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1. Introduction
The description of brushless motors as trapezoidal and sinusoidal arises from the shape of the back emfs produced by the stator windings. In this Section the motors are generally referred to as the squarewave and sinewave types, the main interest being in the form and control of the stator current.
In order to ensure a unidirectional output torque, the current in the stator conductors of the brushless motor must always be in the same direction relative to that of the rotor pole flux. The commutation process has to ensure that the action of switching the direction of the current is synchronized with the movement of the flux in the air gap, and so the motor must have a sensor for measuring the position of the flux wave relative to that of the stator windings. FIG. 1 shows the current to be supplied by a unit normally known as the motor drive, which has the control circuit and the inverter as its main components. Power is drawn from a DC supply by the drive and supplied to the motor during periods determined from the sensor signals.
The inverter shapes the waveform of the current fed to the motor. Although normally used for a circuit which converts DC to sinusoidal AC, which is indeed the requirement for the sinewave motor, the name of inverter may also be given to the circuit which supplies the rectangular waveform of current to the squarewave type.
FIG. 1 Motor drive and current supply
The control circuit manages the speed and position of the motor shaft according to the application. Feedback of information is received from shaft position and speed sensors, allowing the external reference command to be compared with the actual state of the motor. The output from the control circuit is fed through the switching logic circuit to the inverter, where any changes to speed or position are made by adjusting the motor current. The inverter is therefore used to control the magnitude of the stator current, as well as for the formation of its waveform.
2. Sensors
This section describes the devices used for the measurement of the rotor pole position, shaft speed and shaft position. The methods of measurement are explained in Sub-Section 4.
Hall effect (pole position)
FIG. 2 The Hall-effect voltage, VH
The Hall-effect sensor is used to detect the position of the rotor of the squarewave motor. FIG. 2 shows a current i flowing through a plate of semiconductor material. Voltage VH is generated by the Hall effect when a magnetic field of density B passes through the plate. If the plate is fixed on the motor stator in a position exposed to the air gap flux, the voltage generated by the Hall effect will be linked to the rotating flux waveform. An advantage of the stator location of the plate is that the generated voltage follows the pattern of the true flux wave in the air gap, including any armature reaction effects.
A drawback is that the plate is subject to stator heating and its performance may be affected at high operating temperatures. Overheating is avoided if the sensor is mounted inside the rear housing of the motor, in the path of the flux from an auxiliary magnet which is fixed to the motor shaft. This provides accurate sensing where there is no significant distortion of the flux in the air gap, due to armature reaction.
The brushless AC tacho (shaft speed)
The AC tachogenerator has a three-winding, trapezoidal, brushless structure. It is mounted at the end of the shaft of the squarewave motor in the rear housing, where it generates a set of three-phase voltages which are fed to the drive. The waveforms are identical to the patterns of back emf shown in FIG. 10, enabling the drive to determine the motor speed from the magnitude of the tacho voltage.
DC tachos
These are the same as AC tachos, except that a circuit board in the rear housing uses the three-phase output to provide a DC signal which is then fed to the drive.
The resolver (pole position, shaft speed and position)
The brushless resolver has a rotor and a stator. The stator carries the input and output windings which are linked by the rotating transformer action of the rotor winding. It is normally fitted to the shaft of the sinewave motor in the rear housing. FIG. 3 shows a common arrangement where there is one AC input and two output windings which are displaced electrically by 90 degree The input winding on the stator forms the primary of a rotating transformer and is usually referred to as the rotor input. The input frequency is typically 5-10 kHz, and AC outputs at the same frequency appear by transformer action at any rotor position. The rotor winding is sinusoidally distributed, with the result that the outputs are amplitude modulated according to the rotor position.
FIG. 3 Brushless resolver terminals
Digital encoders
The resolver provides the drive with analogue signals, and so digitally controlled drives must incorporate analogue to digital converters. The encoder can provide the drive with signals which are already in digital form. The signals are derived optically from patterned tracks on a disc of translucent material which rotates with the motor shaft. The material can be glass or plastic. Light-emitting and light- sensing devices are placed either side of the disc as shown in FIG. 4. The light sensors produce the binary 0 or 1 signals when the light is either obscured by the pattern, or transmitted where the disc is exposed. The encoder is driven by the motor shaft in the rear housing, as shown in FIG. 5.
Incremental encoders
FIG. 4(a) shows the basic principle of the incremental encoder. As the disc rotates, the light sensor supplies the drive with a signal consisting of a train of pulses. In practice the pattern is also designed to provide the drive with signals sensitive to the direction of rotation of the disc [3]. The drive determines the position of the shaft by adding or subtracting the number of pulses which arrive from either side of a known reference position. With this type of encoder, it is obviously not possible to define the absolute position of the motor shaft without regard to a reference.
FIG. 4 Principle of the optical encoder
FIG. 5 Encoder driven from the rear end of the motor shaft
Absolute encoders
One form of absolute encoder is a development of the optical, incremental type. Unlike the incremental type, however, the signals generated represent discrete shaft positions. Each position is given its own binary number and each digit of the number must have a separate track on the glass disc. Each track has its own scanning, the scans being checked with respect to each other so that reading errors are avoided. The basic principle is shown in FIG. 4(b). If the disc starts in an anticlockwise direction from the position shown, the shaft positions are defined by the signals
1111 ~ 0000
0001 . . . ; 1110.
The simple four-track encoder shown would be capable of defining only 16 positions of the shaft.
A 10-track disc defines 21~ or 1024 positions, and so on.
Absolute encoders clearly have great complexity and are relatively expensive to produce. The design must combine the photoelectric requirements with a resistance to adverse conditions such as mechanical shock and vibration [4]. There are other designs of absolute encoder. The Sincos type produces sine and cosine signals in analogue form which can be passed directly to the drive, unlike the resolver where a signal from the drive is amplitude-modulated and passed back to the drive. More significantly, the signals from the Sincos device can also be encoded locally and passed to the drive in digital form. Although many times more expensive than a resolver, the Sincos device has clear advantages in the digital control of interconnected servo systems.
3. Power electronics
In FIG. 1, current is supplied to the brushless motor from a power electronic inverter which must repeatedly change the direction of the stator current. The direction cannot be changed without the interruption and reinstatement of a current which may be tens, or even hundreds of amps. There are at least four semiconductor devices which can be used as switches for controlling the direction of currents at such levels:
(a) the thyristor,
(b) the metal oxide, semiconductor field-effect transistor, or MOSFET,
(c) the bipolar junction transistor, or BJT,
(d) the insulated gate, bipolar transistor, or IGBT.
The MOSFET, BJT and IGBT switches close in response to a switching signal input, and open again when the signal is removed. The thyristor switch closes when the switching signal arrives, but remains 'latched' when the signal is removed.
The thyristor
The thyristor was previously known as the silicon-controlled- rectifier, or SCR. FIG. 6 shows the electrical symbol for the device to have three terminals, known as the gate (G), the anode (A) and the cathode (C). The switch is operated by the application of a gate current IG which has a low value compared to the switched power current IA. Current IG is normally applied in short pulses. FIG. 6(a) shows V as a constant voltage. Current IA switches on as soon as the first gate pulse arrives, and then stays on as the switch latches. In FIG. 6(b), V is alternating and so the current is turned off naturally when V falls to zero, or soon after depending on circuit inductance.
The best uses for the thyristor lie in applications where operational advantage can be taken of natural current zeros, such as rectification of an AC supply. FIG. 6(b) is an example of such rectification where the average value of the power current is positive and of a magnitude which can be controlled by the position of the gate pulses relative to the supply voltage zeros. We have seen that the needs of the brushless motor are quite different. The stator current is derived from a DC source and must be repeatedly switched on and off at moments dictated by the position of the rotor.
Extra circuitry is needed to force the thyristor current down to zero, with the result that overall switching times are too long for accurate commutation of the brushless motor.
FIG. 6 Thyristor control of direct and alternating currents
Gate turn-off thyristor
The gate turn-off (GTO) thryristor has a modified structure which allows the device to be turned off by extracting a pulse of current from the gate. The GTO must be provided with an initial pulse of gate current to effect turn-on, after which a small gate current must be maintained throughout the required period of power current conduction. Although the GTO was a relatively early development, advances in other directions in semiconductor technology have obviated its use in brushless motor drives.
The power MOSFET
The circuit symbol of the MOSFET is shown in FIG. 7. The switched current flows between the drain (D) and source (S) terminals, falling to zero when the gate signal is removed. The power version of the MOSFET is used where advantage can be taken of its very low gate current and high frequency switching features, for example in switched mode power supplies. The main limitation is that at a fixed manufacturing cost, the resistance of the MOSFET during the 'switched-on' periods rises according to its designed operating voltage. This means that it is normally used in applications which have operating voltages lower than the levels used for industrial brushless servomotors.
FIG. 7 Semiconductor power switches
The power BJT
Technical development of the brushless motor did not really move quickly until the 1970s, with the commercial development of the bipolar junction transistor, or BJT. Since then, development of the high power BJT has gone hand in hand with the dramatic improvements in the design and performance of the brushless servomotor. Modern semiconductor switches based on the BJT are well able to cope with the needs of industrial motion control.
FIG. 7 shows the circuit symbol for the transistor to have three terminals, the base (B), the emitter (E) and the collector (C). In microelectronic, analogue applications the transistor is often used as an amplifier. On the other hand, the power transistor is used almost entirely as a switch. Switched current flows between the collector and emitter terminals in response to current signals fed to the base. Compared to a MOSFET of equivalent cost, the power BJT has a low resistance to the flow of high currents at high operating voltages. A drawback is that the base current must commence and remain at a level of several amps if (using the mechanical analogy) the switch is to be kept firmly closed and without significant 'contact' resistance.
The IGBT
The very low power requirements of the gate of the MOSFET, and the BJT characteristic of low resistance at high current and high voltage, are brought together in the IGBT, which is sometimes referred to as a MOS-gated BJT. The circuit symbol is shown FIG. 7. The device is used widely in brushless motor drives, although it does suffer from a high turn-off time in comparison with the MOSFET and must be applied carefully where high switching frequencies are needed. The design of the device varies according to the broad band of operating frequency required, the central band being from 1 to 10 kHz.
To summarize, it can be said that the IGBT is much easier than the power BJT to drive, but has a lower switching speed compared to the MOSFET. The power MOSFET has a high switching speed, but has a relatively low switched current capability at the higher voltages. The BJT normally has the lowest cost, followed in order by the IGBT and the power MOSFET.
Power electronic inverters
A single semiconductor switch from the types described above can be used to turn a current on or off for current flow in only one direction. Two switches are needed for a current which must be turned on and off in both directions.
Single phase
The single-phase inverter is not normally used to supply the industrial servomotor, but it does provide a simple introduction to the principle of operation of the three-phase circuit. FIG. 8 shows a single-phase brushless motor connected to a half-bridge single-phase inverter. The rectangular waveform of current which must be supplied to the motor is shown at the top of the diagram. The input signals to the switches are derived from the pole-position sensor and supplied through the switching logic circuit, as shown in FIG. 1. The three-wire DC supply provides voltages of + V/2.
FIG. 8 Half-bridge, single-phase inverter
For (a), 0 is between 0 and 180 degree Q1 is on, Q2 is off and a current flows in the motor stator in the direction shown. In (c), 0 is between 0 and 180 degree Q2 is on and Q1 is off and so current flows in the opposite direction through the stator to that in (a). The two switches must never be allowed to be on together, otherwise the supply would be short-circuited, and so Ql must turn off before Q2 turns on and vice versa.
However, the stator winding has inductance and so the stator current must be allowed to flow along an alternative path while both switches are off. After Q1 turns off, the stator current circulates through 'freewheeling' diode D2 around the path shown in (b) and dies away. The circulating current flows towards the positive supply voltage and so the power source must be capable of accepting the associated flow of energy.
Similar currents and energies flow around the upper half of the circuit after Q2 turns off and before Q1 turns on.
The half-bridge circuit makes poor use of the power source as only half the supply voltage appears across the load. The full- bridge circuit of FIG. 9 has no such drawback, although it does need two extra semiconductor switches. Current flows through the motor along the path shown when Q3 and Q4 are on, and reverses when the conducting pair changes to Q] and Q2. All switches must be off during the changeover, leaving the current to die away through D1, D2 and the power supply, which must be able to accept reverse current.
FIG. 9 Full-bridge, single-phase inverter with PWM regulation
Full-bridge three.phase circuit
The inverter circuit for the three-phase brushless motor is similar to the full-bridge single-phase circuit except that it has three pairs of semiconductor switches and three pairs of diodes. The details are covered in Section 4.
Control of current magnitude
Power electronic inverters convert direct current into alternating current of rectangular or sinusoidal form. They are also used to control the magnitude of the current and hence the motor torque. In the usual method, the current is 'chopped' by one or both of the pair of conducting switches.
For example, in FIG. 9 the lower switch of the Q3-Q4 pair is repeatedly turned on and off during the conduction period. The switching signal comes through the switching logic circuit from the control circuit in FIG. 1. When Q4 turns off, the motor becomes disconnected from the voltage supply. The motor current then decays around the D1-Q3 path at a rate determined by the resistance and inductance of the stator winding. When Q4 turns on again, the supply voltage is reconnected and the current rises.
PWM
In FIG. 9, the average current is controlled by PWM or pulse width modulation. As the pulse width 0p is increased, the average current rises. The current is maximum when the space 0s = 0, and zero when 0p = 0. To avoid undue ripple in the current waveform, 0p + 0s is normally 10% or less of the half-cycle angle, or 18 electrical degrees. For example, the rotor of a four-pole squarewave motor running at 6000 rpm, or 1 revolution (720 elec degree every 10 milliseconds, would take 10 • 18/720- 0.25 ms to pass through 18 electrical degrees.
The PWM switching frequency required would be at least 4 kHz.
Current regulation
In the PWM method the current is controlled by adjusting the width of current pulses which occur at a fixed rate. In the current regulation method, the chopping switch is turned on or off if the current is too low or too high respectively. The magnitude is measured continuously by means of a current transducer and switching occurs at the limits of a narrow band around the average value required ( FIG. 10).
FIG. 10 Current regulation
In the simplest case, switching occurs at an irregular rate, depending on fluctuations in the current requirement. In an alternative current regulation method, the irregularities are avoided by preventing the switch from turning on again until the end of a switching period of a fixed length.
4. Three-phase commutation
Introduction
The block diagram of FIG. 1 shows the main components of the brushless motor drive. The diagram also shows the speed and position sensors in the rear housing of the motor.
In Sub-Section 2 (above) we looked at the various types of sensor used for the generation of signals which are dependent on the speed and position of the motor shaft, and the position of the rotor poles. The drive shown in FIG. 1 is assumed to develop digital commutation signals. Any analogue signals from the sensors must be passed through an A/D converter, either within the drive or locally at the motor. The subject of Power Electronics was introduced in Sub-Section 3, and the operation of the power electronic inverter was described by taking the single-phase case. The work covered the simple commutation of the motor current using signals from a pole position sensor, and also the basic methods of control of the current magnitude.
In this section we will see how the commutation of the motor current and the speed and position of the shaft are controlled on a three-phase basis. There are two areas of interest:
1. the operation of the three-phase inverter,
2. the methods of three-phase measurement of pole positions and shaft speed and position.
Operation of the full-bridge three-phase inverter
The general layout of the inverter often used for the commutation of the squarewave or sinewave motor is shown in FIG. 11. It is a simple extension of the full-bridge single- phase circuit of FIG. 9. Only two phases of the squarewave motor require a current supply at any one time. The upper half of FIG. 12 indicates the switches which must conduct at each stage of the flow of phase currents to the squarewave motor from the inverter of FIG. 11. For example, when 0- 30 degree Q1 and Q2 are on and current flow is A---,C and when 0 = 270 degree Q5 and Q6 are on and current flow is C---~B.
FIG. 11 Inverter for the three-phase squarewave and sinewave motors
The sinewave motor requires a continuous current supply to all three phases, the current in each being zero only at the zero-crossing points of the sinusoid. Three switches must conduct at any one time. The lower half of FIG. 12 shows the required sequence of conduction of the inverter switches for the sinewave motor, as the angle of the rotor changes.
Current magnitude There are several ways in which voltage PWM or current regulation may be applied to the three-phase full-bridge inverter. The current in each phase of the squarewave motor flows for 120 electrical degrees and so the upper switches in FIG. 11 can conduct continuously and the lower ones can be interrupted over the full 120 degree , as in the single-phase circuit of FIG. 9. On the other hand, the current in each pair of phases may be seen in FIG. 12 to flow for only 60 degree , and alternative switching strategies are possible where 120 degree chopping of each phase results from operation of the chopping switches over only 60 degree .
FIG. 12 Inverter switching of squarewave and sinewave currents
FIG. 13 Outputs from Hall-effect sensors
FIG. 14 AC tacho outputs to the drive
Commutation of the Squarewave Motor
Measurement of pole position
The Hall-effect sensor is used to detect the rotor pole positions at which the direction of each phase current must be reversed. The current in each phase of a squarewave motor must be individually controlled and so three sensors are needed.
These may be mounted evenly at the 120 electrical degree intervals of a set of three-phase windings. However, at least one manufacturer mounts the sensors over an angle of only 120 of the 360 electrical degrees, giving a spacing of 60 degree For a four-pole motor, the 120 electrical degree zone for the sensors would be 60 mechanical degrees. FIG. 13 shows the outputs p, q, r from position sensors mounted on a two-pole motor over an angle of 120 degree The rotor angle 0 is given in mechanical degrees, which are the same as electrical degrees for the two- pole motor. Selection of the positive half-cycles from p and q, and the inverted, negative half-cycle from r, gives the three correctly spaced signals shown in the diagram. These are fed to the drive where they are used to trigger the commutation.
Measurement of shaft speed
The speed of the motor is related to the magnitude of the alternating back emf generated by each pair of phase windings of the Y-connected motor by the expression
E= KEω
where KE is expressed as line-to-line volts per rad/sec. The emf of the loaded motor is of course inaccessible as a means of measuring the speed. Instead, the output from an AC tacho is used by the drive to produce a signal proportional to the line-to-line emf of the motor, and therefore to its speed.
FIG. 14 shows the outputs from a two-pole Y-connected brushless tacho which is fitted to a two-pole Y-connected motor. For a four-pole motor fitted with a four-pole tacho, the complete electrical cycle of 360 degree would occur over an angle of 180 mechanical degrees.
FIG. 15(a) shows the three rotor position signals. The tacho output is typically 10 V/krpm and is reduced in the drive to a manageable level. When the signals are used by the drive to commutate the tacho phase emfs, which are rectified at the same time, the result is the DC voltage shown in 15(b). The voltage is made up from the top sections of each half-cycle of each emf waveform, drawn with rounded rather than ideal fiat tops to give the diagram clarity. For example, when 0 = 30 degree tc turns off and rectified tb turns on, using p+ and when 0 - 90 degree rectified tb turns off and ta turns on, using The DC voltage in FIG. 15(b) is proportional to the speed of the brushless motor at all rotor angles, as can be seen by comparison with the line-to-line emfs ( FIG. 15(c)). The ideal fiat tops are again rounded in the diagram and only one emf is shown as a complete waveform:
Eca -- Ec -- Ea
The waveform of the rectified, commutated, per-phase emfs from the tacho is seen to be synchronized with the envelope of the (rectified) line-to-line emfs of the motor.
FIG. 15 Measurement of shaft speed of the trapezoidal motor
Measurement of shaft position
Each phase current of the squarewave motor is commutated at the beginning and end of 180 electrical degrees of the pole rotation. No information about intermediate positions is given to the drive by the Hall plate or tacho sensors and so nothing is known about the position of the motor shaft between the commutation points. If a squarewave motor is to be used in an application which requires position and speed control, it can be fitted with an incremental encoder in addition to the tacho.
Commutation of the sinewave motor
In the ideal squarewave motor, the phase current is independent of the rotor angle between the commutation points. PWM is applied as a means of altering the magnitude of the rectangular current waveform. In the sinewave motor, the current must depend on the sine of the rotor angle and so PWM is used to produce the sinusoidal shape of the waveform as well as to control its magnitude.
The two conducting supply lines of the squarewave motor carry the same current. For the sinewave motor, however, FIG. 12 shows the inverter output currents in general to have different magnitudes at all rotor angles. This means that PWM must be applied separately to each line current, and also that the rotor angle of the sinewave motor must be known at all times.
Measurement of rotor angle
The sinewave motor is often fitted with a brushless resolver which continuously monitors the position of the rotor. As the position is known at all times, separate shaft speed and position sensors are not needed. FIG. 16 shows the two outputs which are fed to the drive from the resolver. They consist of the resolver input signal, modulated according to the sine and cosine of the rotor angle in mechanical degrees.
FIG. 16 Resolver signals
FIG. 17 Definition of shaft position
FIG. 18 Mechanical positions of rotor poles
A positive increase in angle normally indicates clockwise rotation of the motor shaft, looking at the drive end. The actual direction of rotation is found from the phase sequence of the two signals. FIG. 17 shows how the two signals are compared. The drive is able to determine the quadrant of the angular position as only one is common to the sine and cosine measurement.
The resolver outputs occur at the same frequency as the phase emfs only in the case of a two-pole motor, where the mechanical and electrical rotor angles coincide. FIG. 18 shows the ideal emfs generated by the a-phase of four-, six-, and eight-pole motors as the rotors turn through 360 mechanical degrees. The figure also shows the signal which originates from the resolver for the sine of the mechanical angle of the rotor. The drive converts the mechanical angle determined from the resolver signals into the electrical angular position required for commutation, according to the number of rotor poles.
5. The motor-sensor combination
There are two types of brushless motor and several types of sensor, giving many possible combinations. The combination used in practice is chosen partly according to its cost- effectiveness for the application in hand. The choice is also affected by the potential scale and future development of the application. Sinusoidal drive systems are generally more expensive than the trapezoidal type, and there is a great difference between the price of an absolute and an incremental encoder. In general, the least expensive sensors are used with trapezoidal motors.
Trapezoidal motor-Hall-effect sensor
The speed of the trapezoidal motor can be estimated by using the signals from the Hall-effect sensor already fitted for the purpose of commutation. The signals are too widely spaced to be used for position control, but speed regulation above about 500 rpm is possible. The method is limited mainly to on-off, fixed speed applications, one example being the brushless industrial fan motor. In this example, the rival pricewise is the induction motor and inverter unit.
Trapezoidal motor-tacho and incremental encoder
The shaft speed sensor of the trapezoidal motor is normally in the form of a tacho, and an incremental encoder is added when measurement of the shaft position is required. The encoder output can be processed to give a measurement of motor speed, but the resulting signal is not usually good enough at the mid to low end of the range. This is due to the presence of a ripple which is inversely proportional to speed. The ripple may be reduced by increasing the number of lines on the encoder, but this increases the cost and also limits the maximum encoder speed. Low speed control of the trapezoidal motor is in any case subject to the effect of its cogging torque. The encoder signal can, however, give accurate positioning of a load, particularly where the load movement is reduced in comparison to that of the motor shaft through a transmission mechanism. A pulley and belt driven packaging machine, for example, may easily be controlled to within 0.5 mm.
Sinusoidal motor-resolver or absolute encoder
This combination is used for applications which demand very high accuracy of load speed and position. Many such cases occur in the control of machine tools such as lathes and milling machines. Choosing between the resolver and the absolute encoder on the basis of cost tends to be unrealistic.
The drive accepts the signals from an absolute encoder in digital form, but must first process the analogue signals from a resolver. Even if a resolver is only 10% of the price of a Sincos absolute encoder, the overall costs of drive plus sensor may not differ significantly. The absolute encoder can be the best choice for relatively large scale installations where an integrated approach is taken to the digital control system.