Design Article
Basics of the Electric Servomotor and Drive - Part 3: Brushless PM Motors
George Ellis
8/5/2008 2:45 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.]
15.6 Brushless PM Motors
The weaknesses of the brush PM motor have caused the brushless DC motor (sometimes referred to as synchronous AC PM motor) to dominate many servo-motor markets. The brushless motor replaces the mechanical commutator with electronic commutation, eliminating the brushes and their problems. However, brushless motors are more difficult to control.
Brushless controllers must sense the electrical position of the motor with a feedback device, such as a resolver or encoder, or, in some cases, with coarse digital sensors called Hall-effect sensors. In many nonservo applications, the BEMF of the motor is used to measure position; this is called sensorless control. In all cases, the electrical position is used to calculate commanded phase currents, with the goal being to maintain the commutation angle (θE in Equation 15.7) at or near the optimal 90°.
15.6.1 Windings of Brushless PM Motors
Windings of brushless PM motors are distributed about the stator in multiple phases. Usually there are three phases, each separated from the others by 120° (electrical). Brush motors can have many more phases, but a large number of phases in brushless PM motors is impractical because each phase must be individually controlled from the drive, implying a separate motor lead and set of power transistors for each phase. A simplifed winding diagram of a three-phase motor is shown in Figure 15-20.
Figure 15-20. Simple winding set for a three-phase four-pole motor.
Brushless motors rely on electronic commutation. The drive monitors the rotor position and excites the appropriate winding to maintain a 90° commutation angle. Consider Figure 15-21, which shows a brushless rotor in a sequence of three positions as it rotates counterclockwise. The large arrows show the flux created by the windings. To simplify the drawing, the field flux is not shown, but recall that it points out of the north poles and into the south poles. Notice that the winding flux in each of the three motor positions is maintained in quadrature.
Figure 15-21. Commutation sequence maintaining the winding flux between the magnet poles.
In brush motors, the commutation angle is maintained by mechanically switching phases in and out. Because the brush motor has many phases, each phase represents only a few electrical degrees of rotation and the torque from a brush motor is smooth. An equivalent technique is used on brushless motors in a commutation method called six-step, but it produces large torque perturbations at each transition because brushless motors usually have just three phases.
15.6.2 Sinusoidal Commutation
Unlike a brush motor controller, a brushless motor controller controls current in multiple phases independently. This allows the controller to move the winding flux (ΦT) angle in small increments. Figure 15-21 shows how flux created from the three windings interacts with flux from the rotor magnets. Were the position of the rotor in Figure 15-21 midway between positions 1 and 2, flux from the windings could be positioned properly by placing equal current in phase A and phase B. In general, quadrature can be maintained precisely by independently regulating the phase currents according to Equations 15.14 - 15.16:
IA = IS × sin(θE) (15.14)
IB = IS × sin(θE - 120 °) (15.15)
IC = IS × sin(θE - 240 °) (15.16)
where IS is the magnitude of current in the motor and sin(θE) is the electrical position of the motor. This is called sinusoidal commutation.
Sinusoidal commutation provides smooth, efficient operation of the brushless motor. Torque is approximately proportional to IS. In fact, brushless motors are usually given a torque constant based on IS, so T ≈ KT × IS, assuming that commutation is performed correctly.
Phase Control of Brushless PM Motors
15.6.3 Phase Control of Brushless PM Motors
Phase control for brushless PM motors is shown in Figures 15-22 and 15-23. The concept is straightforward: Command each of the phase currents (IAC commands IA, and so on) to follow Equations 15.14 - 15.16, assuming T = KT × IS. Phase control regulates each of the phase currents with independent current loops. Two current sensors are required; the third phase current is calculated from the other two because all three currents must sum to zero in a wye-connected three-phase motor, such as the
Figure 15-22. Three-phase modulator controlling a brushless motor.
Figure 15-23. Phase-controlled brushless PM drive.
motor in Figure 15-22. The current commands for the three phases are calculated according to Equations 15.17 - 15.19:
IAC = TC/K*T × sin(θE) (15.17)
IBC = TC/K*T × sin(θE - 120 °) (15.18)
ICC = TC/K*T × sin(θE - 240 °) (15.19)
15.6.3.1 Modulation
In phase control, the modulation is equivalent to that of the brush motor, the biggest difference being that there are three phases to modulate rather than the two phases of Figure 15-19. The H-bridge is also nearly the same, except the brushless motor requires a third leg of the power stage, as shown in Figure 15-22.
The electrical model of the brushless motor is similar to that of the brush motor. Three copies of the electrical model of the brush motor are required, one for each phase. The main difference is that the BEMFs are sinusoidal when the motor is moving at a constant speed, whereas in a brush motor the BEMF is constant during constant speed. The commanded currents are sinusoidal at constant speed as well. Also, the inductive losses do affect steady-state torque in a brushless motor because phase currents are changing, even at constant speed and constant load. This is one factor that makes brushless motors more difficult than brush motors to control; the bandwidth of the current loop affects the torque-speed curve. Figure 15-23 shows a block diagram of a phase-controlled brushless PM drive.
Phase-controlled brushless motors produce smooth torque. However, there are torque perturbations, including those caused by the current sensors. Current sensors commonly have 1% or 2% current DC offset. In the brush motor, such an offset does not contribute to torque ripple; the brush motor will rotate smoothly, but the actual torque is offset from the command torque by a small amount.
In the brushless motor, problems caused by current-sensor offset are more serious. DC offset in the current sensors causes ripple at the electrical frequency of the motor. To determine this frequency, multiply the motor speed in revolutions per second by poles over two. For example, if a six-pole motor were rotating at 300 RPM, offset in the current sensor would generate torque ripple at 300/60 × 6/2 = 15 Hz. A 2% offset in a current sensor indicates that the current sensor may cause offset as much as 2% of the drive peak current. For a 10-A drive with a peak rating of 20 A, 2% would be 400 mA. Were the motor rotating with a small load (say, drawing just 1 A), the ripple caused by 400 mA of offset would be a problem for some applications. This is one reason it is important not to specify larger brushless drives than necessary; the offset increases with the drive rating, so oversized drives can cause unnecessary torque ripple. The area of three phase-modulation is well studied, including Refs. 41 and 51.
Angle Advance
15.6.3.2 Angle Advance
The performance of brushless DC motors at higher speeds can be enhanced by advancing the commutation angle, that is, by adding an offset to θE in Equation 15.7. There are three reasons to advance the commutation angle. First, advancing the angle offsets the phase lag caused by the current loop. Second, the angle can be advanced to weaken the field flux. Third, some brushless motors can generate reluctance torque, and advancing the angle can optimize torque output. Each of these reasons is discussed in detail in the following.
15.6.3.3 Angle Advance for Current-Loop Phase Lag
Current loops, like all control loops, cannot produce an output that precisely mimics the command. As discussed throughout this book, control loops produce phase lag and attenuation at higher frequencies. Attenuation is of little concern for this discussion, but phase lag is important because it reduces torque output according to sin (θE - θLAG).
For example, suppose a four-pole motor is rotating at 3000 RPM, creating an electrical frequency of 150 Hz. Suppose also that the current controller had a phase lag of 25° at 150 Hz. If the controller commanded current using Equations 15.15 - 15.17, the resulting loss of torque would be sin(90°) - sin (65°) = 10%.
Angle advance can cure phase loss by commanding a phase advance equal to the phase lag from the current loops. It can also anticipate the delay from sampling and correct for it as well. The higher the electrical frequency of the motor with respect to the current loop bandwidth, the more angle advance can be used to improve the commutation angle.
15.6.3.4 Field Weakening
The field flux ΦF can be reduced by advancing the angle of the actual current (not just the commanded current as earlier). A sine wave that has been advanced can be considered to be the sum of two sine waves, one unadvanced and another advanced by 90°. For example, IA from Equation 15.17 can be advanced 20°:
IA = IS × sin(θE + 20°) (15.20)
Now use the trigonometric identity
sin(A + B) = cos(A) × sin(B) + sin(A) × cos(B)
to divide IA into the two components:
sin(θE + 20°) = cos(20°) × sin(θE) + sin(20°) × cos(θE) (15.21)
so that Equation 15.20 can be rewritten as
IA = (0.94 × IS)sin(θE) + (0.35 × IS)cos (θE) (15.22)
The sine term is 90° advanced from the field flux; the cosine term, which is another 90° advanced from the sine term, is thus 180° in front of the field flux. The sine term produces ΦT in Equation 15.7; the cosine term generates flux in direct opposition to ΦF. So with 20° of advance, 94% of the current magnitude produces torque and 35% of the current magnitude produces flux in opposition to the flux created by the magnet.
The flux in opposition to magnet flux reduces, or weakens, the field of the magnets. Reducing the flux from the magnets will reduce the BEMF constant of the motor and, since at any given bus voltage BEMF is the fundamental limit to motor top speed, reducing the BEMF allows higher-speed operation of the motor. Advancing the angle more will allow the motor to rotate at higher speeds. The angle should not be advanced more than is required to run at any given speed because excessive angle advance generates needless I2R power losses.
Angle advance can be depicted graphically, as shown in Figure 15-24. The optimal angle between flux from the magnets (IF) and from the winding in the absence of field weakening is 90° according to Equation 15.7. However, at high speed the angle can be advanced to weaken the field, as shown in Figure 15-24a. The components of the flux generated from the winding can be divided into Cartesian coordinates, with one component at the optimal 90° and the other 180° from the field, as shown in Figure 15-24b. The winding flux in opposition to the field (ΦF-WINDING) can be summed with the magnet flux (ΦF-MAGNET); the result is that the overall field flux is weakened, as shown in Figure 15-24c. The reduction in field flux results in a reduced BEMF constant (KB) and a proportionally smaller motor torque constant (KT).
Figure 15-24. Angle advance depicted in three ways.
Figure 15-25 shows the phase-current controller with angle advance. The commutation angle is enhanced with an advance angle, θA. A graph for angle advance in a typical brushless system is shown at the bottom of the figure (θA vs. VM). The rest of the controller is identical to Figure 15-23.
Figure 15-25. Brushless phase-current controller with angle advance.
15.6.3.5 Reluctance Torque
Reluctance torque is the torque generated because the motor is moving to a position where the reluctance seen by the armature flux is declining. A simple application of this principle is the refrigerator magnet, which is held in place by reluctance force. Because the reluctance along the path of the magnet flux is minimized when the magnet is as close as possible to (in contact with) the refrigerator, the magnet holds its position. Motors can be made to take advantage of this phenomenon by building the rotor to have a lower reluctance to the winding flux than to the field flux, such as is the case for interior permanent magnet, or IPM, motors, as shown in Figure 15-26.
Figure 15-26. Rotor of an interior permanent magnet (IPM) motor with high- and low-reluctance paths.
In the IPM motor of Figure 15-26, the reluctance seen by the field flux is much higher than the reluctance seen by the winding flux. The reason is that the only nonsteel material in the path of the winding flux is the motor air gap. However, the field flux must pass through the magnets as well as the air gap; the permeability of magnets is close to that of air, so the field flux endures two large-reluctance materials. The difference in reluctance is frequently 2:1 or more. Such motors are often called hybrid PM/reluctance motors.
The optimum angle to apply current for the magnet component of torque is 90° (Equation 15.7); for Figure 15-26, the optimum angle of current (with respect to magnet flux) for the reluctance component of torque is 135°. The optimum angle for a hybrid motor at low speeds (that is, without field weakening) will be between 90° and 135°. Since the reluctance component is usually a fraction of the magnet torque in PM motors, the optimal angle is much closer to 90° than it is to 135°. Still, some angle advance (perhaps 10° or 15°) will often increase the torque of a motor as much as 15%. This is one example of how to take advantage of reluctance torque; there are other motor structures that use reluctance torque differently.
Figure 15-27 shows a PM rotor constructed with surface-mounted magnets. Here, the flux from the field sees about the same reluctance as the flux from the winding, because the permeability of magnet material for most modern brushless motors is so close to that of air. As a result, motors based on surface-mounted magnets do not produce reluctance torque.
Figure 15-27. Surface magnet rotor with similar- (high-) reluctance paths.
Part 4 continues a look at brushless PM motors with a discussion of DQ and six-step control, a brief discussion of alternative brushless technologies, and a comparison chart of brush and brushless motors.
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.
Related links:
Basics of the Electric Servomotor and Drive - Part 1: Basic Magnetics and Motor Control Overview | Part 2: Permanent-Magnet Brush Motors
The basics of control system design: Part 1 - Moving beyond PID | Part 2: Tuning a Proportional Controller | Part 3: Tuning a PI Controller | Part 4: Tuning a Pl+ Controller | Part 5: Tuning a PID Controller | Part 6: Tuning PID+ and PD controllers
Implementing Embedded Speed Control for Brushless DC Motors: Part 1 | Part 2 | Part 3 | Part 4 | Part 5 | Part 6
Using block diagrams as a system design "language" - Part 1 | Part 2
Advances in servo system development
