

loop is commanded to zero current at low speeds and increased for field weakening at higher speeds.

Modulation in DQ Control
15.6.4.1 Modulation in DQ Control
The output voltage commands of the current controllers (U_QC and U_DC) are first commutated and then modulated. Two phase currents are measured (the third can be formed from the other two) and combined into I_D and I_D and fed back to the current controllers.

15.6.4.2 Field Weakening DQ Control
Field weakening in DQ control it is a matter of regulating I_D as a function of speed. I_D is commanded to be zero at low speeds. When the speed increases so much that the BEMF is a large fraction of the applied bus voltage (U_BUS), the BEMF must be reduced. Increasing I_D reduces BEMF because the flux created by I_D (Φ_F-WINDING) is in opposition to the field flux, just as it was for phase control (see Section 15.6.3.4).

15.6.5 Magnetic Equations for DQ
This section will provide a brief introduction to the magnetic equations of the DQ reference frame. For a more complete discussion on this topic, readers are referred to Ref. 56. One of the benefts of the DQ reference frame is that the magnetic equations of the motor are similar to those of the brush motor (Equation 15.13). Here there are two independent current paths, one for each of the direct and quadrature currents. As with Equation 15.13, applied voltage is balanced with voltage drops in the motor:

V_Q = I_Q × R + L_Q × dI_Q/dt + Velocity × K_B - I_D × L_D × Velocity × Poles/2 (15.25)
V_D = I_D × R + L_D × dI_D/dt + I_Q × Velocity × L_Q × Poles/2 (15.26)

The parallels between Equations 15.13 and 15.25 are apparent: Both represent torque- producing current and both have resistive, inductive, and back-EMF losses. Equation 15.25 adds a fourth term, field weakening (I_D × L_D × Velocity). Here, I_D reduces the total flux, as shown in Figure 15-28. Torque is produced as a combination of the direct and quadrature currents, as shown in Equation 15.27:

T_E = K_T × I_Q + 3/2 × Poles × I_Q × I_D × (L_D - L_Q) (15.27)

The first term on the right side is equivalent to torque in the brush motor (Equation 15.10). The second term represents reluctance torque (Section 15.6.3.5). Note that this term is nonzero only when the L_D and L_Q terms differ, as in the IPM motor (Figure 15-26).

15.6.6 Comparing DQ and Phase Control
There are many parallels between phase control and DQ control. Modulation is similar, and both control methods generally require two current sensors. Angle advance in phase control is equivalent to regulating I_D in DQ controls; angle advance and DQ both work to control the commutation angle across the speed range.

Both phase-control and DQ-control current loops are usually PI loops. The key distinction in terms of the control system is that in DQ control, the commutation frequency does not pass through the current loops. As can be seen in the comparison of Figure 15-31, commutation comes before the current loops in phase control, so the commutation frequency must pass through the current loop; in DQ control, commutation is done inside the current loop, so the commutation frequency does not pass through the loop.

Figure 15-31. Schematic comparison of phase and DQ control.

Moving commutation inside the current loop allows the DQ controller to get higher torque at high speeds. In the phase-control method, the current loops attenuate the current (and, thus, torque) because the current commands contain the commutation frequency; angle advance corrects for the phase lag in the current loop but does not correct for current-loop attenuation. As long as the current loops are not driven into saturation, attenuation does not occur in DQ control; when the motor has constant torque and speed, I_D and I_D are constant and the current loops process only a DC signal.

The command format of the two methods differs because the phase controller takes the command in polar coordinates whereas the DQ controller takes the equivalent command in Cartesian coordinates. To convert from polar to rectangular, use

I_D = I_S × cos(θ_A) (15.28)
I_Q = I_S × sin(θ_A) (15.29)

To convert from rectangular coordinates to polar, use

I_S = √(I²_Q + I²_D) (15.30)
θ_A = Tan^-1(I_Q/I_D) (15.31)

Six-Step Control of Brushless PM Motor
15.7 Six-Step Control of Brushless PM Motor
An inexpensive alternative to phase control and DQ control is called six-step. Six-step control works with only one current path active at any time; for example, in one position, current may flow from phase A to phase B, but no current is allowed in phase C.

There are six combinations of current flow in a wye-connected three-phase motor, such as the motor in Figure 15-22: A to B, A to C, B to C, B to A, C to A, and C to B. Six-step commutation requires a position sensor with only the coarse resolution of 60°, electrical. Often, an inexpensive magnet ring is fitted to the rotor and three magnetic sensors, called Hall-effect sensors, are positioned along its perimeter. Commutation is performed by modifying Equations 15.17 - 15.19to accommodate the coarse resolu- tion, as shown in Equations 15.29 - 15.31. This approximation is graphed for I_AC in Figure 15-32.

Figure 15-32. Six-step approximation to a sine wave.

I_AC = T_C/K*_T for 30° < θ_E < 150°, -T_C/K*_T for 210° < θ_E < 330°,                                   (15.32)
0 elsewhere.
I_BC = T_C=K*_T for -90° < θ_E < 30° - T_C/K*_T for 90° < θ_E < 210°,                                   (15.33)
0 elsewhere.
I_CC = T_C=K*_T for 150° < θ_E < 270°, -T_C/K*_T for -30° < θ_E < 90°,                                   (15.34)
0 elsewhere.

Six-step commutation is simpler than sinusoidal commutation for several reasons. As discussed, the commutation method requires only a coarse position sensor. Because current travels through only one winding path at a time, a single current loop can be used, although different phase currents must be switched in and out of current control at different positions. In fact, six-step commutation makes brushless motors almost as easy to control as brush motors.

The chief problem with six-step commutation is torque ripple, For applications where torque ripple is of little consequence, six-step can be an appealing low-cost alternative to other commutation methods. Field weakening is used in six-step systems occasionally, especially in unidirectional motors, where the Hall sensors can be mechanically rotated slightly ahead.

15.7.1 Sensing Position for Commutation
Brushless motor drives must sense position to control the commutation angle. The most common feedback devices are encoders, resolvers, and Hall sensors. The use of encoders and resolvers for closing position and velocity loops was discussed in Chapter 14. Sensing position for those loops is much more demanding than sensing for com- mutation. However, commutation does have a few special requirements that bear discussion.

Commutation requires knowledge of rotor position with regard to the magnetic poles of the motor. For resolvers, which normally provide an absolute position within one revolution of the motor, this problem is most often solved by mechanically aligning the resolver to the magnetic poles of the motor. In that case, the electrical angle of the motor can be read from the resolver after multiplying by Poles/2 to convert the mechanical angle to electrical.

Multispeed resolvers, resolvers with multiple electrical cycles per mechanical revolution, can be used for commutation, but the poles of the motor are usually an integer multiple (including "1") of the resolver pole pairs. For example, a three-speed (six-pole) resolver mounted on a six-pole motor reads electrical angle directly.

Most industrial encoders provide incremental A/B channels: These channel output pulses indicate that the motor has moved. However, upon power-up, the electrical position of the motor cannot be determined from the A and B channels. Some encoders provide coarse "Hall channels" and an index marker, which makes a transi- tion one time for each revolution of the motor. The Hall channels allow six-step commutation upon power-up. After power-up, the drive is configured to monitor the index channel, which indicates a precise electrical position of the motor (assuming that the encoder is aligned to the magnetic poles of the motor, as it must be for the Hall tracks to work). After the index pulse is encountered, the encoder position is stored and the drive sums subsequent pulses from the A and B channels to measure the electrical position precisely. At this point, the electrical position can be determined well enough to support sinusoidal commutation.

Encoders with Hall channels work well, but there are two problems. First, many wires must be run to connect to the A, B, and index channels and to the Hall channels. Second, encoders with Hall channels are less common and frequently more expensive. This second problem can be addressed by having separate Hall sensors, but this requires a second mechanical assembly on the motor.

Another solution is to provide an initialization mode where the motor is excited by injecting current in many combinations (phase A to phase B, phase B to phase C, and so on) and then monitoring the direction in which the motor rotates to provide a crude electrical position for startup. This is sometimes called wake and shake. The drive is still configured to monitor the index channel; when the index pulse is encountered, it provides a much more accurate indication of electrical position. This is similar to having Hall sensors provide a coarse position for power-up, as discussed earlier, except the wake-and-shake method reduces wire count and does not require a special encoder. However, many applications cannot tolerate being moved about on power-up; for example, applications with vertical movement usually require full control anytime the holding brake is released.

Smart-format serial encoders, such as ENDAT encoders from Heidenhain, (www.heidenhain.com) and Hiperface encoders from Stegmann (www.stegmann.com), allow the drive to pole the motor for electrical position at power-up over a three- or four-wire communication network. These encoders reduce wire count and still support full sinusoidal commutation at power-up.

Comparison of Brush and Brushless Motors
15.7.2 Comparison of Brush and Brushless Motors
Table 15-2 provides a brief comparison of brush, sinusoidally commutated brushless, and six-step brushless systems.

TABLE 15-2 COMPARISON OF BRUSH AND BRUSHLESS MOTORS

15.8 Induction and Reluctance Motors
There are alternative brushless technologies to those based on permanent magnets, the most popular being induction motors and reluctance motors. These motor types both avoid brushes while promising to reduce motor cost, the primary reason being the elimination of magnets, which are the most expensive material in PM motors. Induction and reluctance motors both offer wider speed ranges because field weakening is passive. Recall that for PM brushless motors, field weakening requires that flux be added to oppose the magnet flux. At very high speeds, the necessary field weakening may require an impractical amount of current. For non-PM motors, the field must be created by current; thus, reducing the field requires reducing, not adding, flux, from the windings.

Induction and reluctance motors do have shortcomings. Induction motor rotors are complex to manufacture because the rotor contains an electrical circuit. Also, the rotor generates heat, which is difficult to eliminate, just as was the case for brush motors. The flux densities of high-energy rare-earth magnets commonly used in modern servo applications are not equaled by induction motors. Thus, induction motors are usually larger than PM brushless motors and have larger rotors, making them less suitable for high-acceleration applications. Reluctance motors have simple rotors. The most volumetrically efficient reluctance motors are called switched reluctance motors. These motors are simple and inexpensive to manufacture, but they are difficult to control and usually generate significant torque ripple.

Printed with permission from Academic Press, a division of Elsevier. Copyright 2004. "Control System Design Guide, 3e" by George Ellis. For more information about this title and other similar books, please visit www.elsevierdirect.com.