Current/Torque Control

34.6.3 Current/Torque Control

You may have noted that the discussion has been about current in the windings rather than the voltage across them. In very

There is an extra difficulty that must be addressed with high- simple small brushless DC machines, like the one in the muffin performance, high-efficiency, well-made machines, and it adds fan in your computer power supply, voltages are connected another layer to the control of the motor. Such machines can directly to the windings. For these small motors, the resistance easily be designed with very low resistance windings. It is not of the windings is relatively high and this helps limit the actual uncommon to have windings for a 200 V machine at the 20 kw current that flows and swamps inductive effects.

954 M. F. Rahman et al. When starting, or at a low speed, the current in a wind- current level and initiates turn-off of S1 and S4 and turn-on

ing is limited only by the very low resistance and, for the of S2 and S3. (If they were all turned off at once, the inductive machine above by Ohm’s law, I = E/R would result in more nature of the circuit would produce very high voltages which than 2000 amperes.

would cause arcing in mechanical switches, or breakdown and The most common requirement for a steady current in failure of semiconductor switches, see later.) The current then the windings is to provide a steady torque. There is always begins to reduce. It reduces a small amount, down to half the

a back-emf generated in the windings whenever the motor is hysteresis band of the comparator below the desired current rotating, which is proportional to speed and subtracts from level and then the switches reverse again. Thus a desired cur- the applied voltage. Thus currents cannot be determined just rent level is achieved, with an arbitrarily small triangular ripple by terminal voltage. The winding does however have induc- superimposed, as shown in Fig. 34.64. tance. Whenever the copper conductors are put in coils in an

The general process of controlling by switching a voltage iron structure, particularly if there are low reluctance mag- fully on or fully off at high speed is called pulse width mod- netic paths with only small airgaps, the creation of quite large ulation (PWM) and the specific method of current control inductances cannot be avoided. These are used to very good achieved above with PWM, is called hysteresis band current effect.

control (HBCC).

The nature of inductance is that when a voltage is applied to Of course to keep this current ripple small, the switching an inductor, instantaneous current does not result, rather the may need to be very fast, but with the modern semicon- current begins to increase and ramps up in a quite controlled ductor switches there is no great problem up to 100 kHz for fashion. If the voltage across the inductor is reversed the cur- small machines and typically above 15 kHz for acoustic noise rent does not immediately reverse, rather it ramps down, will reasons, for machines rated up to several hundred kilowatts. go through zero and reverses if the reversed voltage is left there

A perceived “drawback” of HBCC is that the switching fre- long enough. However, if the voltage is alternated by switch- quency is determined by the circuit inductance, the width of ing rapidly, as can be done with power electronics, the current hysteresis band, the back-emf, and the applied voltage, ranging can be controlled to ramp-up and ramp-down either side of very widely in normal operation. It is not difficult, but it is a

a desired current, staying within any determined tolerance of little more complicated, to use a fixed frequency, and a linear that desired current.

analog of the current error to modify the pulse width of the Figure 34.63 looks very much like the simple “H” bridge PWM signal. commutation circuit, but is performing a very different func- tion. It is controlling the current amplitude to stay within a desired band. If S1 and S4 are turned on then the current will

34.6.3.1 Switching Losses

begin to increase from left to right in the winding. The current There is a practical limit to how often semiconductor switches sensor in the circuit detects when the current reaches a value can be operated. At every change of state, if the switch is carry- of half the hysteresis band of the comparator above the desired ing current as it is opened, then as the voltage rises across the

Current sensor,

voltage output

to current

− Comparator

PWM logic signal output.

Desired Current (torque),

with hysteresis, eg

Turns on S1 and S4 if high (current below reference),

or S2 and S3 if low (current above reference) positive or negative torque.

eg ±5V represents maximum

±100 mV

FIGURE 34.63 Hysteresis band current control using pulse-width modulation (PWM).

34 Motor Drives 955 Desired current

Current

Actual current

PWM Logic signal

Time

output

FIGURE 34.64 Hysteresis band current control and PWM waveforms.

switch and the current through it falls, there is a short pulse This is a very common control scheme and will need some of power dissipated in the switch. Similarly, as the switch is extra logic to reverse the direction of rotation of the motor, by closed, the voltage will take some time to fall and the current either turning S4 off and S3 on continuously, or by swapping will take some time to rise, again producing a pulse of power the control signals to the left and right “legs.” For full-servo dissipation. This loss is called switching loss. Fairly obviously operation normal H-bridge switching can be used and the logic it will represent a power loss proportional to the switching fre- is slightly different, but not significantly more complicated. quency and so the switching frequency is generally set as low However, following the discussion above, the switching losses as it can be without impinging on the effective operation of will be higher. the circuit. “Effective operation” might well include criteria for acoustic noise and levels of vibration.

34.6.3.3 Combining Commutation and PWM Current

34.6.3.2 High Efficiency Method of Managing the

Control

Switching in the H Bridge

The real break-through is that one set of six switches can be

A very common way to control the current with the smallest used for both PWM and commutation. That is the clever part number of switching transitions is to combine HBCC with, and also the confusing part when one first tries to understand for example, alternating only S1 and S2 in Fig. 34.65 leaving what is going on. S4 on all the time, on the understanding that there will be a

Thus, in a controller there are two control loops. The first back-emf in the winding and the current can still be increased is an inner current loop switching at, for example, 15 kHz to or decreased as desired.

control carefully and exactly the current in two of the coils. Thus when the motor is rotating and the back-emf is Then at a much lower rate, for example at 50 times per second somewhere between zero and the rail voltage, alternating two at 3000 rpm, the two coils doing the work are changed accord- switches rather than four will still allow current control in the ing to Table 34.2, controlled by an outer commutation loop, coil, using for example HBCC, exactly as before.

using information from the Hall effect shaft position sensors.

A complete controller is shown in the block diagram form in Fig. 34.66. Various aspects of this block diagram will now

be examined and explained in detail.

34.6.3.3.1 Hardware Details – Semiconductor Switches The +

Vin −

+ Ea −

three most likely semiconductor switches for a six step con- troller are the bipolar junction transistor (BJT), the metal- oxide silicon field effect transistor (MOSFET) and the insulated

PWM S2

On S4

gate bipolar transistor (IGBT). Older controllers used BJTs, however contemporary controllers tend to use MOSFETs for lower voltages and powers and IGBTs for higher voltages and

FIGURE 34.65 H-bridge switching with one switch steadily on and a powers. Both of these devices are controlled by a gate signal back-emf.

and will turn-on when the voltage of the gate above the source

956 M. F. Rahman et al.

Hall effect

shaft position

sensors Desired current

Gate drives G1 to G6

(torque) command

Analog and digital signal processing

FIGURE 34.66

A complete controller showing the two feedback paths, one for the position sensors and one for the current sensors.

or emitter is greater than a threshold, which is typically about switches in the same “leg,” (e.g. S1 and S2) are never turned

5 V. Use of about 10 V is common. The devices are thus off on at the same time. If the controller attempts to turn one when the gate voltage below the threshold. Systems typically off and the other on at the same instant and switch turn-off use zero volts for the off state. The controller of Fig. 34.66 is slower than turn-on (as it is with BJTs and IGBTs), then shows MOSFETs used for the six switches.

a short circuit will result for a brief time. The bus capaci- The trick is that the voltage at terminal a, also S1’s source, is tor is usually very large to provide ripple current (see later) either ground or the positive potential of the battery, depend- and usually of very high quality being fabricated especially for ing on which switches are on. Driving S2, S4, and S6 is easy power-electronic applications, and can easily provide thou- since the MOSFET sources are all at the potential of the neg- sands of amperes for a few microseconds, which is enough to ative rail and the lower gate drive signals are referred to this destroy the semiconductor switches. rail.

The second issue, discussed in Section 34.6.3 “Current/ There is a range of dedicated integrated circuits which can Torque control,” is that one cannot turn-off both switches in drive the switches S1, S3, and S5, and which use a “charge

a leg at the same time, even for a few nanoseconds, since the pump” principle to generate the drive signal and the drive voltages resulting from attempting to interrupt current in an power internally, all related to the MOSFET source potential. inductor will cause avalanche breakdown and failure of the Various approaches to this technical challenge of providing a semiconductors. This sounds like quite a dilemma. floating gate drive are commonly discussed under the generic

There is actually a very simple and effective solution. At any heading of “high side drives.”

transition, the control circuitry ensures that the active switches For the most sophisticated drives, transformer coupling is are all turned off before any switch is turned on, usually for a used to provide a tiny power supply especially for the isolated few microseconds. This is known as “dead time” and its pro- gate drive and send the control signals either through an opto- vision is an essential part of most of the dedicated integrated coupler or a separate transformer coupling. The high-side circuits in use. Then a “flyback”/“freewheel” diode is put in drive problems here are exactly the same as those encountered anti-parallel with each semiconductor switch and this provides in the traditional buck converter, or in drives for induction the current path during dead time. These diodes are shown in motors and PMSMs.

Fig. 34.66.

The diode has a little more loss than the switch, since the diode forward drop is more than the switch drop. This is sig- 34.6.3.3.2 Dead Time and Flyback Diodes Two issues have nificant in a low voltage controller. However, as stated above, been mentioned above that must be addressed when using for a low voltage controller, MOSFETs are the device of choice. high-speed electronic switches in inductive circuits.

They have a lesser known property, that when gated on, they The first, in Section 34.6.2 “Electronic Commutation,” was can carry current in both directions. Intriguingly the “on” state that care should be taken to ensure that the upper and lower resistance is lower in reverse than in the forward direction!

34 Motor Drives 957

PWM logic signal

Time

output

I up logic signal

Dead time

I down logic signal

FIGURE 34.67 Dead time introduced into the PWM logic signal, for switch drive.

Thus for low voltage controllers, when the switch forward drop design will limit the length of conductors in which the cur- represents a significant contribution to losses, the MOSFET is rent is changing rapidly. Thus, a very large capacitor is placed turned on after dead time for both the current directions. Thus physically as close to the positive bus of the switches as possi- the higher loss in the diode is only for a few microseconds.

ble, aiming to have a steady current in the longer conductors It is not difficult to produce from the PWM signal an “I up” from the dc supply, up to the capacitor. When the motor is logic signal which is used to cause the current to increase and running at, say, half speed and providing large torques, a very an “I down” logic signal used to decrease it, with the timing as high level of ripple current is carried by this capacitor. Kirch- shown in Fig. 34.67. The function can be executed in sequential hoff ’s current law (KCL) must be applied at node A, as shown logic, or with the simple analog timing circuits.

in Fig. 34.68. Good capacitors have a ripple current maximum buried away in their specification sheet. It turns out that in

general, the size of the capacitor in a given design has very In MOSFETs and most IGBTs, there is a diode already within little to do with how much voltage ripple you can tolerate at

A. Semiconductor Detail

the device; it is unavoidable and results from the fabrication the bus, but rather is determined by the ability to carry the processes. In modern power semiconductors, this intrinsic ripple current without the capacitor heating up and failing. It diode is optimized to be a good switching diode. The seri- has been known that the small electrolytics in prototype con- ous designer, however, will check the specifications for reverse trollers mysteriously explode. On searching, it is found that recovery of this diode, since in highly optimized controller they are in parallel with the main capacitor and quite close designs, reverse recovery losses in the intrinsic diode can be to it, so they carry a lot of ripple current, then heat up and significant and are very difficult to control. In low voltage explode! controllers, you can put a Schottky diode in parallel with the intrinsic body diode. The Schottky diode, with its lower for- ward voltage drop will tend to take the current and has no reverse recovery problems, but the current must commutate

34.6.4 The Signal Processing for Producing

to it from the semiconductor die and the inductance of the

Switch Drive Signals from Hall Effect

connections is critical.

Sensors and Current Sensors

B. The Smoothing Capacitor on the Input to the Controller

34.6.4.1 Operation of the Hall Sensors

This is a substantial capacitor, often very expensive, (it is shown The flux density directly under a magnet pole can be anywhere in Fig. 34.66 as C in) and its design is quite challenging. The from 500 to 800 millitesla with Nd–Fe–B magnets. Hall effect issue of smoothing is quite serious. If there are high-frequency (HE) sensors with a digital output, called Hall effect switches, or sudden current changes in the leads from the dc supply to change state at very close to zero flux density. Thus, they will the controller, they will radiate electromagnetic energy. Good change state when the north and south pole are equidistant

958 M. F. Rahman et al.

I supply

I controller

I capacitor

To controller switches Voltage source

FIGURE 34.68 Kirchhoff ’s current law at node A.

TABLE 34.3 Hall effect switch outputs for rotor positions as shown, HE a switches placed as in Fig. 34.69

When the center of the rotor

HE1 outputs

HE2 outputs HE3 outputs

north pole is in this sector

1 1 1 FIGURE 34.69 Possible Hall effect switch positions in a three-phase

machine.

0 1 from them, so that for example, in Fig. 34.69, the switch HE1 1 is just changing state with the rotor as shown.

In practice, a motor designer needs to consider what magne- tomotive force comes from the current in the windings which might result in flux which would trip the HE sensor at a slightly different time. If you follow all the above logic about six step

switching, you will see that you only need the magnet poles to have a span of a bit more than 120 ◦ . Using 180 ◦ magnet poles can add considerably to the cost, as well as having an impact on such things as cogging torque. Actual designs often add extra “sense” magnets to cover 180 ◦ just at the circumferential strip where the HE switches are located, adding minimally to

the magnet mass and ensuring good and accurate triggering. However, if the switches operate as above, then Table 34.3 will result for the HE switches located as shown in Fig. 34.69.

34 Motor Drives 959

TABLE 34.4 Current sensors to use as input to the current Figure 34.66 shows two current sensors. In the most sophisti-

34.6.4.2 Sensing the Current in the Motor Windings

controller, for each of the six rotor position sectors cated systems, there are two current sensors, one in each of the

Hall effect switch outputs

Monitor current as read by

two motor phases. The current sensing is done at the winding

(HE1, HE2, HE3)

and isolated with either an HE sensor in a soft ferromagnetic

Negative of (sensor a + sensor b)

magnetic core surrounding the conductor (commercial items

Negative of (sensor a + sensor b)

are available), or by using a resistive shunt sensor and some

Sensor b

accurate analog signal isolation/coupling through transformers

Sensor b

or opto-couplers. The isolation is necessary since the potential

Sensor a

at points a, b, and c is either the dc bus voltage or zero, depend- Sensor a ing on which switches are on, so that any current measure such

as the small voltage across a shunt is superimposed on these very large voltage changes. This is a very similar problem to TABLE 34.5 Distribution of control signals to the switches using “High that for the high side gate drives discussed earlier. The current Efficiency Method of Managing the Switching in the H Bridge” in the third winding is determined by the algebraic application HE states(1,2,3)

of KCL, given the other two readings. Simple controllers sometimes avoid the complexities of iso- 100

0 0 0 1 I up I down

lated current measurement and instead measure the current I down

I down 0 0

in the return negative supply, for example from the bottom of 000

0 0 I up

I down 0 1

the three lower switches to the bottom of the supply smooth- 100

I up

I down

ing capacitor. This arrangement senses current when an upper 110

I up

I down

and a lower switch is on, but not when the current is being carried in flyback diodes or by two lower switches. While it is inexpensive, it does not provide fully accurate control. The system works because the current should be decreasing when the combinational logic for directing, or steering, the switching

a measure is not available, heading towards zero, so switch or signals to the right switches. A typical scheme for a specific system failure due to over-current should not occur.

controller is shown in Table 34.5.

It is usual also to include some shutdown logic from ded- icated protection circuits, for example sensing over-current,

over-bus voltage, under voltage for gate drive and over- The controller must select the right current to increase or temperature both in the motor and in the controller power

34.6.4.3 Management of Current Sensing

decrease, dependent on rotor position. The following con- stage. For simplicity, this is not shown in the table. vention is adopted. Positive current provides torque in the counterclockwise direction and therefore goes into winding a,

34.6.5 Summary

b , or c. All systems are capable of regeneration, which implies that What is Discussed in the above negative torque can be commanded (without reversing the The physical principles of the operation of a PMBDCM have direction of rotation) to make the machine operate as a been discussed which lead to the development of the necessary generator, developing retarding torque.

parts of a power electronic controller. One specific type of Thus for the above sequence of sector determinations, refer- current control, hysteresis band current control was explained

ring back to Table 34.2, the output of current sensors should in detail, and one specific type of switch logic pattern was

be directed to the current controller as shown in Table 34.4. developed. The exposition has included many of the issues The addition and negation required can be carried out that can cause difficulties for controller designers if they are

with the standard operational-amplifier circuitry. The three not careful. required analog measures are then fed to a three to one ana- log multiplexer, gated from the HE switch signals suitably What is Not Discussed in the above processed in combinational logic. The resulting single analog Many PMBDCMs have more than one pair of poles. The output is fed to the current comparator.

arguments above can all be extended to higher pole count machines, by taking any mention of degrees to be electrical degrees rather than mechanical degrees. The controller dis-

34.6.4.4 Distribution of Control Signals

cussed in detail only manages one direction of rotation. It is

an excellent exercise, and straightforward, but not trivial, to Given that the dead time is introduced elsewhere in sequential repeat the above steps, preparing the tables for clockwise rota- logic, or with timing circuits, it is a simple matter to develop tion of the simple machine discussed above. Then, following

to the Switches

960 M. F. Rahman et al. the discussion in the first part of Section 34.6.3, Current/Torque percentage regulation, and stiffness. While servo bandwidth

Control about H bridge switching, prepare the logic tables indicates the ability of the drive to track a moving or cyclic again for full bidirectional control, using the I up and I down reference, the percentage regulation and stiffness stipulates the logic signals exactly as above, but applying them to both “legs” drive’s static holding performance for speed or position, in the determined by the rotor position. Only one form of cur- face of disturbances from the load and in the supply condi- rent sensing was discussed in detail. There are many simpler tions. The servo bandwidth, specified as a frequency in Hertz schemes in use which do not have quite the flexibility and or rad/sec, is often found from the system frequency response accuracy of the above, but which can suit certain applications. plot, such as the Bode diagram. Similarly, there are other forms of current control such as the

The percentage regulation of a speed-controlled system constant-frequency linear method briefly discussed. Shaft posi- often refers to the percentage change in speed from no load tion sensors take many forms. Adherence to the HE sensor was to full load. In a type-zero system, this figure will have a finite for simplicity, and to reinforce the magnetic field aspects of the value. Many systems are type zero, albeit with a high gain so machine operation.

that the regulation is acceptably low. For such systems, the regulation is often necessary for operational reasons. In some