Patent Publication Number: US-8988021-B2

Title: Control of a brushless motor

Description:
REFERENCE TO RELATED APPLICATIONS 
     This application claims the priority of United Kingdom Application No. 1006395.6, filed Apr. 16, 2010, the entire contents of which are incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates to control of a brushless motor. 
     BACKGROUND OF THE INVENTION 
     A brushless motor typically includes a control system for controlling the excitation of phase windings of the motor. When driven by an AC supply, the control system often includes an active power factor correction (PFC) circuit, which outputs a regular DC voltage for use in exciting the phase windings while ensuring that current drawn from the AC supply is substantially sinusoidal. As a result, a relatively high power factor may be achieved. However, an active PFC circuit significantly increases the cost of the control system. Additionally, the PFC circuit requires a high-capacitance DC link capacitor, which is both physically large and expensive, in order to provide a regular feedback voltage to the PFC circuit. 
     SUMMARY OF THE INVENTION 
     In a first aspect, the present invention provides a method of controlling a brushless motor, the method comprising: rectifying an alternating voltage to provide a rectified voltage having a ripple of at least 50%; exciting a winding of the motor with the rectified voltage; and performing one of a first process and a second process in response to current in the winding exceeding a threshold proportional to the rectified voltage, wherein the first process comprises freewheeling the winding, and the second process comprises continuing to excite the winding for an overrun period and freewheeling the winding at the end of the overrun period. 
     Owing to the ripple in the rectified voltage, the threshold and thus the level of current driven into the winding vary with time. Since the threshold is directly proportional to the rectified voltage, the waveform of current drawn from the power supply may approach that of a sinusoidal. A relatively high power factor may therefore be achieved without the need for an active PFC circuit or high-capacitance link capacitor. 
     On reaching the threshold the method performs one of two processes. In the first process, the winding is immediately freewheeled. In the second process, the winding continues to be excited for an overrun period, after which the winding is freewheeled. By freewheeling the winding, the magnetic flux density in the motor may be better controlled. In particular, magnetic saturation may be avoided. 
     The use of an overrun period provides a convenient method of adjusting the conduction period (i.e. the period over which the winding is excited) in response to one or more control variables. For example, the method may comprise adjusting the overrun period in response to a change in one or more of the motor speed, the RMS value of the alternating voltage, a speed demand value, and a torque demand value. 
     The method may involve performing the first process when the speed of the motor is below a predetermined speed threshold and performing the second process when the speed of the motor is above the speed threshold. For example, the first process may be performed while the motor accelerates from stationary, and the second process may be performed when the motor operates at a steady state. At relatively low speeds, the electrical half-cycle period of the motor is relatively long and thus current in the winding is likely to exceed the threshold after a relatively short electrical angle. If the winding were then freewheeled until the end of the electrical half-cycle of the motor, relatively little current and thus power would be driven into the winding. As a result, the motor may not accelerate or would accelerate at a much slower rate. Accordingly, the first process may involve freewheeling the winding for a fixed period of time. At the end of the freewheel period, the winding is then excited again until current exceeds the threshold. The winding is thus repeatedly excited and freewheeled over each electrical half-cycle of the motor. Consequently, more current and thus power may be driven into the winding over each electrical half-cycle. When operating at a steady state, the method may comprise exciting and freewheeling the winding only once over each electrical half-cycle of the motor. The method therefore uses the same threshold to achieve current control during acceleration and to achieve a current waveform approaching that of a sinusoid during steady state. Since the same threshold is used irrespective of the speed of the motor, control of the motor is simplified. 
     Irrespective of whether the first or the second process is performed, the winding is initially excited until current in the winding exceeds a threshold. The length of this initial period is not therefore predetermined but instead depends upon the physical characteristics of the motor as well as the behaviour of the alternating voltage. As a result, this initial excitation period acts to compensate for certain timing errors that might otherwise arise due to tolerances and limitations within the motor system. Consequently, a more stable current waveform may be achieved. 
     The method may comprise varying the overrun period in response to changes in the motor speed or the RMS value of the alternating voltage. As a result, a particular power profile may be achieved over a range of motor speeds and/or voltages. In particular, the overrun period may be adjusted so as to achieve constant average power (input or output power) over a range of motor speeds and/or voltages. 
     The length of the overrun period may vary over each half-cycle of the alternating voltage. In particular, the length of the overrun period may increase over the first half of each half-cycle of the alternating voltage and decrease over the second half. The amount by which the overrun period varies over each half-cycle may then be adjusted in response to, for example, changes in the motor speed or the RMS value of the alternating voltage. As a result, the magnitude of low-order harmonics within the current waveform may be better controlled in response to changes in motor speed and/or RMS voltage. In particular, the magnitude of low-order harmonics may be kept below predetermined thresholds (e.g. such as those set by governing bodies) over an operating speed range and/or voltage range. 
     The length of the overrun period may comprise the sum of a first component and a second component. The first component is then constant over each half-cycle of the alternating voltage, while the second component varies over each half-cycle of the alternating voltage. The second component may vary as a half-sinusoid over each half-cycle of the alternating voltage. This then helps maintain a current waveform for which the magnitude of low-order harmonics is relatively small. The second component may be determined using the length of time that has elapsed since a zero-crossing in the alternating voltage. This then ensures that the overrun period is synchronized with the waveform of the alternating voltage resulting in a smoother envelope for the current waveform. Defining the overrun period as the sum of two components provides a convenient method of adjusting the overrun period (and thus the conduction period) in response to changes in motor speed and/or RMS voltage. In particular, the method may involve adjusting the first component only in response to a change in motor speed and/or RMS voltage. Consequently, a particular power profile (e.g. constant average power) may be achieved over a range of motor speeds and/or voltages while at the same time ensuring that the magnitude of low-order harmonics within the current waveform is kept below predetermined thresholds (e.g. such as those set by governing bodies). 
     There may be a time delay associated with measuring the current in the winding. As a result, the measured current may not correspond to the actual current in the winding. The time delay therefore introduces a phase shift between the waveform of the measured current and the waveform of the actual current in the winding. This phase shift, if kept relatively small, aids in reducing the magnitude of low-order harmonics within the current waveform drawn from the power supply. 
     In a second aspect, the present invention provides a method of controlling a brushless motor, the method comprising: rectifying an alternating voltage to provide a rectified voltage having a ripple of at least 50%; exciting a winding of the motor with the rectified voltage; and freewheeling the winding in response to current in the winding exceeding a threshold proportional to the rectified voltage. 
     In a third aspect, the present invention provides a method of controlling a brushless motor, the method comprising: rectifying an alternating voltage to provide a rectified voltage having a ripple of at least 50%; exciting a winding of the motor with the rectified voltage; continuing to excite the winding for an overrun period in response to current in the winding exceeding a threshold proportional to the rectified voltage; and freewheeling the winding at the end of the overrun period. 
     In a fourth aspect, the present invention provides a control system for a brushless motor, the control system performing the method described in any one of the preceding paragraphs. 
     The control system may comprise a rectifier for rectifying the alternating voltage, a current sensor for sensing current in the winding, an inverter coupled to the winding, and a controller for generating one or more control signals for controlling the inverter. The inverter excites the winding with the rectified voltage in response to first control signals and freewheels the winding in response to second control signals. The controller then generates the first control signals to excite the winding and subsequently generates the second control signals to freewheel the winding. The second control signals are generated in response to current in the winding exceeding the threshold (when performing the first process) or after an overrun period has expired since current in the winding exceeded the threshold (when performing the second process). 
     The control system may comprise an RC filter for filtering the signal output by the current sensor. The time constant of the RC filter introduces a time delay between the measured current and the actual current in the winding. This time delay may aid in reducing the magnitude of low-order harmonics within the current waveform drawn from the power supply. 
     In a fifth aspect, the present invention provides a motor system comprising a permanent-magnet motor and a control system as described in any one of the preceding paragraphs. 
     The motor therefore comprises a permanent-magnet rotor, which induces a back EMF in the winding of the motor. The back EMF makes it difficult to accurately control the amount of current drawn from the power supply. Consequently, conventional permanent-magnet motors typically include an active PFC circuit that outputs a regular DC voltage for use in exciting the winding while ensuring that current drawn from the power supply is substantially sinusoidal. With the motor system of the present invention, on the other hand, the winding is excited until current in the winding exceeds a threshold that is proportional to the rectified voltage. As a result, a waveform approaching that of a sinusoid may be achieved for current drawn from the power supply. Consequently, a motor system having a relatively high power factor may be achieved without the need for a PFC circuit or high-capacitance link capacitor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order that the present invention may be more readily understood, embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  is a block diagram of a motor system in accordance with the present invention; 
         FIG. 2  is a schematic diagram of the motor system; 
         FIG. 3  is a sectional view of the motor of the motor system; 
         FIG. 4  details the allowed states of the inverter in response to control signals issued by the controller of the motor system; 
         FIG. 5  is a schematic diagram of the current regulator of the motor system; 
         FIG. 6  illustrates the overrun period used by the controller when operating in single-switch mode; 
         FIG. 7  illustrates a three-step process used by the controller when measuring analog input signals; 
         FIG. 8  details the various operating modes of the motor system; 
         FIG. 9  details the direction in which the motor is driven in response to control signals issued by the controller; 
         FIG. 10  illustrates various waveforms of the motor system when operating in Low-Speed Acceleration Mode; 
         FIG. 11  illustrates various waveforms of the motor system when operating in High-Speed Acceleration Mode; 
         FIG. 12  illustrates various waveforms of the motor system when operating in Running Mode; 
         FIG. 13  illustrates the current waveform drawn from the power supply of the motor system when operating in Running Mode; 
         FIG. 14  illustrates various waveforms and interrupts of the motor system when operating in overcurrent single-switch mode; 
         FIG. 15  illustrates various waveforms and interrupts of the motor system when operating in unlimited-freewheel single-switch mode; 
         FIG. 16  is a schematic diagram of a timer and comparator module arranged to generate a control signal; 
         FIG. 17  is a schematic diagram of a timer and PWM module arranged to generate a control signal; 
         FIG. 18  illustrates various waveforms and interrupts of the motor system when operating in limited-freewheel single-switch mode; 
         FIG. 19  details the values of various hardware components for a particular embodiment of motor system in accordance with the present invention; 
         FIG. 20  details various constants and thresholds employed by the controller of the particular motor system; 
         FIG. 21  illustrates the flux-linkage characteristics of a link inductor of the particular motor system; 
         FIG. 22  illustrates the flux-linkage characteristics of the motor of the particular motor system; 
         FIG. 23  details the various operating modes of the particular motor system; 
         FIG. 24  details a map of control values used by the controller of the particular motor system when operating in multi-switch mode; 
         FIG. 25  details a map of control values used by the controller of the particular motor system when operating in overcurrent single-switch mode; 
         FIG. 26  details a portion of the advance lookup table used by the controller of the particular motor system when operating in unlimited-freewheel single-switch mode; 
         FIG. 27  details a portion of the offset lookup table used by the controller of the particular motor system when operating in unlimited-freewheel single-switch mode; 
         FIG. 28  details a portion of the phase lookup table used by the controller of the particular motor system when operating in unlimited-freewheel single-switch mode; 
         FIG. 29  details a portion of the sine map used by the controller of the particular motor system when operating in single-switch mode; 
         FIG. 30  illustrates possible waveforms for the conduction period used by the controller in single-switch mode; and 
         FIG. 31  illustrates possible waveforms for the advance period of an alternative motor system in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The motor system  1  of  FIGS. 1 to 3  comprises a brushless motor  2  and a control system  3 . Power to the motor system  1  is provided by an AC supply  4 . The AC supply  4  is intended to be a domestic mains supply, though other power supplies capable of providing an alternating voltage might equally be used. 
     The motor  2  comprises a four-pole permanent-magnet rotor  5  that rotates relative to a stator  6 . The stator  6  comprises a pair of c-shaped cores that define four stator poles. Conductive wires are wound about the stator  6  and are coupled together to form a single phase winding  7 . 
     The control system  3  comprises a rectifier  8 , a DC link filter  9 , an inverter  10 , a gate driver module  11 , a current sensor  12 , a position sensor  13 , a zero-cross detector  14 , a temperature sensor  15 , and a controller  16 . 
     The rectifier  8  is a full-wave bridge D 1 -D 4  that rectifies the output of the AC supply  4  to provide a DC voltage. 
     The DC link filter  9  comprises a link capacitor C 1  and a link inductor L 1 . The link capacitor C 1  acts to smooth the relatively high-frequency ripple that arises from inverter switching. As described below in more detail, the link capacitor C 1  is not required to smooth the rectified DC voltage at the fundamental frequency. Consequently, a link capacitor of relatively low capacitance may be used. The link inductor L 1  acts to smooth any residual current ripple that arises from inverter switching. Again, since the link inductor L 1  is intended to reduce ripple at the switching frequency of the inverter  10 , an inductor of relatively low inductance may be used. In order that saturation is avoided, the link inductor L 1  has a saturation point that exceeds the peak current drawn from the AC supply  4  during normal operation of the motor system  1 . 
     The inverter  10  comprises a full bridge of four power switches Q 1 -Q 4  that couple the DC link voltage to the phase winding  7 . Each power switch Q 1 -Q 4  is an IGBT, which is capable of operating at the voltage level typically of most mains power supplies. Other types of power switch, such as BJTs or MOSFETs, might alternatively be used depending on the rating of the power switch and the voltage of the AC supply  4 . Each of the switches Q 1 -Q 4  includes a flyback diode, which protects the switch against voltage spikes that arise during inverter switching. 
     The gate driver module  11  drives the opening and closing of the switches Q 1 -Q 4  of the inverter  10  in response to control signals received from the controller  16 . 
     The current sensor  12  comprises a pair of shunt resistors R 1 ,R 2 , each resistor located on a lower arm of the inverter  10 . The resistance of each shunt resistor R 1 ,R 2  is ideally as high as possible without exceeding dissipation limits during normal operation of the motor system  1 . The voltage across each shunt resistor R 1 ,R 2  is output to the controller  16  as a current sense signal, I_SENSE_ 1  and I_SENSE_ 2 . The first current sense signal, I_SENSE_ 1 , provides a measure of the current in the phase winding  7  when driven from right to left (as is described below in more detail). The second current sense signal, I_SENSE_ 2 , provides a measure of the current in the phase winding  7  when driven from left to right. In locating the shunt resistors R 1 ,R 2  on the lower arms of the inverter  10 , current in the phase winding  7  continues to be sensed during freewheeling (again, as is described below in more detail). 
     The position sensor  13  is a Hall-effect sensor that outputs a digital signal, HALL, that is logically high or low depending on the direction of magnetic flux through the sensor  13 . By locating the position sensor  13  adjacent the rotor  5 , the HALL signal provides a measure of the angular position of the rotor  5 . More particularly, each edge of the HALL signal indicates a change in the polarity of the rotor  5 . When rotating, the permanent-magnet rotor induces a back EMF in the phase winding  7 . Consequently, each edge of the HALL signal also represents a change in the polarity of the back EMF in the phase winding  7 . 
     The zero-cross detector  14  comprises a pair of clamping diodes D 5 ,D 6  that output a digital signal, Z_CROSS, that is logically high when the voltage of the AC supply  4  is positive and logically low when the voltage of the AC supply  4  is negative. Each edge of the Z_CROSS signal thus represents a point in time at which the voltage of the AC supply  4  crosses zero. 
     The temperature sensor  15  comprises a thermistor R 7  that outputs an analog signal, TEMP, that provides a measure of the temperature within the motor system  1 . 
     The controller  16  comprises a microcontroller having a processor  17 , a memory device  18 , a plurality of peripherals  19  (e.g. ADC, comparators, timers etc.), a plurality of input pins  20 , and a plurality of output pins  21 . The memory device  18  stores software instructions for execution by the processor  17 . The memory device  18  also stores a plurality of lookup tables, which are indexed by the processor  17  during operation of the motor system  1 . 
     The controller  16  is responsible for controlling the operation of the motor system  1 . In response to signals at the input pins  20 , the controller  16  generates control signals at the output pins  21 . The output pins  21  are coupled to the gate drive module  11 , which controls the opening and closing of the switches Q 1 -Q 4  of the inverter  10  in response to the control signals. 
     Seven signals are received at the input pins  20  of the controller  16 : I_SENSE_ 1 , I_SENSE_ 2 , HALL, Z_CROSS, TEMP, DC_LINK and DC_SMOOTH. I_SENSE_ 1  and I_SENSE_ 2  are the signals output by the current sensor  12 . HALL is the signal output by the position sensor  13 . Z_CROSS is the signal output by the zero-cross detector  14 . TEMP is the signal output by the temperature sensor  15 . DC_LINK is a scaled-down measure of the DC link voltage, which is obtained by a potential divider R 3 ,R 4  located between the DC link line and the zero volt line. DC_SMOOTH is a smoothed measure of the DC link voltage, obtained by a potential divider R 5 ,R 6  and smoothing capacitor C 2 . 
     In response to the signals received at the inputs, the controller  16  generates and outputs four control signals: TRIP#, DIR 1 , DIR 2 , and FREEWHEEL#. 
     TRIP# is a failsafe control signal. When TRIP# is pulled logically low, the gate driver module  11  opens all switches Q 1 -Q 4  of the inverter  10 . As described below in more detail, the controller  16  pulls TRIP# logically low in the event that current through the phase winding  7  exceeds a failsafe threshold. 
     DIR 1  and DIR 2  control the direction of current through the inverter  10  and thus through the phase winding  7 . When DIR 1  is pulled logically high and DIR 2  is pulled logically low, the gate driver module  11  closes switches Q 1  and Q 4 , and opens switches Q 2  and Q 3 , thus causing current to be driven through the phase winding  7  from left to right. Conversely, when DIR 2  is pulled logically high and DIR 1  is pulled logically low, the gate driver module  11  closes switches Q 2  and Q 3 , and opens switches Q 1  and Q 4 , thus causing current to be driven through the phase winding  7  from right to left. Current in the phase winding  7  is therefore commutated by reversing DIR 1  and DIR 2 . If both DIR 1  and DIR 2  are pulled logically low, the gate drive module  11  opens all switches Q 1 -Q 4 . 
     FREEWHEEL# is used to disconnect the phase winding  7  from the DC link voltage and allow current in the phase winding  7  to re-circulate or freewheel around the low-side loop of the inverter  10 . Accordingly, in response to a FREEWHEEL# signal that is pulled logically low, the gate driver module  11  causes both high-side Q 1 ,Q 2  switches to open. Current then freewheels around the low-side loop of the inverter  10  in a direction defined by DIR 1  and DIR 2 . 
       FIG. 4  summarizes the allowed states of the switches Q 1 -Q 4  in response to the control signals of the controller  16 . Hereafter, the terms ‘set’ and ‘clear’ will be used to indicate that a signal has been pulled logically high and low respectively. 
     When a particular control signal changes, there is a short delay between the changing of the control signal and the physical opening or closing of a power switch. If a further control signal were changed during this delay period, it is possible that both switches on a particular arm of the inverter (i.e. Q 1 ,Q 3  or Q 2 ,Q 4 ) may be closed at the same time. This short-circuit, or shoot-through as it is often termed, would damage the switches on that particular arm of the inverter  10 . Accordingly, in order to prevent shoot-through, the controller  16  employs a dead time, T_DT, between the changing of two control signals. So, for example, when commutating the phase winding  7 , the controller  16  first clears DIR 1 , waits for the dead time, T_DT, and then sets DIR 2 . The dead time is ideally kept as short as possible so as to optimize performance while ensuring that the gate driver module  11  and the power switches Q 1 -Q 4  have sufficient time to respond. 
     Commutation 
     The controller  16  commutates the phase winding  7  in response to edges of the HALL signal. Commutation involves reversing DIR 1  and DIR 2  (i.e. clearing DIR 1  and setting DIR 2 , or clearing DIR 2  and setting DIR 1 ) so as to reverse the direction of current through the phase winding  7 . The phase winding  7  may be freewheeling at the point of commutation. Accordingly, in addition to reversing DIR 1  and DIR 2 , the controller  16  sets FREEHWEEL#. 
     Synchronous Commutation 
     Below a predetermined speed threshold, SPEED_ADV, the controller  16  commutates the phase winding  7  in synchrony with the edges of the HALL signal. Each edge of the HALL signal represents a change in the polarity of back EMF in the phase winding  7 . Consequently, at speeds below SPEED_ADV, the controller  16  commutates the phase winding  7  in synchrony with the zero-crossings of back EMF. 
     As the rotor  5  accelerates, the period of each electrical half-cycle decreases and thus the time constant (L/R) associated with the inductance of the phase winding  7  becomes increasingly important. Additionally, the magnitude of back EMF in the phase winding  7  increases, which then influences the rate at which current rises in the phase winding  7 . Consequently, if the controller  16  continued to commutate the phase winding  7  in synchrony with the edges of the HALL signal, a speed would be reached at which it would be no longer possible to drive additional current into the phase winding  7  over each electrical half-cycle. Accordingly, on reaching SPEED_ADV, the controller  16  switches from synchronous commutation to advanced commutation. By commutating the phase winding  7  in advance of the edges of the HALL signal, the voltage used to excite the phase winding  7  is boosted by the back EMF. As a result, the direction of current through the phase winding  7  may be more quickly reversed. Additionally, phase current may be caused to lead the back EMF, which then helps to compensate for the slower rate of current rise. Although this then generates a short period of negative torque, this is normally more than compensated by the subsequent gain in positive torque. 
     Advanced Commutation 
     At speeds at or above the speed threshold, SPEED_ADV, the controller  16  commutates the phase winding  7  in advance of each edge of the HALL signal by an advance period, T_ADV. Since the electrical half-cycle period decreases and the back EMF increases with rotor speed, the electrical angle at which commutation occurs in advance of the edges of the HALL signal ideally increases with rotor speed. For a particular advance period, T_ADV, the corresponding advance angle, A_ADV, may be defined as:
 
 A _ADV (elec. deg)= T _ADV (sec)*{ω (rpm)/60}*360 (mech. deg)* n/ 2
 
where A_ADV is the advance angle in electrical degrees, T_ADV is the advance period in seconds, ω is the rotor speed in rpm, and n is the number of rotor poles. From this equation, it can be seen that the advance angle is directly proportional to the rotor speed. Consequently, even for a fixed advance period, the advance angle increases with rotor speed. However, better control over acceleration, power and efficiency may be achieved by employing different advance periods at different rotor speeds. The controller  16  therefore comprises an advance lookup table that stores an advance period for each of a plurality of rotor speeds.
 
     In response to an edge of the Z_CROSS signal, the controller  16  selects from the advance lookup table an advance period, T_ADV, corresponding to the speed of the rotor  5 . The speed of the rotor  5  is determined from the interval, T_HALL, between two successive edges of the HALL signal. This interval will hereafter be referred to as the Hall period. The speed of the rotor  5  is then defined by:
 
ω (rpm)=60 /{n*T _HALL (sec)}
 
where ω is the speed of the rotor in rpm, T_HALL is the Hall period in seconds, and n is the number of poles of the rotor. The controller  16  uses the selected advance period to commutate the phase winding  7  in advance of the edges of the HALL signal. The same advance period, T_ADV, is then used by the controller  16  until such time as a further edge of the Z_CROSS signal is detected. In response to the further edge of the Z_CROSS signal, the controller  16  selects from the advance lookup table a new advance period corresponding to the speed of the rotor  5 . The advance period is therefore updated only when the voltage of the AC supply  4  crosses zero, and is constant over each half-cycle of the AC supply  4 .
 
     In order to commutate the phase winding  7  in advance of a particular edge of the HALL signal, the controller  16  acts in response to the preceding edge of the HALL signal. In response to an edge of the HALL signal, the controller  16  subtracts the advance period, T_ADV, from the Hall period, T_HALL, in order to obtain a commutation period, T_COM:
 
 T _COM= T _HALL− T _ADV
 
     The controller  16  then commutates the phase winding  7  at a time, T_COM, after the edge of the HALL signal. As a result, the phase winding  7  is commutated in advance of the subsequent edge of the HALL signal by the advance period, T_ADV. 
     As noted above, the advance period, T_ADV, remains fixed over each half-cycle of the AC supply  4 . However, the speed of the rotor  5  varies over each half-cycle of the AC supply  4  owing to the sinusoidal increase and decrease in DC link voltage. The Hall period, T_HALL, therefore varies over each half-cycle of the AC supply  4 . Consequently, in contrast to the advance period, the controller  16  calculates the commutation period, T_COM, for each edge of the HALL signal. 
     Current Control 
     A number of the peripherals  19  of the controller  16  are configured to define a current regulator  22 . The current regulator  22  monitors and regulates current in the phase winding  7 . The current regulator  22  performs two functions. First, the current regulator  22  clears TRIP# in the event that current in the phase winding  7  exceeds a failsafe threshold. Second, the current regulator  22  generates an overcurrent signal in the event that current in the phase winding  7  exceeds an overcurrent threshold. 
     As illustrated in  FIG. 5 , the current regulator  22  comprises a failsafe module  23  and an overcurrent module  24 . 
     The failsafe module  23  comprises a multiplexer  25 , a comparator  26 , a NOT gate  27 , and an SR latch  28 . The multiplexer  25  has two inputs for selecting one of the two current-sense signals, I_SENSE_ 1  and I_SENSE_ 2 . The selection made by the multiplexer  25  is controlled by the processor  17  in response to the direction of current through the phase winding  7 . In particular, when DIR 1  is set, the multiplexer  25  is caused to select I_SENSE_ 1 , and when DIR 2  is set, the multiplexer is caused to select I_SENSE_ 2 . The output of the multiplexer  25  is delivered to the comparator  26 , which compares the voltage of the selected current-sense signal against a predetermined failsafe voltage, TRIP_REF. TRIP_REF is set such that the output of the comparator  26  is pulled logically high when current through the selected shunt resistor R 1 ,R 2  is greater than a predetermined failsafe threshold, I_MAX. TRIP_REF is thus defined by I_MAX and the resistances of the shunt resistors R 1 ,R 2 . The output of the comparator  26  is delivered to the NOT gate  27 , the output of which is delivered to the S-input of the SR latch  28 . The Q# output of the SR latch  28  is output by the current regulator  22  as the TRIP# signal. Consequently, when the voltage of the current-sense signal, I_SENSE_ 1  or I_SENSE_ 2 , is greater than TRIP_REF, TRIP# is cleared. 
     As noted above, the gate driver module  11  opens all switches Q 1 -Q 4  of the inverter  10  in response to a cleared TRIP# signal. The failsafe module  23  of the current regulator  22  thus prevents current in the phase winding  7  from exceeding a failsafe threshold, I_MAX, above which the switches Q 1 -Q 4  may be damaged and/or the rotor  5  may be demagnetized. By employing hardware to clear the TRIP# signal, the current regulator  22  responds relatively quickly when current in the phase winding  7  exceeds the failsafe threshold. If software executed by the processor  17  were instead employed to clear the TRIP# signal, a delay might arise between current exceeding the failsafe threshold and the clearing of the TRIP# signal, during which time current may rise to a level that damages the switches Q 1 -Q 4  or demagnetizes the rotor  5 . 
     The processor  17  polls the TRIP# signal in response to each edge of the HALL signal. If the TRIP# signal is clear for five successive HALL edges, the processor  17  writes a ‘Failsafe Exceeded’ error to the memory device  18  and enters Fault Mode, which is described below in more detail. Monitoring the TRIP# signal in this manner ensures that the controller  16  does not inadvertently enter Fault Mode due to transient noise in the TRIP# signal. 
     The overcurrent module  24  comprises a multiplexer  29  and a comparator  30 . The multiplexer  29 , like that of the failsafe module  23 , has two inputs for selecting one of the two current-sense signals, I_SENSE_ 1  and I_SENSE_ 2 . Again, the selection made by the multiplexer  29  is controlled by the processor  17  in response to the direction of current through the phase winding  7 . Consequently, when DIR 1  is set, the multiplexer  29  selects I_SENSE_ 1 , and when DIR 2  is set, the multiplexer  29  selects I_SENSE_ 2 . The output of the multiplexer  29  is delivered to the comparator  30 , which compares the voltage of the current-sense signal against the voltage of the DC_LINK signal. When the current-sense signal, I_SENSE_ 1  or I_SENSE_ 2 , is greater than DC_LINK, the output of the comparator  30  is pulled logically low. The overcurrent module  24  thus outputs an overcurrent signal that is pulled logically low when current in the phase winding  7  exceeds an overcurrent threshold that is proportional to the DC link voltage. 
     The output of the overcurrent module  24  is coupled to the processor  17 , which executes an overcurrent routine in response to a low overcurrent signal. Since the overcurrent threshold is proportional to the DC link voltage, the overcurrent threshold varies as a rectified sinusoid across each cycle of the AC supply  4 , the benefits of which are explained in more detail below. 
     The resistances of the potential divider R 3 ,R 4  are selected such that the peak voltage of the DC_LINK signal does not exceed TRIP_REF. Consequently, the current regulator  22  triggers an overcurrent event before current in the phase winding  7  exceeds the failsafe threshold. The overcurrent module  24  and the processor  17  are thus expected to regulate current in the phase winding  7 . The failsafe module  23  is expected to clear TRIP# only in the unlikely event of a fault within the processor  17  (e.g. a software fault) or if the current in the phase winding  7  rises at such a rate that the failsafe threshold, I_MAX, is reached before the processor  17  is able to respond to the overcurrent event. 
     In response to an overcurrent event, the controller  16  performs a different series of actions depending on the speed of the rotor  5 . At speeds below a predetermined threshold, SPEED_SINGLE, the controller  16  operates in a ‘multi-switch mode’. At speeds at or above the predetermined threshold, the controller  16  operates in a ‘single-switch mode’. 
     Multi-Switch Mode 
     In response to an overcurrent event in multi-switch mode, the controller  16  freewheels the phase winding  7  by clearing FREEHWEEL#. Freewheeling continues for a freewheel period, T_FW, during which time current in the phase winding  7  is expected to decay to a level below the overcurrent threshold. If current in the phase winding  7  continues to exceed the overcurrent threshold, the controller  16  again freewheels the phase winding  7  for the freewheel period, T_FW. If, on the other hand, current in the phase winding  7  has dropped below the overcurrent threshold, the controller  16  resumes excitation of the phase winding  7  by setting FREEWHEEL#. 
     For a particular freewheel period, T_FW, the corresponding electrical angle, A_FW, may be defined as:
 
 A _FW (elec. deg)= T _FW (sec)*{ω (rpm)/60}*360 (mech. deg)* n/ 2
 
where A_FW is the freewheel angle in electrical degrees, T_FW is the freewheel period in seconds, ω is the rotor speed in rpm, and n is the number of rotor poles. Consequently, for a fixed freewheel period, the corresponding freewheel angle increases with rotor speed. However, as the freewheel angle increases, the remaining period over which current and thus power is driven into the phase winding  7  decreases. The controller  16  therefore employs a freewheel period, T_FW, that decreases with increasing rotor speed such that the corresponding freewheel angle, A_FW, does not become excessively large as the rotor  5  accelerates.
 
     The controller  16  comprises a freewheel lookup table that stores a freewheel period for each of a plurality of rotor speeds. In response to an edge of the Z_CROSS signal, the controller  16  selects from the freewheel lookup table a freewheel period, T_FW, corresponding to the speed of the rotor  5 . The controller  16  then uses the selected freewheel period to freewheel the phase winding  7  in response to an overcurrent event. The same freewheel period, T_FW, is used by the controller  16  until such time as a further edge of the Z_CROSS signal is detected. In response to the further edge of the Z_CROSS signal, the controller  16  selects from the freewheel lookup table a new freewheel period corresponding to the speed of the rotor  5 . Consequently, as with the advance period, the freewheel period is updated only when the voltage of the AC supply  4  crosses zero, and remains constant over each half-cycle of the AC supply  4 . 
     The controller  16  operates in multi-switch mode only while the rotor  5  accelerates from stationary to SPEED_SINGLE. As such, the length of time spent by the controller  16  in multi-switch mode is relatively short. A relatively coarse speed resolution may therefore be used for the freewheel lookup table without adversely affecting the power or efficiency of the motor system  1 . Indeed, one might conceivably use a fixed freewheel period, so long as the corresponding freewheel angle does not become excessively large as the rotor  5  approaches SPEED_SINGLE. 
     At relatively low rotor speeds, the back EMF induced in the phase winding  7  by the rotor  5  is relatively small. Consequently, current in the phase winding  7  rises to the overcurrent threshold relatively quickly. Owing to the relatively short period of time taken for the current to reach the overcurrent threshold, the controller  16  will typically switch the phase winding  7  between excitation and freewheel multiple times during each electrical half-cycle of the motor  2 . It is for this reason that the controller  16  is said to operate in a multi-switch mode at speeds below SPEED_SINGLE. As the rotor speed increases, the Hall period naturally decreases. Additionally, the back EMF increases and thus the time taken for current in the phase winding  7  to reach the overcurrent threshold increases. Consequently, the controller  16  switches the phase winding  7  between excitation and freewheel less frequently as the rotor  5  accelerates. Eventually, the speed of the rotor  5  rises to a level at which the controller  16  switches the phase winding  7  only once between excitation and freewheel during each electrical half-cycle of the motor  2 . 
     Single-Switch Mode 
     In response to an overcurrent event in single-switch mode, the controller  16  does not immediately freewheel the phase winding  7 . Instead, the controller  16  continues to excite the phase winding  7  for an overrun period, T_OVR. After the overrun period has elapsed, the controller  16  freewheels the phase winding  7  by clearing FREEHWEEL#. Freewheeling then continues indefinitely until such time as the controller  16  commutates the phase winding  7 . The controller  16  thus switches the phase winding  7  from excitation to freewheel only once during each electrical half-cycle of the motor  2 . 
     Referring now to  FIG. 6 , the overrun period, T_OVR, is defined by the equation:
 
 T _OVR= T _OVR_OFFSET+ T _OVR_AMP*abs{sin (θ)}
 
where T_OVR_OFFSET is an offset value, T_OVR_AMP*abs{sin(θ)} is a rectified sine wave having an amplitude defined by T_OVR_AMP, and θ is the angle in the voltage cycle of the AC supply  4 .
 
     The angle θ may be expressed as a time interval from a zero-crossing in the voltage of the AC supply  4 :
 
θ (deg)= t  (sec)* f  (Hz)*360 (deg)
 
where t is the time elapsed in seconds since a zero-crossing in the AC supply  4 , and f is the frequency in Hertz of the AC supply  4 . The overrun period may then be defined as:
 
 T _OVR= T _OVR_OFFSET+ T _OVR_AMP*abs{sin( t*f* 360 deg)}
 
     More simply, the overrun period, T_OVR, may be regarded as the sum of two components:
 
 T _OVR= T _OVR_OFFSET+ T _OVR_SINE
 
where T_OVR_OFFSET is an overrun offset value that is independent of time, and T_OVR_SINE is an overrun sine value that is dependent on time.
 
     T_OVR_SINE is stored by the controller  16  as an overrun sine lookup table. The overrun sine lookup table comprises an overrun sine value, T_OVR_SINE, for each of a plurality of times. In response to an edge of the HALL signal, the controller  16  determines the period of time, t, that has elapsed since the last edge of the Z_CROSS signal. The controller  16  then selects from the overrun sine lookup table an overrun sine value, T_OVR_SINE, corresponding to the elapsed period of time. The controller  16  then sums the overrun offset value, T_OVR_OFFSET, and the overrun sine value, T_OVR_SINE, to obtain the overrun period, T_OVR. 
     As is described below in more detail, by selecting appropriate values for the advance period, T_ADV, the overrun offset, T_OVR_OFFSET, and the overrun amplitude, T_OVR_AMP, the efficiency of the motor system  1  may optimized for a specific average input power or average output power. Moreover, appropriate values may be selected such that the waveform of current drawn from the AC supply  4  complies with harmonic standards set by governing bodies. 
     Timeout 
     Irrespective of rotor speed, an overcurrent event is expected to occur at least once during each electrical half-cycle of the motor  2 . Should an overcurrent event fail to occur, the controller  16  would continue to excite the phase winding  7  and thus current in the phase winding  7  would continue to rise. At relatively high rotor speeds, the magnitude of back EMF in the phase winding  7  is relatively large. As a result, current in the phase winding  7  is unlikely to reach an excessive level even in the absence of an overcurrent event. However, at relatively low rotor speeds, the back EMF induced in the phase winding  7  is relatively small. As a result, current in the phase winding  7  may rise to an excessive level in the absence of an overcurrent event. Indeed, the current may rise to the failsafe threshold, I_MAX, which would then cause the controller  16  to enter Fault Mode. Consequently, when operating in multi-switch mode, the controller  16  automatically executes the overcurrent routine after the phase winding  7  has been excited constantly in the same direction for a timeout period, T_TO. The timeout period thus acts as a failsafe mechanism by ensuring that the maximum period of time over which the phase winding  7  can be excited is limited. 
     As the speed of the rotor  5  increases, the magnitude of back EMF induced in the phase winding  7  also increases. Consequently, the rate at which current rises in the phase winding  7  decreases with increasing rotor speed. Put another way, the electrical angle over which current in the phase winding  7  rises to the overcurrent threshold increases with rotor speed. The controller  16  therefore employs a timeout angle, A_TO, that increases with rotor speed. For a particular timeout period, T_TO, the corresponding timeout angle, A_TO, may be defined as:
 
 A _TO (elec. deg)= T _TO (sec)*{ω (rpm)/60}*360 (mech. deg)* n/ 2
 
where A_TO is the timeout angle in electrical degrees, T_TO is the timeout period in seconds, ω is the rotor speed in rpm, and n is the number of rotor poles. Consequently, for a fixed timeout period, the corresponding timeout angle increases linearly with rotor speed. The controller  16  may therefore use a fixed timeout period, T_TO. However, better control may be achieved if the controller  16  uses a different timeout period for different rotor speeds. The controller  16  therefore comprises a timeout lookup table that stores a timeout period, T_TO, for each of a plurality of rotor speeds.
 
     In response to an edge of the Z_CROSS signal, the controller  16  selects from the timeout lookup table a timeout period, T_TO, corresponding to the speed of the rotor  5 . The same timeout period is then used by the controller  16  until such time as a further edge of the Z_CROSS signal is detected. In response to the further edge of the Z_CROSS signal, the controller  16  selects from the timeout lookup table a new timeout period corresponding to the speed of the rotor  5 . Accordingly, as with the advance period and the freewheel period, the timeout period is updated only when the voltage of the AC supply  4  crosses zero, and remains constant over each half-cycle of the AC supply  4 . 
     Constant Power 
     The controller  16  operates primarily in advanced commutation, single-switch mode. Within this mode, the speed of the rotor  5  varies as the rotor  5  experiences different loads. As the rotor speed varies, so too does the magnitude of back EMF induced in the phase winding  7 . If the controller  16  were to employ a fixed advance period and overrun period, the average input power and the average output power of the system  1  would vary with rotor speed. However, there may be applications for which it is desirable to have a motor system  1  that maintains constant average input or output power over a particular speed range. 
     The average input and output power of the motor system  1  are also dependent upon the RMS voltage of the AC supply  4 . However, the RMS voltage may not be regular. Again, there may be applications for which it is desirable to have a motor system  1  that maintains constant average input or output power irrespective of changes in the voltage of the AC supply  4 . Additionally, the mains power supply in two different countries may differ in RMS voltage but not in frequency. It would be therefore be advantageous if the same performance were achieved by the motor system  1  in both countries. 
     Consequently, in order to maintain constant average power (input or output) over a particular speed range and/or voltage range, the controller  16  adjusts the advance period and the overrun period in response to changes in rotor speed and/or RMS voltage of the AC supply  4 . 
     The advance lookup table therefore stores an advance period, T_ADV, for each of a plurality of rotor speeds and a plurality of voltages. The controller  16  also comprises an overrun offset lookup table that stores an overrun offset value, T_OVR_OFFSET, for each of a plurality of rotor speeds and a plurality of voltages. Each lookup table is thus two-dimensional and is indexed by rotor speed and voltage. As described below in more detail, the controller  16  samples the DC_SMOOTH signal to obtain a measure of the RMS voltage of the AC supply  4 , which is then used by the controller  16  to index each of the lookup tables. 
     As with the advance period, the controller  16  updates the overrun offset value in response to edges of the Z_CROSS signal. In particular, the controller  16  selects from the overrun offset lookup table an overrun offset value, T_OVR_OFFSET, corresponding to the rotor speed and RMS voltage of the AC supply  4 . The overrun offset is thus updated only when the voltage of the AC supply  4  crosses zero, and remains constant over each half-cycle of the AC supply  4 . 
     In response to each edge of the HALL signal, the controller  16  selects from the overrun sine lookup table an overrun sine value, T_OVR_SINE, corresponding to the period of time, t, that has elapsed since the previous zero-crossing in the AC supply  4 . The controller  16  then sums the overrun offset value, T_OVR_OFFSET, and the overrun sine value, T_OVR_SINE, to obtain the overrun period, T_OVR. 
     The advance period, T_ADV, and the overrun period, T_OVR, may therefore defined as:
 
T_ADV=T_ADV_TABLE[speed,voltage]
 
 T _OVR= T _OFFSET_TABLE[speed,voltage]+ T _OVR_SINE_TABLE[ t] 
 
     The advance period and the overrun period are thus adjusted in response to changes in the rotor speed and the RMS voltage of the AC supply  4  so as to ensure that constant average power (input or output) is achieved. One might also adjust the overrun amplitude, T_OVR_AMP, in response to changes in rotor speed and/or RMS voltage. For example, the controller  16  might store an overrun amplitude lookup table that stores an overrun amplitude value, T_OVR_AMP, for each of a plurality of rotor speeds and/or voltages. The controller  16  would then update the overrun amplitude value in response to each edge of the Z_CROSS signal. The overrun sine value, T_OVR_SINE, would then be obtained by multiplying the overrun amplitude value, T_OVR_AMP, with the value obtained from the sine lookup table. However, the multiplication of two numbers increases the number of instructions executed by the controller  16 . Additionally, a controller  16  having a higher bit-resolution would be needed in order to handle the multiplication. Accordingly, in order that a relatively simple and cheap microcontroller might be used for the controller  16 , the overrun amplitude is not adjusted. Nevertheless, should it prove necessary or desirable to do so, the overrun amplitude might also be adjusted. 
     Constant average power is maintained over a speed range bounded by SPEED_CP_MIN and SPEED_CP_MAX, and over a voltage range bounded by V_CP_MIN and V_CP_MAX. 
     Beyond these ranges, the controller  16  does not attempt to maintain constant average power. The reasons for this may vary depending on the particulars of the motor system  1 . For example, at voltages below V_CP_MIN, it may not be possible to drive sufficient current into the phase winding  7  over each electrical half-cycle of the motor  2  in order to maintain constant average power. Alternatively, the efficiency of the motor system  1  may drop-off significantly at voltages below V_CP_ MIN or maintaining constant average power below this voltage may result in excessive current harmonics. 
     While constant average power is maintained over a specific speed range and voltage range, the motor system  1  is nevertheless able to operate effectively at speeds and voltages beyond these ranges. The motor system  1  therefore has an operating speed range defined by SPEED_MIN and SPEED_MAX, and an operating voltage range defined by V_MIN and V_MAX. The advance lookup table and the overrun offset lookup table store values covering the full operating speed and voltage ranges of the motor system  1 . However, constant average power is achieved only at speeds between SPEED_CP_MIN and SPEED_CP_MAX, and at voltages between V_CP_MIN and V_CP_MAX. 
     Voltage and Temperature Measurement 
     The peripherals  19  of the controller  16  include an analog-to-digital converter (ADC) having a plurality of channels. A first channel of the ADC is coupled to the input pin of the DC_SMOOTH signal, and a second channel of the ADC is coupled to the input pin of the TEMP signal. 
     In order to measure the RMS voltage of the AC supply  4 , the processor  17  selects the first channel of the ADC and samples the DC_SMOOTH signal using the ADC. The time constant of the R 6 ,C 2  circuit is sufficiently long that the DC_SMOOTH signal appears relatively constant over each half-cycle of the AC supply  4 . The DC_SMOOTH signal thus provides a measure of the peak voltage of the AC supply  4 . Since the peak voltage is directly proportional to the RMS voltage, DC_SMOOTH also provides a measure of the RMS voltage. Although the DC_SMOOTH signal is relatively constant over each half-cycle of the AC supply  4 , the signal nevertheless has a small degree of high-frequency ripple that arises from switching of the inverter  10 . Accordingly, in order to compensate for this ripple, the processor  17  samples the DC_SMOOTH signal numerous times over each cycle of the AC supply  4 . The processor  17  then takes the average of the samples in order to obtain a measure of the RMS voltage of the AC supply  4 . 
     In order to measure the temperature, the processor  17  selects the second channel of the ADC and samples the TEMP signal using the ADC. Again, the processor  17  samples the TEMP signal numerous times and determines the average in order to obtain a measure of the temperature. By taking the average of numerous samples, the controller  16  does not inadvertently react to spurious noise in the TEMP signal or transient temperature changes within the motor system  1 . 
     When operating at relatively high rotor speeds, the time required by the ADC to select a channel and sample the relevant input signal may delay the execution of other routines. As explained below in more detail, any delay is likely to adversely affect the performance of the motor system  1 . Accordingly, when sampling DC_SMOOTH or TEMP, the sampling process is broken-up into three distinct steps, each of which is executed in turn in response to an edge of the HALL signal. 
     In response to a first edge of the HALL signal, the processor  17  selects the appropriate channel of the ADC. In response to a second edge, the processor  17  starts the ADC. In response to a third edge, the processor  17  reads the output register of the ADC. The output read by the processor  17  thus represents a single sample of the selected input signal, i.e. DC_SMOOTH or TEMP. The sample read by the processor  17  is then stored to the memory device  18 . This three-step process is then repeated to obtain a further sample of the input signal, which is then added to the value already stored in the memory device  18 . The value stored in the memory device  18  thus corresponds to the sum of the individual samples read by the processor  17 . The three-step process is repeated a predetermined number of times. The processor  17  then divides the value stored in the memory device  18  by the predetermined number to obtain an average measure of the input signal. 
     By breaking up the sampling process into three distinct steps, the time necessary to sample the input signal is spread across three electrical half-cycles of the motor  2 . Consequently, the time spent by the controller  16  in sampling the input signal during each electrical half-cycle of the motor  2  is significantly reduced and thus the possibility of event clashing is reduced. 
     The controller  16  samples the DC_SMOOTH and TEMP signals concurrently. As illustrated in  FIG. 7 , the controller  16  performs the three-step process on the DC_SMOOTH signal to obtain a single sample of the RMS voltage of the AC supply  4 . The controller  16  then performs the three-step process on the TEMP signal to obtain a single sample of the temperature. This process of alternately sampling DC_SMOOTH and TEMP is then repeated a predetermined number of times. The memory device  18  thus stores a first value corresponding to the sum of the samples of the RMS voltage of the AC supply  4 , and a second value corresponding to the sum of the samples of the temperature. 
     Rather than sampling the DC_SMOOTH and TEMP signals concurrently, the controller  16  may instead sample the two input signals sequentially. In particular, the controller  16  may sample the DC_SMOOTH signal a predetermined number of times before then sampling the TEMP signal a predetermined number of times. By sampling the two input signals sequentially rather than concurrently, the channel of the ADC is changed only once for each set of samples. As a result, the step of selecting a channel may be dropped from all but the very first sample. A two-step process (i.e. start ADC and read ADC) may then be used to sample all but the very first of the samples. Accordingly, a greater number of samples may be collected over a particular time period. However, a drawback with sampling the two input signals sequentially is that, for each signal, there is a period during which the signal is not being measured. 
     The controller  16  has only one ADC, which is required to sample two input signals, namely DC_SMOOTH and TEMP. It is for this reason that the sampling process includes the step of selecting an ADC channel. If the temperature sensor  15  were omitted from the control system  3 , the RMS voltage of the AC supply  4  could be sampled without the need for channel selection. Alternatively, if the peripherals  19  of the controller  16  included an additional ADC, each input signal could be sampled by a dedicated ADC and thus the step of selecting a channel could again by omitted. Nevertheless, in both instances, the sampling process continues to be broken into two steps, such that the time necessary to sample an input signal is spread across two electrical half-cycles of the motor  2 . 
     In the particular embodiment illustrated in  FIG. 7 , each step of the sampling process is executed in response to a successive edge of the HALL signal. This then has the advantage that each sample is obtained relatively quickly, i.e. after three edges of the HALL signal. Nevertheless, it is not essential that each step is executed in response to successive edges of the HALL signal. For example, each step of the sampling process may be executed in response to every second or third edge of the HALL signal. While this then requires a longer period of time to obtain each sample, the controller  16  may use the time when it is not addressing the ADC to execute other routines. 
     Rather than using the average of the various samples as a measure of the input signal, the controller  16  might alternatively use the sum of the samples. Alternatively, the controller  16  might use the peak value of the samples as a measure of the input signal. For example, after reading a sample from the output register of the ADC, the processor  17  might compare the sample against a value stored in the memory device  18 . If the sample is greater than the value stored in the memory device  18 , the processor  17  overwrites the value with that of the sample. The steps of comparing and overwriting are then repeated for each of the predetermined number of samples. After all samples have been collected, the value stored in the memory device  18  represents the peak value of the samples. When measuring the peak value, it is not essential that the input signal representing the voltage of the AC supply  4  is smooth, so long as the samples span at least one half-cycle of the AC supply  4 . Consequently, the smoothing capacitor C 2  may be omitted or the capacitance might be significantly reduced so as to reduce the size and/or cost of the control system  3 . 
     In addition to measuring the voltage of the AC supply  4  and temperature when operating at speed, the controller  16  also measures the voltage and temperature during initial power up. This initial check is made in order to ensure that the RMS voltage of the AC supply  4  and the temperature within the motor system  1  lie within safe operating limits. During this initial stage, the time spent by the controller  16  in sampling the input signal is not critical. Consequently, during initial power up, the controller  16  samples the voltage and the temperature without breaking the process into three steps. 
     Lookup Tables 
     The memory device  18  of the controller  16  stores a number of lookup tables, each having a particular speed and/or voltage resolution. The resolution of each lookup table need not be the same as that of other lookup tables and may vary across the lookup table. For example, the advance lookup table may store an advance period every 10 krpm at relatively low speeds, which gradually increases to 1 krpm at relatively high speeds. 
     Advanced commutation is employed in both multi-switch mode and single-switch mode. In single-switch mode, the advance period is adjusted in response to changes in both rotor speed and RMS voltage of the AC supply  4  in order to maintain constant average power. In multi-switch mode, it is not necessary to adjust the advance period in response to changes in voltage. Accordingly, in order to minimize the amount of memory required to store the advance lookup table, the memory device  18  stores two advance lookup tables: a one-dimensional lookup table that is indexed by rotor speed when operating at speeds below SPEED_SINGLE, and a two-dimensional lookup table that is indexed by rotor speed and voltage at speeds at or above SPEED_SINGLE. 
     Rather than storing absolute values, each lookup table may instead store difference values. The controller  16  then stores a reference value to which the difference values are applied. Consequently, when updating a particular parameter, the controller  16  indexes the relevant lookup table to select a difference value, and applies the difference value to the reference value to obtain the parameter. So, for example, the controller  16  may employ advance periods of 47 μs, 50 μs and 52 μs for the rotor speeds 85 krpm, 90 krpm and 95 krpm. The controller  16  might then store 50 μs as the reference value. The advance lookup table would then store −2 μs, 0 μs, and 1 μs for each of the three speeds. Storing a difference value typically requires less memory than an absolute value. As a result, the lookup tables may be stored more efficiently. A higher resolution for the lookup tables might then be achieved for a given amount of memory. Alternatively or additionally, a cheaper controller having a smaller memory capacity may be used. In a more general sense, therefore, each lookup table may be said to store a control value (e.g. an absolute or difference value) that is used by the controller  16  to determine the relevant parameter, e.g. advance period, overrun offset etc. 
     In order to reduce the number of instructions executed by the controller  16 , the controller  16  only updates those parameters that are required for the relevant mode of operation. For example, when operating in synchronous commutation mode, the controller  16  has no need to select or update an advance period. Similarly, when operating in single-switch mode, the controller  16  has no need to select or update a freewheel period. As a consequence of updating only those parameters required for a particular mode of operation, the controller  16  does not immediately change from multi-switch mode to single-switch mode when the rotor reaches SPEED_SINGLE. If the controller  16  were to immediately change from multi-switch to single-switch mode, the controller  16  would not know what period of time had elapsed since the previous zero-crossing in the voltage of the AC supply  4 . As a result, the controller  16  would not know what overrun period to use. Accordingly, when the rotor speed reaches SPEED_SINGLE, the controller  16  waits until the next edge of the Z_CROSS signal before changing from multi-switch mode to single-switch mode. 
     As the motor  2  accelerates from stationary, the length of the Hall period decreases. Consequently, if a parameter (e.g. the freewheel period) were updated on every nth edge of the HALL signal, the interval between each update would gradually decrease. Each parameter would then be updated less frequently at low speeds and more frequently at high speeds. By updating each parameter in response to a zero-crossing in the voltage of the AC supply  4 , each parameter is updated at regular intervals irrespective of speed. 
     If a parameter were updated on every nth edge of the HALL signal while operating in single-switch mode, the parameter would update at different points within the cycle of the AC supply  4 . This in turn could potentially increase the harmonic content of the current waveform drawn from the AC supply  4 . Additionally, when the motor system  1  is operating at constant average speed, the instantaneous speed of the rotor  5  nevertheless varies over each half-cycle of the AC supply  4  owing to the sinusoidal increase and decrease in the DC link voltage. If a parameter were updated on every nth edge of the HALL signal, a different value for the parameter might be selected in spite of the fact that the average speed of the motor system  1  had not changed. Again, this may result in increased harmonics within the current waveform drawn from the AC supply  4 . By updating each parameter in response to a zero-crossing in the AC supply  4 , the same reference point in the cycle of the AC supply  4  is used. Consequently, a more stable current waveform is achieved. Furthermore, by updating the parameters only once every half-cycle of the AC supply  4 , the instructions executed by the controller  16  are kept relatively simple and thus a simpler and cheaper microcontroller may be used. Of course, if one so desired, the various parameters may be updated less frequently by updating on every nth edge of the Z_CROSS signal. 
     Motor Operation 
     The operation of the motor system  1  as it accelerates from stationary to running speed will now be described. As can be seen from  FIG. 8 , the controller  16  has six operating modes: Initialization, Stationary, Low-Speed Acceleration, High-Speed Acceleration, Running, and Fault. Within the various operating modes, the controller  16  controls the motor  2  through the use of one or more of the following four parameters: freewheel period, advance period, overrun period, and timeout period. 
     Initialization Mode 
     On powering up, the controller  16  enables the peripherals  19  and samples the DC_SMOOTH signal and the TEMP signal in order to obtain a measure of RMS voltage of the AC supply  4  and the temperature within the motor system  1 . If the RMS voltage is less than an under-voltage threshold, V_MIN, or greater than an over-voltage threshold, V_MAX, the controller  16  writes an ‘Under Voltage’ or ‘Over Voltage’ error to the memory device  18  and enters Fault Mode. Similarly, if the temperature is less than an under-temperature threshold, TEMP_MIN, or greater than an over-temperature threshold, TEMP_MAX, the controller  16  writes an ‘Under Temperature’ or ‘Over Temperature’ error to the memory device  18  and enters Fault Mode. 
     If the RMS voltage and the temperature lie within the operating thresholds, the controller  16  determines whether the speed of the rotor  5  exceeds a stationary threshold, SPEED_STATIONARY. As noted above, the speed of the rotor  5  is obtained from the interval between two successive edges of the HALL signal, i.e. the Hall period. If the controller  16  fails to detect two edges of the HALL signal within a period of time corresponding to SPEED_STATIONARY, the controller  16  enters Stationary Mode. Otherwise, the controller  16  enters Low Speed Acceleration Mode. 
     Stationary Mode (ω&lt;SPEED_STATIONARY) 
     The controller  16  drives the motor  2  in reverse for a predetermined reverse-drive time, T_RD. For the purposes of the present description, it will be assumed that the motor  2  is driven forwards in response to driving the phase winding  7  from left-to-right when the HALL signal is logically low and from right-to-left when the HALL signal is logically high. The motor  2  is therefore driven in reverse in response to driving the phase winding  7  from right-to-left when the HALL signal is logically low and from left-to-right when the HALL signal is logically high, as detailed in  FIG. 9 . 
     Momentarily driving the motor  2  in reverse should cause the rotor  5  to either rotate in a forward direction or adopt a particular angular position relative to the stator  6 . Whether the rotor  5  rotates forward or aligns with the stator  6  will depend on the starting position of the rotor  5 . The rotor  5  is therefore either moving in a forward direction or is in a position ready for acceleration in a forward direction. 
     After momentarily driving the motor  2  in reverse, the controller  16  commutates the phase winding  7  so as to drive the motor  2  forward. The forward drive should cause the rotor  5  to rotate in a forward direction. If the rotor  5  is rotating as expected, an edge of the HALL signal should occur within a predetermined time, T_FD. If no edge is detected within the predetermined time, T_FD, the controller writes a ‘Fail to Start’ error to the memory device  18  and enters Fault Mode. Otherwise, the controller  16  commutates the phase winding  7  in response to the edge of the HALL signal so as to continue driving the motor  2  forward. A second edge of the HALL signal should then occur within a period of time corresponding to SPEED_STATIONARY. If the second edge is detected within the predetermined time, the controller  16  enters Low-Speed Acceleration Mode. Otherwise, the controller writes a ‘Fail to Start’ error to the memory device  18  and enters Fault Mode. 
     Low-Speed Acceleration Mode (SPEED_STATIONARY≦ω&lt;SPEED_ADV) 
     When operating in Low-Speed Acceleration Mode, the controller  16  drives the motor  2  in synchronous commutation, multi-switch mode.  FIG. 10  illustrates the waveforms of the HALL signal, the control signals, and the phase current over a few Hall periods. 
     In response to each edge of the HALL signal, the controller  16  immediately commutates the phase winding  7  (i.e. by reversing DIR 1  and DIR 2 , and by setting FREEWHEEL#). The controller  16  then determines the speed of the rotor  5  on the basis of the Hall period, T_HALL. The controller  16  then polls a zero-cross flag, which is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set and the speed of the rotor  5  is greater than or equal to SPEED_ADV, the controller  16  enters High-Speed Acceleration Mode. If, on the other hand, the zero-cross flag is set but the rotor speed is less than SPEED_ADV, the controller  16  updates the freewheel period, T_FW, and the timeout period, T_TO, and clears the zero-cross flag. The freewheel and timeout periods are updated by indexing the freewheel and timeout lookup tables using the rotor speed. 
     After polling the zero-cross flag, and if necessary updating the freewheel and timeout periods, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. If the predetermined number of samples has been collected, the controller  16  determines the average of the samples to obtain a measure of the RMS voltage of the AC supply  4  or the temperature within the motor system  1 . If the RMS voltage is less than V_MIN or greater than V_MAX, or if the temperature is less than TEMP_MIN or greater than TEMP_MAX, the controller  16  writes a corresponding error to the memory device  18  and enters Fault Mode. 
     Following commutation, the controller  16  continues to excite the phase winding  7  until either an overcurrent event occurs or the timeout period, T_TO, expires. In response to either of these two events, the controller  16  freewheels the phase winding  7  (i.e. by clearing FREEHWEEL#) for the freewheel period, T_FW. If, at the end of the freewheel period, current in the phase winding  7  exceeds the overcurrent threshold, the controller  16  again freewheels the phase winding  7  for the freewheel period, T_FW. Otherwise, at the end of the freewheel period, the controller  16  resumes excitation of the phase winding  7  (i.e. by setting FREEWHEEL#). 
     The controller  16  therefore commutates the phase winding  7  in synchrony with the edges of the HALL signal, and updates the freewheel period and the timeout period in response to edges of the Z_CROSS signal. The controller  16  continues to drive the motor  2  in synchronous commutation, multi-switch mode until such time as the speed of the rotor  5  reaches SPEED_ADV. On reaching SPEED_ADV, the controller  16  enters High-Speed Acceleration Mode in response to the next edge of the Z_CROSS signal. 
     High-Speed Acceleration Mode (SPEED_ADV≦ω&lt;SPEED_SINGLE) 
     When operating in High-Speed Acceleration Mode, the controller  16  drives the motor  2  in advanced commutation, multi-switch mode.  FIG. 11  illustrates the waveforms of the HALL signal, the control signals, and the phase current over a few Hall periods. 
     In response to each edge of the HALL signal, the controller  16  determines the speed of the rotor  5  on the basis of the Hall period, T_HALL. The controller  16  then polls the zero-cross flag that is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set and the speed of the rotor  5  is greater than or equal to SPEED_SINGLE, the controller  16  enters Running Mode. If, on the other hand, the zero-cross flag is set and the rotor speed is less than SPEED_SINGLE, the controller  16  updates the advance period, T_ADV, the freewheel period, T_FW, and the timeout period, T_TO, and clears the zero-cross flag. The advance, freewheel and timeout periods are updated by indexing the corresponding lookup tables using the rotor speed. 
     After polling the zero-cross flag, and if necessary updating the advance, freewheel and timeout periods, the controller  16  calculates the commutation period, T_COM, by subtracting the advance period, T_ADV, from the Hall period, T_HALL. The controller  16  then loads the commutation period, T_COM, into a timer. 
     After calculating the commutation period, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. If the predetermined number of samples has been collected, the controller  16  determines the average of the samples to obtain a measure of the RMS voltage of the AC supply  4  or the temperature within the motor system  1 . If the RMS voltage is less than V_MIN or greater than V_MAX, or if the temperature is less than TEMP_MIN or greater than TEMP_MAX, the controller  16  writes a corresponding error to the memory device  18  and enters Fault Mode. 
     The controller  16  subsequently commutates the phase winding  7  (i.e. by reversing DIR 1  and 
     DIR 2 , and by setting FREEWHEEL#) after the timer has counted for the commutation period, T_COM. As a result, the controller  16  commutates the phase winding  7  in advance of the next edge of the HALL signal by the advance period, T_ADV. Following commutation, the controller  16  excites the phase winding  7  until either an overcurrent event occurs or the timeout period, T_TO, expires. In response to either of these two events, the controller  16  freewheels the phase winding  7  (i.e. by clearing FREEHWEEL#) for the freewheel period, T_FW. If, at the end of the freewheel period, current in the phase winding  7  exceeds the overcurrent threshold, the controller  16  again freewheels the phase winding  7  for the freewheel period, T_FW. Otherwise, at the end of the freewheel period, the controller  16  resumes excitation of the phase winding  7  (i.e. by setting FREEWHEEL#). 
     The controller  16  therefore commutates the phase winding  7  in advance of the edges of the HALL signal, and updates the advance period, the freewheel period and the timeout period in response to edges of the Z_CROSS signal. The controller  16  continues to drive the motor  2  in advanced commutation, multi-switch mode until such time as the speed of the rotor  5  reaches SPEED_SINGLE. On reaching SPEED_SINGLE, the controller  16  enters Running Mode in response to the next edge of the Z_CROSS signal. 
     Running Mode (SPEED_SINGLE≦ω) 
     When operating in Running Mode, the controller  16  drives the motor  2  in advanced commutation, single-switch mode.  FIG. 12  illustrates the waveforms of the HALL signal, the control signals, and the phase current over a few Hall periods. 
     In response to each edge of the HALL signal, the controller  16  determines the speed of the rotor  5  on the basis of the Hall period, T_HALL. The speed of the rotor  5  is expected to remain within a speed range bounded by SPEED_MIN and SPEED_MAX. The controller  16  will, however, permit transient speeds outside of this range. Accordingly, if the speed of the rotor  5  drops below SPEED_MIN for a period of time longer than T_US, the controller  16  writes an ‘Under Speed’ error to the memory device  18  and enters Fault Mode. Similarly, if the speed of the rotor  5  exceeds SPEED_MAX for a period of time longer than T_OS, the controller  16  writes an ‘Over Speed’ error to the memory device  18  and enters Fault Mode. However, should the speed of the rotor  5  exceed SPEED_TRIP, the controller  16  immediately writes a ‘Speed Trip’ error to the memory device  18  and enters Fault Mode. At speeds in excess of SPEED_TRIP, the likelihood of mechanical and/or electrical failure significantly increases. 
     The controller  16  then polls the zero-cross flag that is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set, the controller  16  updates the advance period, T_ADV, and the overrun offset value, T_OVR_OFFSET. Each value is updated by indexing the relevant lookup table using the rotor speed and the measured RMS voltage of the AC supply  4 . After updating the advance period and the overrun offset value, the controller  16  clears the zero-cross flag, and starts a zero-cross timer. 
     After polling the zero-cross flag, and if necessary updating the advance period and the overrun offset value, the controller  16  calculates the commutation period, T_COM, by subtracting the advance period, T_ADV, from the Hall period, T_HALL. The controller  16  then loads the commutation period, T_COM, into a timer. After determining the commutation period, the controller  16  indexes the overrun sine lookup table using the time stored by the zero-cross timer, t, to select an overrun sine value, T_OVR_SINE. The controller  16  then sums the overrun offset value, T_OVR_OFFSET, and the overrun sine value, T_OVR_SINE, to obtain the overrun period, T_OVR. 
     After determining the commutation and overrun periods, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. If the predetermined number of samples has been collected, the controller  16  determines the average of the samples to obtain a measure of the RMS voltage of the AC supply  4  or the temperature within the motor system  1 . If the RMS voltage is less than V_MIN or greater than V_MAX, or if the temperature is less than T_MIN or greater than T_MAX, the controller  16  writes a corresponding error to the memory device  18  and enters Fault Mode. 
     The controller  16  subsequently commutates the phase winding  7  (i.e. by reversing DIR 1  and DIR 2 , and by setting FREEWHEEL#) after the timer has counted for the commutation period, T_COM. As a result, the controller  16  commutates the phase winding  7  in advance of the next edge of the HALL signal by the advance period, T_ADV. Following commutation, the controller  16  excites the phase winding  7  until an overcurrent event occurs. In response to the overcurrent event, the controller  16  continues to excite the phase winding  7  for the overrun period, T_OVR. After the overrun period has elapsed, the controller  16  freewheels the phase winding  7  (i.e. by clearing FREEHWEEL#). Freewheeling then continues indefinitely until such time as the controller  16  next commutates the phase winding  7 . The controller  16  therefore commutates the phase winding  7  in advance of each edge of the HALL signal, updates the overrun period in response to each edge of the HALL signal, and updates the advance period and the overrun offset value in response to each edge of the Z_CROSS signal. 
     When operating in Running Mode, the magnitude of back EMF induced in the phase winding  7  by the rotor  5  is of sufficient magnitude that current in the phase winding  7  is unlikely to rise to an excessive level, even in the absence of an overcurrent event. As a result, no timeout period is employed by the controller  16  when operating in Running Mode. This then reduces the number of instructions executed by the controller  16 . 
     The controller  16  drives the motor  2  over an operating speed range bounded by SPEED_MIN and SPEED_MAX, the speed varying in response to changes in load. Within this speed range, the controller  16  selects control values that ensure that constant average power is achieved between SPEED_CP_MIN and SPEED_CP_MAX. Consequently, constant average power is achieved for different loading. The controller  16  also drives the motor  2  over a voltage range bounded by V_MIN and V_MAX. Within this voltage range, the controller  16  selects control values that ensure that constant average power is achieved between V_CP_MIN and V_CP_MAX. Consequently, the same power and performance is achieved irrespective of variances in the voltage of the AC supply  4 . 
     Fault Mode 
     The controller  16  enters Fault Mode in response to an error, with the intention of preventing or limiting damage to the motor system  1 . The controller  16  therefore disables the motor  2  by clearing DIRT and DIR 2  on entering Fault Mode. The controller  16  may require that power to the motor system  1  be turned off before the motor system  1  can be reused. Alternatively, the controller  16  may prevent any further use of the motor system  1 ; this may depend on the type of fault that has occurred. 
     Benefits 
     For a conventional permanent-magnet motor that is driven by an AC supply, the back EMF induced in the phase winding makes it difficult to accurately control the amount of current drawn from the AC supply. As a result, the waveform of current drawn from the AC supply will typically have a high harmonic content, resulting in a poor power factor. In order to address this problem, conventional permanent-magnet motors generally include an active power factor correction (PFC) circuit. The active PFC circuit outputs a regular DC voltage for use in exciting the phase windings while ensuring that current drawn from the AC supply is substantially sinusoidal. As a result, a relatively high power factor can be achieved. However, the inclusion of an active PFC circuit increases the cost of the motor system. Additionally, the PFC circuit requires a high-capacitance DC link capacitor in order that the DC link voltage sampled by the PFC circuit is stable. Without a stable DC link voltage, the PFC circuit would estimate incorrect current demand levels, resulting in poor current harmonics. However, a high-capacitance DC link capacitor is both physically large and expensive. 
     With the motor system  1  of the present invention, the controller  16  employs an overcurrent threshold that is directly proportional to the DC link voltage and an overrun period that varies across each half-cycle of the AC supply  4 . The net result is that the controller  16  excites the phase winding  7 , during each electrical half-cycle of the motor  2 , for a conduction period that varies across each half-cycle of the AC supply  4 . In particular, the length of the conduction period varies substantially as a half-sinusoid over each half-cycle of the AC supply  4 . As a result, the waveform of current drawn from the AC supply  4  approaches that of a sinusoid. A relatively high power factor and low harmonic content are therefore achieved without the need for a PFC circuit or high-capacitance link capacitor. 
       FIG. 13  illustrates the current waveform that is achievable with the motor system  1  of the present invention. The current waveform is overlaid with a perfect sinusoid for the purposes of comparison. By employing a conduction period that varies across each half-cycle of the AC supply  4 , a current waveform may be realized for which the amplitude of low-order harmonics is relatively small. The high-frequency ripple that can be seen in the current waveform of  FIG. 13  arises from inverter switching. 
     A power factor of unity is achieved for a current waveform having no harmonic content. As the harmonic content increases, the power factor decreases. The motor system  1  of the present invention is therefore able to achieve a relatively high power factor. Indeed, with the motor system  1  of the present invention, a power factor of at least 0.95 is achievable. As a result, the motor system  1  is able to achieve a relatively high average input power for a given peak current. In contrast, a motor system having relatively large low-order harmonics will suffer from a poor power factor. As a result, a lower average input power is achieved for the same peak current. In order to remedy this, the level of peak current might be increased. However, as the peak current increases, the efficiency of the system decreases due to increased power losses. Additionally, excessive peak currents may damage the switches of the inverter and/or demagnetize the rotor. 
     Many countries have regulations that impose strict limits on the magnitude of the current harmonics that may be drawn from the mains power supply, e.g. IEC61000-3-2. By employing suitable values for the advance period, the overrun offset, and the overrun amplitude, the motor system  1  is able to comply with the harmonic standards across the full operating speed and voltage ranges of the motor system  1 . Indeed, the current waveform of  FIG. 13 , while not perfectly sinusoidal, complies with harmonic standards set out in IEC61000-3-2. 
     In contrast to conventional motor systems, the motor system  1  of the present invention achieves a current waveform having relatively small low-order harmonics without the need for an active PFC circuit or a high-capacitance link capacitor. The link capacitor C 1  of the control system  3  is employed only to smooth the relatively high-frequency ripple that results from inverter switching. The link capacitor C 1  is not required to smooth the DC link voltage at the fundamental frequency. As such, a link capacitor may be used that results in ripple in the DC link voltage of 50% or more at the fundamental frequency, i.e. Vr=(Vmax−Vmin)/Vmax≧0.5. The controller  16  nevertheless ensures that, even at this level of ripple, low-order harmonics are kept relatively small and thus a good power factor can be achieved at relatively high average input power. Indeed, the current waveform of  FIG. 13  is achieved with a voltage ripple of 100% Since the link capacitor C 1  is required only to filter high-frequency switching ripple, a relatively low capacitance link capacitor may be used, thus significantly reducing the cost and size of the motor system  1 . 
     Owing to the relatively high power factor that is achievable with the motor system  1 , a relatively high average input power can be achieved in spite of the ripple in the DC link voltage. The achievable average input power will naturally depend on the RMS voltage of the AC supply  4 . However, for an RMS voltage of 100 V, a constant average input power in excess of 1000 W is achievable irrespective of ripple in the DC link voltage. Consequently, when used with a mains power supply, the motor system  1  is able to achieve a constant average input power of at least 1000 W. 
     By selecting appropriate values for the advance period, T_ADV, the overrun offset, T_OVR_OFFSET, and the overrun amplitude, T_OVR_AMP, a desired average input or output power may be achieved for the motor system  1 . Moreover, appropriate values may be selected such that the efficiency of the motor system  1  at each operating point (i.e. speed and voltage) is optimized for the desired input or output power. That is to say that various sets of values for T_ADV, T_OVR_OFFSET, and T_OVR_AMP may result in the same desired average input or output power. However, from these various sets of values, a single set may be selected that provides the best efficiency. 
     One or more of the advance period, the overrun offset, and the overrun amplitude may be adjusted in response to changes in rotor speed and/or RMS voltage of the AC supply  4  such that a particular profile for the average input or output power is achieved over a speed range and/or voltage range. In particular, by adjusting at least the advance period and the overrun offset in response to changes in rotor speed and/or RMS voltage, the same average input or output power may be achieved. 
     For a single motor system, appropriate values may be selected such that the variance in average power (input or output) does not exceed ±1% over a speed range spanning at least 10 krpm and/or a voltage range spanning at least 10 V. However, if the same values are used in a plurality of mass-produced motor systems, the variance in average power for each motor system increases owing to component and manufacturing tolerances. Nevertheless, appropriate values may be selected such that the variance in average power does not exceed ±5% for a mass-produced motor system over the aforementioned speed and voltage ranges. Constant average power (i.e. within ±5%) may also be achieved at relatively high speeds. In particular, constant average power may be achieved over a speed range having a minimum greater than 60 kpm and a maximum greater than 80 krpm. Indeed, constant average power may be achieved at speeds in excess of 100 krpm. In addition to achieving constant average power over a speed and/or voltage range, appropriate values may be selected such that an efficiency of at least 80% is maintained over the speed and/or voltage range. 
     The present invention therefore provides a high-power motor system  1  that is able to comply with existing harmonic standards without the need for an active PFC circuit or high-capacitance link capacitor. Moreover, the motor system  1  is able to achieve a relatively high efficiency (i.e. at least 80%) as well as constant average power (i.e. within ±5%) over a range of rotor speeds and RMS voltages. 
     Event Clashing 
     The controller  16  executes different software routines in response to different events. For example, the controller  16  executes a particular routine in response to an edge of the HALL signal. The controller  16  executes a different routine in response to an overcurrent event, and so on. 
     A relatively simple microcontroller typically includes a single-threaded processor. Consequently, when the processor executes a routine in response to a particular event, the processor is unable to respond to other events until such time as it has finished executing the routine. Accordingly, when two events clash, the execution of one of the event routines will be delayed. 
     When operating at relatively low rotor speeds, any delay to the execution of a particular routine will be relatively small in comparison to the overall Hall period. Consequently, the delay is unlikely to adversely affect the performance of the motor system  1 . Moreover, the time spent at speeds below SPEED_SINGLE is expected to be relatively short, and thus any effect that event clashing may have on the performance of the motor system  1  is not regarded as critical at these speeds. However, at speeds at or above SPEED_SINGLE, any delay in the execution of a routine may adversely affect the performance of the motor system  1 . In particular, the delay may affect one or more of the input power, output power, efficiency and current harmonics. 
     For example, when operating in single-switch mode, the controller  16  calculates the commutation period, T_COM, and the overrun period, T_OVR, in response to each edge of the HALL signal. If during this time, an overcurrent event occurs, the overcurrent routine will not be executed until such time as the controller  16  has finished executing the Hall routine. As a result, more current than ideally desired would be driven into the phase winding  7 . 
     Alternatively, if an edge of the HALL signal were to occur while the controller  16  is executing the overcurrent routine, the execution of the Hall routine would be delayed. Since the Hall routine is used to calculate the time at which the phase winding  7  is commutated, any delay in the execution of the Hall routine will have the effect of reducing the advance period. In each of these examples, the clash is likely to occur around the zero-crossing in the voltage of the AC supply  4 , owing to the small overcurrent threshold. Consequently, in spite of the fact that the amount of current driven into the phase winding  7  is not well controlled, the net effect on power and efficiency is unlikely to be significant. However, the net effect on current harmonics is likely to be significant. 
     Various measures may be taken in order to minimize the risk of event clashing. In particular, the risk of clashing may be reduced by simplifying the instructions of each routine such that the time required to execute each routine is kept relatively short. It is for this reason that the controller  16  uses lookup tables that store control values in the form of time periods. By using lookup tables that store time periods, the mathematical calculations performed by the controller  16  may be kept relatively simple. In particular, the mathematical calculations can be limited to simple addition (e.g. when calculating the overrun period) and subtraction (e.g. when calculating the commutation period). Nevertheless, in spite of these measures, event clashing may occur with a relatively simple processor at relatively high speeds. 
     Event clashing may be resolved by having a faster or multi-core processor. However, both options increase the cost of the controller  16 . Accordingly, two alternative schemes for driving the motor  2  in single-switch mode will now be described. Both schemes reduce the number of events that occur during each electrical half-cycle of the motor  2  and thus reduce the possibility of event clashing. Before describing the two alternative schemes, consideration will first be made of the events that occur during each electrical half-cycle of the motor  2  for the above-described scheme. For the purposes of clarity, the control scheme described above for single-switch mode shall hereafter be referred to as ‘overcurrent single-switch mode’. The two alternative control schemes for single-switch mode will be referred to as ‘unlimited-freewheel single-switch mode’ and ‘limited-freewheel single-switch mode’. 
     Overcurrent Single-Switch Mode 
     A common method of event handling is through the use of interrupts. In response to an interrupt, the controller  16  interrupts execution of the main code and services the interrupt by executing an interrupt service routine (ISR). 
     When operating in overcurrent single-switch mode, the controller  16  employs the following four interrupts: Hall, overcurrent, freewheel and commutate.  FIG. 14  illustrates the waveforms of the HALL signal, the control signals and the phase current, as well as the interrupts employed by the controller  16 , when operating in overcurrent single-switch mode. 
     The Hall interrupt is generated in response to an edge of the HALL signal. In servicing the Hall interrupt, the controller  16  first polls the zero-cross flag that is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set, the controller  16  updates the advance period and the overrun offset value, and clears the zero-cross flag. The Z_CROSS signal is thus used to set a flag rather than generate an interrupt. This then minimizes the total number of interrupts and thus the possibility of interrupt clashing. After polling the zero-cross flag, the controller  16  calculates the commutation period, T_COM, and the overrun period, T_OVR. The controller  16  then loads the commutation period into a first timer, Timer  1 . Finally, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. 
     The overcurrent interrupt is generated in response to a logically low overcurrent signal output by the current regulator  22 . In servicing the overcurrent interrupt, the controller  16  loads the overrun period, T_OVR, into a second timer, Timer 2 . 
     The freewheel interrupt is generated by the second timer when the overrun period has elapsed. In servicing the freewheel interrupt, the controller  16  freewheels the phase winding  7 . 
     The commutate interrupt is generated by the first timer when the commutation period has elapsed. In servicing the commutate interrupt, the controller  16  commutates the phase winding  7 . 
     Since the overcurrent ISR is responsible for loading the second timer with the overrun period, it is not possible for the overcurrent and freewheel interrupts to clash. Furthermore, by ensuring that the advance period is longer than the time required to execute the commutate ISR, clashing of the Hall and commutate interrupts can be avoided. Nevertheless, four possible interrupt clashes are still possible, namely Hall and overcurrent, Hall and freewheel, commutate and overcurrent, and commutate and freewheel. 
     Unlimited-Freewheel Single-Switch Mode 
     When operating in unlimited-freewheel single-switch mode, the overcurrent interrupt is disabled, i.e. the controller  16  ignores the overcurrent signal output by the current regulator  22 . In response to an edge of the HALL signal, the controller  16  calculates a conduction period, T_CD, in addition to the commutation period, T_COM. The controller  16  commutates the phase winding  7  at a time, T_COM, after the edge of the HALL signal. Following commutation, the controller  16  excites the phase winding  7  for the conduction period, T_CD, after which the controller  16  freewheels the phase winding  7 . 
     The conduction period resembles the overrun period employed in overcurrent single-switch mode. In particular, the conduction period comprises an offset value and a sine value. However, unlike the overrun period, the waveform of the conduction period includes a phase shift relative to the voltage cycle of the AC supply  4 . 
     In overcurrent single-switch mode, the controller  16  initially excites the phase winding  7  until current in the phase winding  7  reaches an overcurrent threshold. Thereafter, the controller  16  excites the phase winding  7  for the overrun period, T_OVR. The total conduction period over which the phase winding  7  is excited is therefore the sum of the initial excitation period and the overrun period. Current in the phase winding  7  is sensed by monitoring the voltage across each of the shunt resistors R 1 ,R 2 . More specifically, the voltage across each shunt resistors R 1 ,R 2  is output to the controller  16  as a current sense signal, I_SENSE_ 1  and I_SENSE_ 2 . As illustrated in  FIG. 2 , each current sense signal is filtered by an RC filter R 8 ,C 3  and R 9 ,C 4 , which acts to remove high-frequency noise. The time constant of the RC filter introduces a time delay between the measured current and the actual current in the phase winding  7 . The net result is that the waveform of the conduction period is phase-shifted relative to the cycle of the AC supply  4 . This phase shift helps reduce the magnitude of low-order current harmonics. 
     In unlimited freewheel single-switch mode, the overcurrent interrupt is disabled. The RC filters R 8 ,C 3  and R 9 ,C 4  do not therefore influence the waveform of the conduction period. Accordingly, in order to replicate the phase shift that exists in overcurrent single-switch mode, the waveform of the conduction period includes a phase shift relative to the cycle of the AC supply  4 . The conduction period, T_CD, is therefore defined by the equation:
 
 T _CD= T _CD_OFFSET+ T _CD_AMP*abs{sin(θ+ A _CD_PHASE)}
 
where T_CD_OFFSET is an offset value and T_CD_AMP*abs{sin(θ+A_CD_PHASE)} is a rectified sine wave having an amplitude defined by T_CD_AMP. θ is the angle in the voltage cycle of the AC supply  4  and A_CD_PHASE is a phase angle.
 
     Both the angle θ and the conduction phase angle, A_CD_PHASE, may be expressed as time intervals:
 
θ (deg)= t  (sec)* f  (Hz)*360 (deg)
 
 A _CD_PHASE (deg)= T _CD_PHASE (sec)* f  (Hz)*360 (deg)
 
Consequently, the conduction period may be defined as:
 
 T _CD= T _CD_OFF_SET+ T _CD_AMP*abs{ sin({ t+T _CD_PHASE}* f* 360 deg)}
 
More simply, the conduction period, T_CD, may be regarded as:
 
 T _CD= T _CD_OFFSET+ T _CD_SINE
 
where T_CD_OFFSET is a conduction offset value that is independent of time, and T_CD_SINE is a conduction sine value that is dependent on time.
 
     T_CD_SINE is stored by the controller  16  as a conduction sine lookup table, which comprises a conduction sine value, T_CD_SINE, for each of a plurality of times. 
     In overcurrent single-switch mode, the controller  16  adjusts the advance period and the overrun offset value in response to changes in rotor speed and voltage of the AC supply  4  so as to maintain constant average power. Likewise, in unlimited freewheel single-switch mode, the controller  16  adjusts the advance period, T_ADV, and the conduction offset value, T_CD_OFFSET, in response to changes in rotor speed and voltage in order to maintain constant average power. The controller  16  therefore stores an advance lookup table and a conduction offset lookup table, each of which is indexed by rotor speed and voltage:
 
T_ADV=T_ADV_TABLE[speed,voltage]
 
T_CD_OFFSET=T_CD_OFFSET_TABLE[speed,voltage]
 
     In overcurrent single-switch mode, the controller  16  initially excites the phase winding  7  until current in the phase winding  7  reaches an overcurrent threshold. The overcurrent threshold is proportional to the DC link voltage, and thus the length of this initial excitation period is sensitive to changes in the voltage of the AC supply  4 . The length of the initial excitation period is also sensitive to changes in the magnitude of the back EMF induced the phase winding  7  by the rotor  5 . Consequently, the initial excitation period is sensitive to changes in both the rotor speed and the voltage of the AC supply  4 . Owing to the RC filter that operates on each of the current sense signals, this initial excitation period introduces a phase delay in the waveform of the conduction period, which helps reduce the magnitude of low-order current harmonics. In unlimited-freewheel single-switch mode, the phase delay is replicated by phase shifting the waveform of the conduction period relative to the voltage waveform of the AC supply  4 . Since the phase delay is sensitive to changes in the rotor speed and the voltage of the AC supply  4 , the controller  16  adjusts the phase of the conduction period waveform in response to changes in rotor speed and voltage. The controller  16  therefore comprises a conduction phase-shift lookup table that stores a phase-shift value, T_CD_PHASE_SHIFT, for each of a plurality of rotor speeds and a plurality of voltages. The conduction period may thus be defined as:
 
 T _CD= T _CD_OFFSET_TABLE[speed,voltage]+ T _CD_SINE_TABLE[ t+T _CD_PHASE_SHIFT[speed,voltage]]
 
     The advance period, T_ADV, the conduction offset value, T_CD_OFF_SET, and the conduction phase-shift value, T_CD_PHASE_SHIFT, are each updated in response to edges of the Z_CROSS signal. The values are thus updated only when the voltage of the AC supply  4  crosses zero and remain constant over each half-cycle of the AC supply  4 . 
     In response to an edge of the HALL signal, the controller  16  determines the period of time, t, that has elapsed since the last edge of the Z_CROSS signal. The controller  16  then indexes the conduction sine lookup table using the sum of the elapsed time, t, and the conduction phase shift value, T_CD_PHASE_SHIFT, in order to select a conduction sine value, T_CD_SINE. The controller  16  then sums the conduction offset value, T_CD_OFFSET, and the conduction sine value, T_CD_SINE, to obtain the conduction period, T_CD. 
     The controller  16  employs three interrupts when operating in unlimited-freewheel single-switch mode: Hall, freewheel and commutate.  FIG. 15  illustrates the waveforms of the HALL signal, the control signals and the phase current, as well as the interrupts employed by the controller  16 , when operating in unlimited-freewheel single switch mode. 
     The Hall interrupt is generated in response to an edge of the HALL signal. In servicing the Hall interrupt, the controller  16  polls the zero-cross flag that is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set, the controller  16  updates the advance period, the conduction offset value and the conduction phase-shift value, and clears the zero-cross flag. After polling the zero-cross flag, the controller  16  calculates the commutation period, T_COM, and the conduction period, T_CD. The controller  16  then loads the commutation period into a first timer, Timer 1 . Finally, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. 
     The commutate interrupt is generated by the first timer when the commutation period has elapsed. In servicing the commutate interrupt, the controller  16  commutates the phase winding  7  and loads the conduction period into a second timer, Timer 2 . 
     The freewheel interrupt is generated by the second timer when the conduction period has elapsed. In servicing the freewheel interrupt, the controller  16  freewheels the phase winding  7 . In comparison to overcurrent single-switch mode, the controller  16  employs one less interrupt. Moreover, since the commutate ISR is responsible for loading the second timer with the conduction period, it is not possible for the commutation and freewheel interrupts to clash. Consequently, the risk of interrupt clashing is significantly reduced. 
     By ensuring that the advance period is greater than the time required to service the commutate interrupt (T_COM_ISR) and smaller than the Hall period minus the time required to service the Hall interrupt (T_HALL_ISR), clashing of the Hall and commutate interrupts can be avoided, i.e.
 
 T _COM_ISR&lt; T _ADV&lt; T _HALL− T _HALL_ISR
 
     Nevertheless, it is still possible for the freewheel interrupt to clash with the Hall interrupt. However, as will now be described, the controller  16  may be configured such that freewheeling is started at the end of the conduction period without the need to generate an interrupt. 
     Microcontrollers having a timer that is able to operate in output compare mode are known. In output compare mode, a comparator compares the counter register of the timer against an output compare register. When the values of the two registers correspond, the comparator generates an interrupt or sets/clears/toggles an output pin of the microcontroller. The particular action undertaken by the comparator is typically set by means of a register bit. 
     In one embodiment, output compare mode is exploited by the controller  16  to clear the FREEWHEEL# signal without generating an interrupt. As illustrated in  FIG. 16 , the peripherals  19  of the controller  16  comprise two timers  30 , 31  and a comparator module  32 . The memory device  18  comprises a timer register  33 , 34  for each of the timers  30 , 31 , and a compare register  35 . The first timer  30  is used to time the commutation period, T_COM, and the second timer  31  is used to time the conduction period, T_CD. The second timer  31  is configured to operate in output compare mode. Consequently, when servicing the commutate interrupt generated by the first timer  30 , the controller  16  commutates the phase winding  7 , loads the conduction period into the compare register  35 , and resets the second timer  31 . The comparator module  32  then compares the second timer register  34  and the compare register  35 . When the two registers  34 , 35  correspond (which occurs when the conduction period has elapsed), the comparator module  32  resets an SR latch  36 , which in turn clears an output pin  21  of the controller  16 . This output pin  21  is then used by the controller  16  for the FREEWHEEL# signal. 
     Accordingly, when the conduction period elapses, FREEWHEEL# is cleared without an interrupt being generated. Since the output pin is latched, FREEWHEEL# continues to cleared until such time as the controller  16  sets the latch  36  when servicing the commutate interrupt. 
     The controller  16  is therefore able to operate in unlimited freewheel single-switch mode using only two interrupts, namely Hall and commutate. However, as noted above, clashing of the Hall and commutate interrupts may be avoided by ensuring that the advance period is kept within particular limits. Consequently, interrupt clashing may be avoided altogether. 
     Depending on the type of microcontroller that is used for the controller  16 , it may not be possible to use output compare mode to time the conduction period and clear the output pin used for FREEWHEEL#. For example, the microcontroller may not have any timers capable of operating in output compare mode. Alternatively, the microcontroller may have an 8-bit timer and a 16-bit timer, and only the 16-bit timer is capable of operating in output compare mode. However, since the commutation period is typically longer than the conduction period, it may be necessary to use the 16-bit timer for the commutation period. In those instances for which output compare mode is unavailable for clearing FREEWHEEL#, a PWM module may instead be used to clear FREEWHEEL# without recourse to an interrupt, as will now be described. 
       FIG. 17  illustrates an alternative embodiment in which the peripherals  19  of the controller  16  comprise two timers  30 , 31  and a PWM module  37 . The memory device  18  comprises a timer register  33 , 34  for each of the timers  30 , 31 , a duty-cycle register  38  and a period register  39 . The first timer  30  is again used to time the commutation period, T_COM. The second timer  31 , however, is used as a clock signal for the PWM module  37 . The PWM module  37  comprises a pair of comparators  40 , 41  and an SR latch  42 . A first comparator  40  compares the second timer register  34  and the duty-cycle register  38 . When the values of the two registers  34 , 38  correspond, the first comparator  40  resets the SR latch  42 , which in turn clears an output pin  21  of the controller  16 . A second comparator  41  compares the second timer register  34  and the period register  39 . When the values of these two registers  34 , 39  correspond, two things happen. First, the second comparator  41  sets the SR latch  42 , which in turn sets the output pin  21 . 
     Second, the second timer  31  is reset. The output pin  21  of the controller  16  is therefore cleared when the second timer register  34  and the duty-cycle register  38  correspond, and is set when the second timer register  34  and the period register  39  correspond. 
     The output pin  21  toggled by the PWM module  37  is used by the controller  16  for the FREEHWEEL# signal. When servicing the commutate interrupt, the controller  16  commutates the phase winding  7 , loads the conduction period into the duty-cycle register  38 , and loads the second timer register  34  with the same value as that of the period register  39 . In response, the PWM module  37  sets FREEWHEEL# and the second timer register  34  is reset. The second timer  31  then increments the second timer register  34  until such time as the second timer register  34  and the duty-cycle register  38  correspond. When the two registers  34 , 38  correspond (which occurs when the conduction period has elapsed), the PWM module  37  clears FREEWHEEL#. The phase winding  7  is therefore freewheeled without the need for an interrupt. 
     If the period register  39  is set too low, the second timer register  34  and the period register  39  may correspond during the freewheel period. This would then cause the FREEWHEEL# signal to be set prematurely. Accordingly, in order that freewheeling is not terminated prior to commutation, the period register  39  stores a maximum possible value (e.g. an 8-bit period register stores 0xFF). 
     In each of the above embodiments, a comparator compares the value of the second timer register against a value stored in a compare register. When the second timer register and the compare register correspond, the comparator clears the output pin used for FREEWHEEL#. In the first embodiment the comparator forms part of a comparator module  32 , while in the second embodiment the comparator forms part of a PWM module  37 . However, any comparator of the controller  16  may be used, so long as the comparator is able to control (either directly or through associated hardware) an output pin of the controller  16  in response to a comparison of a timer register and a compare register. 
     Limited-Freewheel Single-Switch Mode 
     As with unlimited-freewheel single-switch mode, the overcurrent interrupt is disabled when operating in limited-freewheel single-switch mode. In response to an edge of the HALL signal, the controller  16  calculates a drive-off period, T_DOFF, in addition to the commutation period, T_COM. The controller  16  then continues to excite the phase winding  7  for the drive-off period, T_DOFF, after which the controller  16  freewheels the phase winding  7 . Freewheeling then continues until the controller  16  commutates the phase winding  7 . 
     The drive-off period resembles the conduction period employed in unlimited-freewheel single-switch mode. In particular, the drive-off period, T_DOFF, is defined by the equation:
 
 T _DOFF= T _DOFF_OFFSET+ T _DOFF_AMP*abs{ sin(θ+ A _DOFF_PHASE)}
 
where T_DOFF_OFFSET is an offset value and T_DOFF_AMP*abs{sin(θ+A_DOFF_PHASE)} is a rectified sine wave having an amplitude defined by T_DOFF_AMP. θ is the angle in the voltage cycle of the AC supply  4  and A_DOFF_PHASE is a phase angle.
 
     Both the angle θ and the drive-off phase angle, A_DOFF_PHASE, may be expressed as time intervals:
 
θ (deg)= t  (sec)* f  (Hz)*360 (deg)
 
 A _DOFF_PHASE (deg)= T _DOFF_PHASE (sec)* f  (Hz)*360 (deg)
 
Consequently, the drive-off period may be defined as:
 
 T _DOFF= T _DOFF_OFFSET+ T _DOFF_AMP*abs{sin({ t+T _OVR_PHASE}* f* 360 deg)}
 
     More simply, the drive-off period, T_DOFF, may be regarded as:
 
 T _DOFF= T _DOFF_OFFSET+ T _DOFF_SINE
 
where T_DOFF_OFFSET is a drive-off offset value that is independent of time, and T_DOFF_SINE is an drive-off sine value that is dependent on time.
 
     The drive-off period, T_DOFF, is stored and updated by the controller  16  in the same manner as that described above for the conduction period, T_CD. In particular, the controller  16  stores a drive-off sine lookup table that is indexed by time, and a drive-off offset lookup table and a drive-off phase-shift lookup table that are each indexed by rotor speed and voltage of the AC supply  4 . The drive-off period may thus be defined as:
 
 T _DOFF= T _DOFF_OFFSET_TABLE[speed,voltage]+ T _DOFF_SINE_TABLE[ t+T _DOFF_PHASE_SHIFT[speed,voltage]]
 
The controller  16  employs three interrupts when operating in limited-freewheel single-switch mode: Hall, freewheel and commutate.  FIG. 18  illustrates the waveforms of the HALL signal, the control signals and the phase current, as well as the interrupts employed by the controller  16 , when operating in limited-freewheel single switch mode.
 
     The Hall interrupt is generated in response to an edge of the HALL signal. In servicing the Hall interrupt, the controller  16  polls the zero-cross flag that is set in response to an edge of the Z_CROSS signal. If the zero-cross flag is set, the controller  16  updates the advance period, the drive-off offset value and the drive-off phase-shift value, and clears the zero-cross flag. After polling the zero-cross flag, the controller  16  calculates the commutation period, T_COM, and the drive-off period, T_DOFF. The controller  16  then loads the commutation period into a first timer, Timer 1 , and the drive-off period into a second timer, Timer 2 . Finally, the controller  16  performs one of the three steps used to sample the DC_SMOOTH and TEMP signals. 
     The freewheel interrupt is generated by the second timer when the drive-off period has elapsed. In servicing the freewheel interrupt, the controller  16  freewheels the phase winding  7 . 
     The commutate interrupt is generated by the first timer when the commutation period has elapsed. In servicing the commutate interrupt, the controller  16  commutates the phase winding  7 . 
     Consequently, as with unlimited-freewheel single-switch mode, the controller  16  employs only three interrupts. This is in contrast to the four interrupts used in overcurrent single-switch mode. 
     Moreover, by ensuring that the advance period is greater than the time required to service the commutate interrupt, clashing of the Hall and commutate interrupts can be avoided. 
     As described above for unlimited freewheel single-switch mode, the controller  16  may be configured such that freewheeling is started at the end of the drive-off period without the need to generate an interrupt. For example, the second timer may be configured to operate in output compare mode such that the output pin used for FREEWHEEL# is cleared when the drive-off period elapses. Alternatively, the controller  16  may include a PWM module, which is used to toggle the output pin for FREEWHEEL#. For example, when servicing the Hall interrupt, the controller  16  might load the commutation period into the first timer, load the drive-off period into the duty-cycle register, and reset the second timer. When subsequently servicing the commutate interrupt, the controller  16  then commutates the phase winding  7  and loads the counter register of the second timer with the value of the period register. 
     The controller  16  may therefore be configured to operate in limited freewheel single-switch mode using only two interrupts, namely Hall and commutate. However, as already noted, the clashing of these two interrupts can be avoided by ensuring that the advance period is greater than the time required to service the commutate interrupt. Accordingly, interrupt clashing may be avoided altogether. 
     In limited-freewheel single-switch mode, the drive-off period is referenced relative to an edge of the HALL signal. As a result, freewheeling of the phase winding  7  cannot commence until after the edge of the HALL signal. In unlimited-freewheel single-switch mode, the conduction period is referenced relative to commutation. Since commutation occurs in advance of the edge of the HALL signal, freewheeling of the phase winding  7  may commence before, on or after the edge of the HALL signal. It is for this reason that the two schemes are referred to as limited-freewheel and unlimited-freewheel. 
     In comparison to overcurrent single-switch mode, both unlimited-freewheel and limited-freewheel single-switch modes employ a smaller number of interrupts and thus the risk of interrupt clashing is reduced. Indeed, the controller  16  may be configured such that interrupt clashing is avoided altogether. Nevertheless, in spite of the potential for interrupt clashing, overcurrent single-switch mode has the advantage of self-compensating for tolerances and limitations within the motor system  1 . For example, the controller  16  employs a zero-cross timer to monitor the time elapsed since a zero-crossing in the AC supply voltage  4 . However, the zero-cross timer is started only as part of the Hall routine. There is therefore a variance in the time used to index the sine lookup table. In a further example, there may be a tolerance in the balance of the duty cycle of the HALL signal. Any imbalance in the duty cycle will introduce an error in the Hall period. Tolerances and limitations in the motor system  1  may therefore result in small errors in the timing of certain events (e.g. commutation, freewheeling etc). In overcurrent single-switch mode, the controller  16  initially excites the phase winding  7  until current in the phase winding  7  reaches an overcurrent threshold. The length of this initial excitation period is not timed by the controller  16 . As a result, the initial excitation period acts to compensate for certain timing errors. Consequently, a more stable current waveform may be achieved when operating in overcurrent single-switch mode. In addition to self-compensating for tolerances and limitations within the motor system  1 , the initial excitation period introduces a phase delay that acts to dampen low-order current harmonics. In limited and unlimited freewheel single-switch modes, this phase delay is replicated through the use of a phase-shift lookup table, which consumes valuable memory resources. A cheaper microcontroller having less memory may therefore be used for the controller  16  when operating in overcurrent single-switch mode. Alternatively, the memory that would otherwise be used for a phase-shift lookup table might be used to improve the resolution of the other lookup tables, e.g. the advance, overrun offset or overrun sine lookup tables. 
     Conduction Period 
     In each of the three schemes described above, the controller  16  excites the phase winding  7  for a conduction period, T_CD, over each electrical half-cycle of the motor  2 . 
     In overcurrent single-switch mode, the conduction period, T_CD, may be defined as:
 
 T _CD= T _OC+ T _OVR
 
where T_OC is the time taken for current in the phase winding  7  to reach the overcurrent threshold, and T_OVR is the overrun period. Consequently, the conduction period, T_CD, may be defined as:
 
 T _CD= T _OC+ T _OVR_OFFSET+ T _OVR_SINE
 
     The overcurrent threshold is directly proportional to the DC link voltage and thus varies as a rectified sinusoid. Current in the phase winding  7  rises substantially at the same rate irrespective of the level of DC link voltage; the reasons for this behaviour are beyond the scope of this document. Consequently, the time taken for current in the phase winding  7  to reach the overcurrent threshold, T_OC, varies substantially as a half-sinusoid over each half-cycle of the AC supply  4 . However, owing to the time constant of the RC filter that acts on each of the current sense signals, the T_OC waveform is phase-shifted relative to the voltage waveform of the AC supply  4 . 
     The overrun offset, T_OVR_OFFSET, is constant while the overrun sine value, T_OVR_SINE, varies as a half-sinusoid over each half-cycle of the AC supply  4 . Additionally, the waveform of the overrun sine value is in phase with the voltage waveform of the AC supply  4 . 
     Since the overrun offset is constant over each half-cycle of the AC supply  4 , the variation in the conduction period is defined by the sum of two half-sine components, T_OC and T_OVR_SINE. The phase difference between the two components, which arises from the RC filter, is relatively small. Additionally, the amplitude of TOC is greater than that of T_OVR_SINE. Consequently, in spite of the phase difference, the sum of the two components resembles a rectified sinusoid having a phase shift relative to the voltage waveform of the AC supply  4 . 
     The length of the conduction period, T_CD, therefore varies as a periodic waveform. The waveform may be defined as the sum of two components: a first component (T_OVR_OFFSET) that is constant over each cycle of the waveform and a second component that varies (T_OC+T_OVR_SINE) over each cycle of the waveform. Each cycle of the waveform repeats with each half-cycle of the AC supply  4 . However, the waveform of the conduction period is phase-shifted relative to the voltage waveform of the AC supply  4 . 
     In unlimited-freewheel single-switch mode, the conduction period, T_CD, is defined by:
 
 T _CD= T _CD_OFFSET+ T _CD_SINE
 
     The conduction offset value, T_CD_OFFSET, is constant while the conduction sine value, T_CD_SINE, varies as a half-sinusoid over each half-cycle of the AC supply  4 . Moreover, the waveform of the conduction sine value is phase-shifted relative to the voltage waveform of the AC supply  4 . Indeed, the phase shift is intended to replicate the phase shift that arises from the RC filter in overcurrent single-switch mode. 
     Consequently, as in overcurrent single-switch mode, the length of the conduction period varies as a periodic waveform. The waveform may again be defined as the sum of two components: a first component (T_CD_OFFSET) that is constant over each cycle of the waveform and a second component (T_CD_SINE) that varies over each cycle of the waveform. Each cycle of the waveform repeats with each half-cycle of the AC supply  4 , and the waveform is phase-shifted relative to the voltage waveform of the AC supply  4 . 
     In limited-freewheel single-switch mode, the conduction period, T_CD, may be defined as:
 
 T _CD= T _ADV+ T _DOFF
 
where T_ADV is the advance period and T_DOFF is the drive-off period. Consequently, the conduction period, T_CD, may be defined as:
 
 T _CD= T _ADV+ T _DOFF_OFFSET+ T _DOFF_SINE
 
     The advance period, T_ADV, and the drive-off offset, T_DOFF_OFFSET, are constant while the drive-off sine value, T_DOFF_SINE, varies as a half-sinusoid over each half-cycle of the AC supply  4 . Again, in order to reflect the phase shift that arises from the RC filter in overcurrent single-switch mode, the waveform of the drive-off sine value is phase-shifted relative to the voltage waveform of the AC supply  4 . 
     Consequently, as with the other two single-switch modes, the length of the conduction period varies as a periodic waveform. The waveform may be defined by the sum of two components: a first component (T_ADV+A_DOFF_OFFSET) that is constant over each cycle of the waveform and a second component (T_DOFF_SINE) that varies over each cycle of the waveform. Again, each cycle of the waveform repeats with each half-cycle of the AC supply  4 , and the waveform of the conduction period is phase-shifted relative to the voltage waveform of the AC supply  4 . 
     In each of the three schemes, the length of the conduction period is defined by a periodic waveform that repeats with each half-cycle of the AC supply  4 . More particularly, the waveform varies substantially as a half-sinusoid over each cycle of the waveform. Consequently, the benefits described above in connection with overcurrent single-switch mode apply equally to unlimited and limited single-switch modes. 
     In each scheme the waveform of the conduction period is adjusted in response to changes in the speed of the rotor  5  and/or the RMS voltage of the AC supply  4  so as to achieve a particular performance. For example, the offset of the waveform is adjusted primarily so that constant average power (or a particular profile for average power) is achieved over a range of speeds and/or voltages. The phase of the waveform is adjusted primarily so that the magnitude of low-order harmonics in the current waveform are kept below predetermined thresholds. The length of the conduction period may be expressed as the sum of two components: a first component that is constant over each cycle of the waveform and a second component that varies over each cycle of the waveform. In response to changes in rotor speed and/or RMS voltage, the first component is adjusted so as to maintain constant average power and the second component is adjusted so as to maintain relatively small low-order harmonics. 
     Although three different schemes for single-switch mode have been described, the controller  16  is not necessarily limited to just one of these schemes when operating in single-switch mode. Instead, the controller  16  may use one or more of the three schemes when operating in single-switch mode. For example, the controller  16  may initially employ overcurrent single-switch mode when the rotor speed reaches SPEED_SINGLE. As already noted, overcurrent single-switch mode has the benefit of providing a degree of self-compensation. However, as the rotor  5  accelerates, the Hall period shortens and thus the risk of interrupt clashing increases. Consequently, when the rotor speed reaches a predetermined threshold, the controller  16  may switch from overcurrent single-switch mode to unlimited-freewheel single-switch mode. 
     For each of the three single-switch schemes, values for the advance period, the offset, the amplitude and the phase shift are obtained from simulation. The simulation refines the various values for each operating point (e.g. speed and voltage) so as to obtain the best performance (e.g. best efficiency and/or low-order harmonics) at the desired average input or output power. 
     Specific Example 
     A particular embodiment of the motor system  1  will now be described by way of example only. Values for various hardware components of the motor system  1  are detailed in  FIG. 19 , while  FIG. 20  lists various constants and thresholds employed by the controller  16 .  FIGS. 21 and 22  detail the flux-linkage characteristics of the link inductor L 1  and the motor  2 . 
     As illustrated in  FIG. 23 , the motor system  1  has seven modes of operation: Fault, Initialization, Stationary, Low-Speed Acceleration, Mid-Speed Acceleration, High-Speed Acceleration, and Running. Accordingly, in comparison to that previously described and illustrated in  FIG. 8 , the motor system  1  has one additional mode of operation. 
     Fault, Initialization, Stationary and Low-Speed Acceleration Modes are unchanged from that previously described. Mid-Speed Acceleration Mode corresponds to the previously-described High-Speed Acceleration Mode. Consequently, when operating in Mid-Speed Acceleration Mode, the controller  16  drives the motor  2  in advanced commutation, multi-switch mode. 
     When operating in High-Speed Acceleration Mode, the controller  16  drives the motor  2  in advanced commutation, overcurrent single-switch mode. The length of time spent by the motor system  1  in High-Speed Acceleration Mode is relatively short. Accordingly, in order to conserve memory, the controller  16  does not store an overrun offset lookup table and an overrun sine lookup table. Instead, the controller  16  stores a single overrun lookup table that comprises an overrun period, T_OVR, for each of a plurality of rotor speeds. The controller  16  then updates the overrun period, along with the advance period, in response to edges of the Z_CROSS signal. Consequently, the overrun period employed by the controller  16  is constant over each half-cycle of the AC supply  4 . However, the use of a constant overrun period does not adversely affect the performance of the motor system  1  for two reasons. First, the length of time spent in High-Speed Acceleration mode is relatively short. Second, the controller  16  initially excites the phase winding  7  until current in the phase winding  7  exceeds a threshold that is proportional to the DC link voltage. Consequently, in spite of using a constant overrun period over each half-cycle of the AC supply  4 , the current waveform continues to approach that of a sinusoid. The advance period and the overrun period are updated in response to changes in rotor speed only and are not updated in response to changes in the RMS voltage of the AC supply  4 . This then reduces the size of the lookup tables, thus freeing more memory for the more important tables used in Running Mode. The controller  16  continues to drive the motor  2  in advanced commutation, overcurrent single-switch mode until such time as the rotor speed reaches SPEED_UFW. On reaching SPEED_UFW, the controller  16  enters Running Mode in response to the next edge of the Z_CROSS signal. 
     Running Mode corresponds to that previously described but with one exception. Rather than employing overcurrent single-switch mode, the controller  16  instead employs unlimited-freewheel single-switch mode. Consequently, in addition to updating the advance period and the offset value, the controller  16  also updates the phase-shift value in response to each edge of the Z_CROSS signal. Otherwise, the operation of the controller  16  is essentially unchanged from that previously described. In particular, the controller  16  drives the motor  2  over an operating speed range bounded by SPEED_MIN and SPEED_MAX. Within this speed range, the controller  16  selects control values that ensure that constant average power is achieved between SPEED_CP_MIN and SPEED_CP_MAX. The controller  16  also drives the motor  2  over a voltage range bounded by V_MIN and V_MAX. Within this voltage range, the controller  16  selects control values that ensure that constant average power is achieved between V_CP_MIN and V_CP_MAX. 
     The controller  16  stores three advance lookup tables. The first lookup table is a one-dimensional table that is indexed by rotor speed when operating in multi-switch mode. The second lookup table is a one-dimensional table that is indexed by rotor speed when operating in overcurrent single-switch mode. The third lookup table is a two-dimensional table that is indexed by rotor speed and voltage when operating in unlimited-freewheel single-switch mode. 
     The freewheel lookup table, the timeout lookup table, and the advance lookup table used in multi-switch mode are stored collectively by the controller  16  as a single multi-switch map.  FIG. 24  details the multi-switch map employed by the controller  16 . The map stores a freewheel period, T_FW, a timeout period, T_TO, and an advance period, T_ADV, for each of a plurality of speeds. Electrical angles corresponding to the various periods are also listed. However, the angles do not form part of the map stored by the controller  16  and are provided merely to illustrate the behaviour of the angles with rotor speed. For example, it can be seen that a fixed timeout period, T_TO, of 70 μs is used throughout Mid-Speed Acceleration. However, the corresponding timeout angle, A_TO, increases from 8.4 degrees at 10 krpm to 42.0 degrees at 55 krpm. 
     The advance and overrun lookup tables used in overcurrent single-switch mode are similarly stored as a single map. A portion of the map is detailed in  FIG. 25 . Again, the corresponding electrical angles are provided for the purposes of illustration. 
     The advance, conduction offset and conduction phase-shift lookup tables used in unlimited-freewheel single-switch mode are also stored as a single map. That is to say that the same speed and voltage resolution are used for each of the three lookup tables. Consequently, each element of the map stores an advance period, a conduction offset value and a conduction phase-shift value. However, for the purposes of clarity, a portion of each lookup table is illustrated in  FIGS. 26-28 ; the unit for all three lookup tables is μs. Rather than storing absolute values, the advance lookup table and the conduction offset lookup table store difference values. The controller  16  then stores a reference advance period of 56.2 μs and a reference conduction offset value of 48.8 μs, which correspond to a speed of 94 krpm and an RMS voltage of 230 V. 
       FIG. 29  details a section of the conduction sine lookup table that is stored and used by the controller  16  in unlimited-freewheel single switch mode. Since the frequency of the AC supply is 50 Hz, the lookup table spans 0 to 0.01 seconds, which corresponds to a half-cycle of the AC supply  4 . The resolution of the lookup table is 51.2 μsec, and the conduction amplitude, T_CD_AMP, and the conduction phase angle, T_CD_PHASE are respectively 83.2 μs and 83.2 μs and 320 μs. The conduction phase angle, T_CD_PHASE, is effectively a reference phase-shift for a speed of 94 krpm and a voltage of 230 V. 
     The motor system  1  has an operating speed range of 81 krpm to 106 krpm, and an operating voltage range of 200 V to 260 V. Within these ranges, an average input power of 1600 W 25 W is maintained at speeds between 85 krpm and 106 krpm and at voltages of between 219 V to 256 V. Moreover, an efficiency of around 85% is achieved over the constant-power speed and voltage range. 
     The controller  16  is a PIC16F690 microcontroller manufactured by Microchip Technology Inc. This is a relatively simple 8-bit microcontroller having a clock speed of 20 MHz, a single ADC, two comparators, three timers, 4096 words of program memory, and 512 bytes of data memory. Yet even with this relatively simple microcontroller, the controller  16  is capable of driving the motor  2  at speeds in excess of 100 krpm, with an average input power of around 1600 W. 
     Reference has thus far been made to a conduction period having a waveform that varies as a half-sinusoid over each cycle of the waveform (and thus over each half-cycle of the AC supply  4 ). However, other types of periodic waveform may be employed for the conduction period. In particular, waveforms for which the conduction period varies as a triangle or trapezoid over each cycle of the waveform have both been found to work well in obtaining a relatively good power factor.  FIG. 30  illustrates the voltage waveform of the AC supply  4  along with the three aforementioned waveforms for the conduction period: (a) half-sinusoid; (b) triangle; and (c) trapezoid. For each of these waveforms, the conduction period increases over the first half of each cycle of the waveform and decreases over the second half of the cycle. Of these three waveforms, the half-sinusoid has thus far been found to give the best results in terms of low-order harmonics. Nevertheless, for a motor system having different characteristics, it is quite possible that improved performance may be obtained using a different waveform. 
     In the embodiments described above, the advance period is constant over each half-cycle of the AC supply  4 . This then simplifies the instructions executed by the controller  16 . However, improved performance may be achieved by employing an advance period that varies across each half-cycle of the AC supply  4 . 
     By commutating the phase winding  7  in advance of the edges of the HALL signal, the DC link voltage used to excite the phase winding  7  is boosted by the back EMF. As a result, the direction of current through the phase winding  7  may be more quickly reversed. Additionally, the current in the phase winding  7  may be caused to lead the back EMF, such that more current may be driven into the phase winding  7  during the period of positive torque. As the DC link voltage increases, the time required to reverse the direction of phase current decreases and the rate at which phase current rises increases. Accordingly, a shorter advance period may be employed and any shortfall in the amount of phase current may be made up by increasing the conduction period. Importantly, by decreasing the advance period, the period of negative torque is decreased and thus a more efficient motor system  1  may be realized. The controller  16  may therefore employ an advance period that varies across each half-cycle of the AC supply  4 . To this end, the length of the advance period may be defined by a periodic waveform, each cycle of the waveform repeating with each half-cycle of the AC supply  4 . The length of the advance period is longer in the region around the zero-crossings in the voltage of the AC supply  4 , and is shorter in the region around the peak voltage. Suitable waveforms for the advance period include inverted half-sinusoid, inverted triangle and inverted trapezoid.  FIG. 31  illustrates the voltage waveform of the AC supply  4  along with three possible waveforms for the advance period: (a) inverted half-sinusoid; (b) inverted triangle; and (c) inverted trapezoid. The advance period is defined, stored and updated by the controller  16  in much the same manner as that described above for the conduction period. For example, an advance period, T_ADV, that varies as an inverted half-sinusoid may be defined as:
 
 T _ADV= T _ADV_OFFSET− T _ADV_AMP*abs{sin({ t*f* 360 deg)}
 
     The controller  16  then uses the time that had elapsed since a zero-crossing in the voltage of the AC supply  4  to determine an advance period for each electrical half-cycle of the motor  2 . The controller  16  may additionally update the waveform of the advance period in response to changes in rotor speed and/or changes in RMS voltage of the AC supply  4 . For example, the controller  16  may adjust one or more of the offset, the amplitude and the phase of the waveform in response to changes in rotor speed and/or voltage. Again, as with the conduction period, the advance period may be defined as the sum of two components: a first component that is constant and a second component that varies across each cycle of the advance period waveform. The controller  16  then adjusts one or both components in response to changes in rotor speed and/or RMS voltage. 
     The parameters (e.g. advance period, conduction offset etc.) employed by the controller  16  are adjusted in response to changes in the RMS voltage of the AC supply  4  only when operating in Running Mode. This then reduces the size of the lookup tables that are used by the controller  16  during acceleration. As a result, more memory is made available for the more important lookup tables used during Running Mode. However, there may be instances for which it is desirable to adjust the one or more parameters during acceleration in response to changes in the RMS voltage of the AC supply  4 . For example, without adjusting the control values, the motor system  1  may start with higher power or lower power should the RMS voltage of the AC supply  4  be higher or lower than a nominated voltage. By adjusting the parameters during acceleration, better control over power may be achieved. The controller  16  may therefore store a voltage compensation table for one or more of the parameters used during acceleration, e.g. freewheel period, timeout period, advance period, and overrun period. The voltage compensation table stores a compensation value for each of a plurality of voltages. When updating a particular parameter, the controller  16  indexes the relevant lookup table using the rotor speed to select a control value. Additionally, the controller  16  indexes the relevant voltage compensation table using the RMS voltage of the AC supply  4  to select a compensation value. The controller  16  then sums the control value and the voltage compensation value to obtain the value of the parameter. In this particular example, the voltage compensation table is one dimensional. However, any voltage compensation ideally depends not only on the RMS voltage of the AC supply  4  but also the speed of the rotor  5 . Accordingly, rather than storing two one-dimensional lookup tables for each parameter, the controller  16  may instead store a full two-dimensional lookup table for each parameter, as is done for those parameters used during Running Mode (e.g.  FIG. 26-28 ). However, a full two-dimensional table requires considerably more memory than two one-dimensional tables. 
     In the embodiments described above, the motor  2  comprises a four-pole rotor  5  and a four-pole stator  6 . However, the rotor  5  and stator  6  might have fewer or greater number of poles. As the number of poles increases, the number of electrical cycles per mechanical cycle increases. Consequently, for a given rotor speed, each Hall period is shorter. A faster controller  16  might therefore be needed in order to execute the necessary instructions during each Hall period. Additionally, faster switches for the inverter  10  might be needed. As a result, the number of permissible poles is likely to be limited by the operating speed of the motor  2  and/or the components of the control system  3 . 
     The current controller  22  described above and illustrated in  FIG. 5  makes use of the internal peripherals of the PIC 16F690 microcontroller. Alternative configurations for the current controller  22  are possible, depending on the particular microcontroller that is used for the controller  16 . Moreover, it is not essential that the current regulator  22  forms part of the controller  16 . Instead, the current regulator  22  may be formed separately from the controller  16 . The controller  16  would then include an input pin  20  coupled to the current regulator  22  for receiving the overcurrent signal. 
     The position sensor  13  employed by the motor system  1  is a Hall-effect sensor. However, alternative position sensors capable of outputting a signal indicative of the position of the rotor  5  might equally be employed, e.g. optical sensor. Similarly, rather than employing a pair of clamping diodes, other arrangements may be used for the zero-cross detector  12 , e.g. Schmitt trigger. 
     The controller  16  freewheels the phase winding  7  by opening the high-side switches Q 1 ,Q 2  of the inverter  10 . This then enables current in the phase winding  7  to re-circulate around the low-side loop of the inverter  10 . Conceivably, freewheeling might instead occur by opening the low-side switches Q 3 ,Q 4  and allowing current to re-circulate around the high-side loop of the inverter  10 . However, the shunt resistors R 1 ,R 2  of the current sensor  12  would then be required to be located on the upper arms of the inverter  10  in order that current can continue to be sensed during freewheeling. This in turn would lead to higher power losses since the shunt resistors R 1 ,R 2  would be subject to higher voltages during excitation. Additionally, the voltage across the shunt resistors R 1 ,R 2  would be floating rather than being referenced to neutral and thus measuring the current in the phase winding  7  would be difficult. 
     In the embodiments described above, the motor system  1  comprises a control system  3  that drives a permanent-magnet motor  2 . However, many aspects of the control system  3  might equally be used to drive other types of brushless motor. 
     The use of a conduction period and/or an advance period that varies periodically with time may be used to excite the phase windings of other types of brushless motor, e.g. reluctance motors. For a reluctance motor, the rotor does not induce a back EMF in the phase windings of the motor. It is therefore possible to obtain a substantially sinusoidal current waveform without the need for a variable conduction period or advance period. However, a conduction period and/or an advance period that varies over each half-cycle of the AC supply  4  may be used to achieve a particular envelope for the magnetic flux density in the motor. 
     Owing to the ripple in the DC link voltage, the windings of the reluctance motor are excited with a voltage that varies over each half-cycle of the AC supply  4 . If a constant conduction period were used over each half-cycle of the AC supply  4 , the envelope of the magnetic flux density in the motor would reflect that of the DC link voltage. The controller  16  may therefore employ a conduction period that varies over each half-cycle of the AC supply  4  so as to shape the envelope of the magnetic flux density. In particular, the controller  16  may employ a conduction period that reduces the peak magnetic flux density. By reducing the peak magnetic flux density, a more efficient and/or a smaller motor may be realized. In order to reduce the peak magnetic flux density, the controller  16  employs a conduction period that is longer in the region around the zero-crossings in the voltage of the AC supply  4 , and is shorter in the region around the peak voltage. Suitable waveforms for the conduction period include inverted half-sinusoid, inverted triangle and inverted trapezoid. 
     In order to compensate for the variation in the length of the conduction period, the controller  16  may additionally employ an advance period that varies periodically with time. In particular, as the conduction period decreases, the controller  16  may employ a longer advance period so as to compensate for the shorter conduction period. Accordingly, in contrast to the conduction period, the controller  16  employs an advance period that is short in the region around the zero-crossings in the voltage of the AC supply  4 , and is longer in the region around the peak voltage. Suitable waveforms for the advance period include half-sinusoid, triangle and trapezoid. 
     For the permanent-magnet motor  2 , the controller  16  excites the phase winding  7  in advance of zero-crossings of back EMF in the phase winding  7 , e.g. as determined from the signal output by the position sensor  13 . For a reluctance motor, the controller  16  excites the winding in advance of rising inductance, which may again be determined by means of a position sensor. In both instances, the controller  16  excites the phase winding in advance of predetermined positions of the rotor. More particularly, the controller  16  excites the phase winding in advance of unaligned rotor positions. 
     While a conduction period and/or an advance period that varies periodically with time may be used with different types of brushless motor, variable conduction and/or advance periods are of particular benefit when used to drive a permanent-magnet motor. As noted above, the back EMF induced in the phase winding  7  by the permanent-magnet rotor  5  makes it difficult to accurately control the amount of current drawn from the AC supply  4 . By employing a conduction period that varies periodically with time, a waveform approaching that of a sinusoid may be achieved for current drawn from the AC power supply without the need for an active PFC or high-capacitance link capacitor. 
     Updating control parameters (e.g. advance period, conduction period, freewheel period and timeout period) in response to zero-crossings in the voltage of an AC supply may be used with other types of brushless motor. As noted above, by updating a control parameter in response to zero-crossings in the AC supply, the control parameter is updated at regular intervals irrespective of motor speed. Moreover, the control parameter is updated regularly without the need for a dedicated timer. The control parameter is also updated in synchrony with the cycle of the AC supply. As a result, the waveform of current drawn from the AC supply is generally more stable. 
     Interrupt clashing is a potential problem for many types of brushless motor. Consequently, the use of a timer and comparator (e.g. forming part of a dedicated comparator module or as part of a PWM module) to generate a control signal in hardware rather than software may be used with other types of brushless motor so as to reduce the total number of interrupts. Additionally, when the controller is required to sample an analog signal, interrupt clashing may be further reduced by dividing the sampling process into a number of steps, each step being performed in response to a different edge of the position-sensor signal. As a result, the sampling process is spread over a number of electrical half-cycles of the motor, thereby freeing up more time for the controller to execute other routines during each electrical half-cycle.