Method of operating a magnetically coupled system

Abstract

A stator 102 and dual rotor 104 / 106 system wherein movement of the rotors is magnetically coupled or potentially geared. A sensor, which may be a torque transducer, detects the rotational state of the system, which may be load angle, rotational position or similar, and is further monitored by a controller to execute a method of determining normal operating conditions, comprising calculating via the sensor an actual torque, determining via a system parameter an expected torque and using a residual between the two to indicate deviation from normal if it is below a predetermined threshold. This fault condition may also be delineated into multiple separate conditions if the residual is above or below the threshold or has certain characteristics. The fault condition may also trigger the issuance of a command to the system that is corrective or abortive and may be executed by a processor.

Description

Field The present disclosure relates to a method of operating a magnetically coupled system, to an associated system, and to an associated computer-readable medium. Background Magnetic motors, magnetic gears, and other magnetic machines for operating vehicles and machinery, are known. They have numerous advantages, including improved durability, improved efficiency, and in many cases reduced weight and complexity when compared with non-magnetic alternatives. A problem exists, however, that fault detection in the context of magnetic machines can be challenging. Additional sensors can be used to detect prolonged degradation and instantaneous faults on magnetic machines, or on vehicles and machinery using such magnetic machines. However, such sensors may increase complexity, and may themselves be susceptible to failure. As an example, a magnetic machine may be used as a servo actuator, for example a servo actuator for an aircraft flight surface or for a robotic arm. In another example, a magnetic machine may be used to drive a rotary motor for driving a locomotive. In each of these examples, it may be important for the magnetic machine to be reliable and robust. It may therefore be preferable for the magnetic machine to use minimal extraneous components, which could themselves be susceptible to failure. Accordingly, there exists a need for improved fault detection in the context of magnetic machines. There is also a need to ensure robustness of magnetic machines. Summary The present disclosure has been developed to address at least some of the above problems. In a first aspect there is provided a method of operating a magnetically coupled system, the magnetically coupled system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; at least one sensor arranged to detect a rotational state of the system; and a controller configured to monitor the magnetically geared system; the method comprising: calculating, based on the detected rotational state of the system, an actual torque on the system; calculating, based on at least one operating parameter of the system, an expected torque on the system; determining that the system is under normal operating conditions when a residual between the actual torque and the expected torque is below a first predetermined threshold. In a second aspect there is provided a method of operating a magnetically coupled system, the magnetically coupled system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; a torque transducer; and a controller configured to monitor the magnetically geared system; the method comprising: determining, based on an output from the torque sensor, an actual torque on the system; calculating, based on at least one operating parameter of the system, an expected torque on the system; determining that the system is under normal operating conditions when a residual between the actual torque and the expected torque is below a first predetermined threshold. As the reader will understand, a residual is defined as the difference between an actual value and an estimated (or expected) value. The methods of the first and second aspects may therefore comprise calculating a residual between the actual torque and the expected torque. The methods of the first and second aspects may further include determining that the system is under a first fault condition when the residual is above the first threshold and has a first characteristic. The method may further include determining that the system is under a second fault condition when the residual is above the first threshold and has a second characteristic which is different from the first characteristic. According to the first aspect and the second aspect, not only is a fault detected using the existing components and properties of the magnetic machine (i.e. with minimal use of additional or extraneous components), but a type of fault may also be determined (namely, determination of which of a first fault condition and a second fault condition is present). Accordingly, in addition to improving reliability by reducing additional or extraneous componentry, the presence of a fault in the system is detected, and in some examples useful information on a type of fault may also be provided, which in turn helps to better inform system diagnostics and / or restorative actions for remedying the fault. As noted above, minimal additional or extraneous componentry is need. Namely, the controller detects a fault and determines between types of faults based on measurable properties of the magnetically coupled system itself. In a third aspect there is provided a system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; at least one sensor arranged to detect a rotational state of the system; and a controller configured to monitor the magnetically geared system; wherein the controller is further configured to implement a method according to the first aspect. In a fourth aspect there is provided a system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; a torque transducer; and a controller configured to monitor the magnetically geared system; wherein the controller is further configured to implement a method according to the second aspect. As the skilled reader will understand, the fact that the rotating magnetic field couples with the second magnetic field through the second rotor, in turn causes a magnetic coupling between the first and second rotors, which in turn gives rise to a geared interaction between the first and second rotors. In a fifth aspect there is provided a computer-readable medium having instructions stored thereon which, when executed by a processor, cause the processor to implement a method according to the first aspect or the second aspect. Further optional features of the aspects will now be described. The or each sensor of the first aspect may be a rotary encoder or a rotary resolver. The or each sensor may output a signal indicative of an angular position. The method according to the first aspect may further comprise, based on the detected rotational state of the system, calculating a load angle of the system; wherein the actual torque on the system is calculated based on the calculated load angle. The at least one sensor may comprise a first rotational sensor arranged to detect a rotational position of the first rotor relative to the stator, and a second rotational sensor arranged to detect a rotational position of the second rotor relative to the stator. An angular displacement between the first rotor and the second rotor may be calculated as a difference between the rotational position of the first rotor relative to the stator and the rotational position of the second rotor relative to the stator. The load angle may be a measure of the angular displacement (e.g. phase difference) between the second magnetic field and a magnetic field induced in the pole pieces of the second rotor. As the skilled person will understand, for a given system (having a given number of permanent magnets and a given number of pole pieces), load angle may be governed by the angular position of the first rotor and the angular position of the second rotor. Herein, load angle, 0e, may be defined as follows: = — ^R2^R2> where 0R1 is the rotational angle of the first rotor, NR1 is the number of pole pairs (which may be equal to the number of permanent magnets) on the first rotor, 0R2 is the rotational angle of the second rotor, and NR2 is the number of pole pieces on the second rotor. For a given system, NR1 and NR2 are known, and are fixed. The actual torque on the system (e.g. at a given time) may be calculated based on the instantaneous load angle on the system (e.g. at the given time), the dynamics (e.g. rate of change) of the load angle on the system (e.g. at the given time), and / or the electrical torque applied to the system (e.g. at the given time). For example, the actual torque may be calculated based on the instantaneous load angle on the system (0e), the second time derivative of the load angle on the system, and the electrical torque (Ti) applied to the system. For example, The actual torque (Tt) on the system may be calculated using the following equation: Ji d2ee ( h \ Ji Ti = + VTT +Gr)TP U Lz LX* I* \ L- / j j Where 0e is the load angle, Te is the electrical torque on the system, and the rest are known parameters of the system, namely: • Ji is the inertia of the second rotor, • Gr is the gear ratio of the magnetic gear, • p is the number of magnetic pole pairs on the first rotor, • Jm is the inertia of the first rotor, and • TP is the pull out torque of the magnetic gear. The inventors have found, in particular, that the dynamics of the load angle on the system provide a particularly robust and accurate means for analysing faults within the system. Electrical torque (Te) may itself be calculated using the following equation: Te= Kt.I where I is a magnitude of the current supplied to the windings, and Kt is a known parameter of the system, namely the motor constant of the system. Alternatively, according to the second and fourth aspects, the torque transducer is used to determine the actual torque on the system. The torque transducer may comprise a rotational strain gauge, a magnetoelastic torque transducer, an optical torque transducer, or a rotary transformer. The expected torque on the system may be calculated based on a model of the system, for example a predetermined model representing healthy operation of the system. The model may be a model which predicts the expected torque based on an operating parameter of the system. The operating parameter may be one of output velocity of the system, or output angular position of the system. Therefore, in practice, the expected torque on the system may be determined based on an output angular velocity or an output angular position of the system, wherein the relationship between expected torque and output angular velocity or output angular position is known from the predetermined model. Herein, output velocity of the system may be a rotational velocity of the second rotor. Output angular position of the system may be an angular position of the second rotor. In alternative examples, output angular velocity or output angular position of the system may be a rotational velocity or a rotational position of the first rotor. In an alternative example, the operating parameter is torque measured at a component which is driven by the system. Where intervening components are present for transmitting torque from a drive shaft of the system to the component which is driven by the system, the expected torque will therefore represent the torque which would be expected at the drive shaft of the system in the absence of any system faults between the drive shaft of the system and the component which is driven by the system. The model may have been determined from laboratory or field testing, for example laboratory or field testing of the system or of a comparable system. Alternatively, the first threshold may have been predetermined from simulation. In other examples, the model may have been determined during normal operation of the system. For example, the model may be periodically determined based on real-time measurement of the system, e.g. real-time measurement of torque at a range of output angular velocities or output angular positions, under normal operation conditions. The first threshold may have been predetermined from laboratory or field testing, for example laboratory or field testing of the system or of a comparable system. Alternatively, the first threshold may have been predetermined from simulation. The first characteristic and the second characteristic may similarly have been predetermined based on laboratory testing, field testing, or simulation. For example, the first characteristic may comprise a first predefined residual trend which is indicative of the first fault condition being present, and the second characteristic may be a second predefined residual trend which is indicative of the second fault condition being present. The method may therefore comprise comparing the residual to each of the first predefined trend and the second predefined trend, and based on the comparison determining which of the fault conditions is present. That is, if the residual resembles the first trend, it may be determined that the first fault condition is present; and if the residual resembles the second trend, it may be determined that the second fault condition is present. The first and second trends may be predefined based on laboratory or field testing of the system or of a comparable system. In other examples, the first and second trends may be predefined based on simulations. The first characteristic / trend may comprise the residual being between the first threshold and a second threshold; and the second characteristic may comprise the residual being greater than the second threshold. The second threshold may be higher than the first threshold. The first and third thresholds may have been predetermined based on laboratory testing, field testing, or simulation. The residual may be a single residual value representing a difference between a single actual torque value and a single expected torque value. A magnitude of the residual may be used for the detection and diagnosis. In alternative examples, a statistical determinant, for example an average residual value, may be used to determine whether the system is under normal operating conditions and optionally to determine which fault condition is present. The average residual value may be calculated from a plurality of residual values (for example the magnitudes of the plurality of residual values), each of the plurality of residual values being calculated as the difference between an actual torque value and a corresponding expected torque value. The plurality of residuals may comprise a time series of residual values. That is to say, the residuals may be obtained at different respective times from one another. The time series may be converted into a statistical distribution of residuals. The average residual value may be used to determine whether the system is under normal operating conditions and optionally to distinguish between the first fault condition and the second fault condition. Therefore, the method may comprise: calculating, based on the detected rotational state of the system, a plurality of actual torque values for the system (or, according to the second aspect, determining a plurality of actual torque measurements for the system based on a plurality of outputs from the torque sensor); calculating, based on the at least one operating parameter of the system, a plurality of corresponding expected torque values for the system; calculating, for each actual torque value and corresponding expected torque value for the system, a residual value; calculating, based on the calculated residual values, an average residual value for the system; and determining that the system is under normal operating conditions when the average residual value is below the first predetermined threshold. Determination between the first fault condition and the second fault condition may also be done based on the average residual value. In order to accumulate a statistical distribution of residuals from which to calculate the average residual, a time series of actual torques and corresponding expected torques may be calculated, from which the plurality of residuals may be calculated. The average residual value may be a mean residual value, namely a mean average of the plurality of residual values. The mean average may be taken from the magnitudes of the plurality of residual values. Alternatively, one of the following may be used instead of mean residual value: • Root mean square (“RMS”) of the plurality of residual values; • Sum of squares of the plurality of residual values (“RSS”); • L2 norm of the plurality of residual values; or • Mean squared error (“MSE”) of the plurality of residual values, i.e. the mean average of the squares of the plurality of residual values. Above, the calculation of an average value and the comparison of that average value with one or more threshold values has been described for the purpose of distinguishing between types of fault condition. In alternative examples, a statistical comparison may be made between a distribution of the plurality of residual measurements, and one or more known distributions. For example, if a distribution of the plurality of residual measurements has a first distribution or shape, e.g. resembles a first distribution or shape, it may be determined that the first error condition is present. If a distribution of the plurality of residual measurements has a second distribution or shape, e.g. resembles a second distribution or shape, it may be determined that the second error condition is present. The first distribution or shape may therefore correspond to the first characteristic; and the second distribution or shape may correspond to the second characteristic. The determination may therefore comprise comparing the distribution of the plurality of residuals to the first distribution or shape and to the second distribution or shape. The statistical comparison may comprise decomposing the statistical distribution into a plurality of bins, wherein at least one bin is selected as being determinative of the first distribution or shape, and at least one bin is selected as being determinative of the second distribution or shape. The statistical comparison may then comprise determining which error condition is present based on the split of the statistical distribution between the bins. In one example, a first bin may be defined below the first threshold and may be indicative of normal operation; a second bin may be defined between the first and second thresholds and may be indicative of the first error condition; and a third bin may be defined above the second threshold and may be indicative of the second error condition. The calculation of the actual and expected torque(s) on the system may be performed when the system is in a zero speed state (e.g. a fixed rotational position). The calculation of the actual and expected torque(s) on the system may be performed once the current supplied into the coils has been in the zero speed state for at least a predetermined period of time. Alternatively, the calculation of the actual and expected torque(s) on the system may be performed when the system is in a constant velocity state. Alternatively, the calculation of the actual and expected torque(s) on the system may be performed when the system is in an acceleration or deceleration condition (e.g. constant acceleration or deceleration condition). A plurality of actual and expected torque measurements may be taken in order to accumulate a statistical distribution of residuals. Where a plurality of actual and expected torque measurements are made (i.e. for the calculation of a plurality of residuals), the plurality of measurements may be made in a plurality of measurement windows. The measurement windows may be selected to correspond to one or more zero speed stated of the system, e.g. a state in which the output velocity of the system is zero. Alternatively, the measurement windows may be selected to correspond to one or more constant velocity states of the system, e.g. a state in which the output velocity of the system is constant and non-zero, e.g. when the system is transitioning from a first zero speed state to a second zero speed state. Alternatively, the measurement windows may be selected to correspond to one or more acceleration or deceleration states of the system, e.g. a state in which the output velocity of the system is increasing or decreasing. In each case, the measurement windows may be non-contiguous. The measurement windows may be temporal measurement windows. Therefore, the plurality of actual and expected torque measurements may comprise a time series of actual and expected torque measurements, wherein the measurements are obtained during one or more measurement windows. The method may comprise causing the system to cycle between a plurality of system states (e.g. a plurality of zero speed states, or a plurality of constant velocity states, or a plurality of acceleration / deceleration states), and obtaining residual values from a plurality of measurement windows, wherein the plurality of measurement windows correspond to the plurality of system states. The first fault condition may correspond to a change in spring constant in an idealised or simulated system, and may for example be indicative of accumulated system degradation, such as accumulated drag torque caused by a failing component, for example a failing bearing. The second fault condition may correspond to a reduction in spring pre-tension in an idealised or simulated system, and may be indicative of an instantaneous fault, such as snapping of a drive shaft, snagging or jamming of a system component, or sudden decoupling of the motor from a load. Methods according to the present disclosure may further comprise: when the first fault condition is present, issuing a first command; and when a second fault condition is present, issuing a second command; wherein the first command is for a first corrective measure to be implemented; and wherein the second command is for a second corrective measure that is different from the first corrective measure to be implemented. The corrective measures may include: alerting the user to the fault; setting a motor associated with the system to limp home mode (e.g. reducing a power supplied to the system); powering down the system (e.g. cutting off power to the system), or diverting power from the system to another motor, for example another motor in a dual-redundant or multiple-redundant system. In one example, the first command (issued when the fault condition is indicative of accumulated system degradation) may comprise initiating a limp home mode; and the second command (issued when the fault condition is indicative of an instantaneous fault) may comprise powering down the system. The second rotor may comprise a plurality of pole pieces. The stator may further comprise a plurality of permanent magnets having an associated first magnetic field. In alternative examples, the stator may comprise windings and no permanent magnets. The system may further comprise an output shaft coupled to the second rotor. In some examples, the magnetically geared system may comprise a magnetic motor coupled to a magnetic gear. A first drive shaft may couple an output rotor of the magnetic motor to an input rotor of the magnetic gear. A second drive shaft may be coupled to an output rotor of the magnetic gear. The controller may supply a drive current to the windings, the drive current selected to generate the rotating magnetic field. One of the first rotor and the second rotor may be a drive rotor configured for attachment to an external load. The other of the first rotor and the second rotor is a passive rotor. Herein, the passive rotor may be defined as not being connected to a load external to the system. It may be driven only by the rotating magnetic field. The drive rotor may be connected to a drive shaft, for driving an external load. The second rotor may be located between the first rotor and the stator. The second rotor may be the drive rotor. The first rotor may be the passive rotor. The magnetically coupled system may be a motor. The stator may further comprise a plurality of permanent magnets having an associated first magnetic field. The second rotor may be arranged to couple the magnetic fields of the stator (that is, the first magnetic field and the rotating magnetic field) with the second magnetic field. The second rotor may comprise a plurality of pole pieces through which the magnetic field(s) of the stator couple with the second magnetic field. Each pole piece may comprise an unmagnetised magnetisable material (for example an unmagnetised ferromagnetic material, such as unmagnetised steel). In a sixth aspect there is provided a method of operating a magnetically coupled system, the magnetically coupled system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; at least one sensor arranged to detect a rotational state of the system; and a controller configured to monitor the magnetically geared system; the method comprising: calculating, based on the detected rotational state of the system, a first torque on the system; calculating, based on a magnitude of the current supplied to the windings, a second torque on the system; determining that the system is under normal operating conditions when a residual between the first torque and the second torque is below a predetermined threshold. The method may further comprise, when the residual between the first torque and the second torque is above the predetermined threshold, determining that a demagnetisation has occurred in one or more permanent magnets of the system. When the residual between the first torque and the second torque is above the predetermined threshold, the method may issue a command or abortive action. The command may comprise alerting a user to the fault, or issuing a command to reduce a power supplied to the system. The abortive action may comprise issuing a command to power down the system. The first torque (Ti) may be calculated using the following equation: = Tp sin^O^, where Tp is the pull out torque of the magnetic gear and is a known quantity of the system; and where 0e is the load angle of the system, and is given by equation [1] below. The second torque (T2) may be calculated using equation [3] below, i.e. may be equal to the electrical torque on the system. In a seventh aspect there is provided a system comprising: a stator comprising a plurality of windings arranged to generate a rotating magnetic field; a first rotor comprising a plurality of permanent magnets having an associated second magnetic field; a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor; at least one sensor arranged to detect a rotational state of the system; and a controller configured to monitor the magnetically geared system; wherein the controller is further configured to implement a method according to the sixth aspect. In an eighth aspect, there is provided a computer-readable medium having instructions stored thereon which, when executed by a processor, cause the processor to implement a method according to the sixth aspect. As the reader will understand, optional features applicable to the first through fifth aspects are equally applicable to the sixth to eighth aspects. Brief description of the drawings Embodiments of the present disclosure will now be described, with reference to the accompanying drawings, in which: Figure 1a shows a cross-sectional view of a magnetically geared system according to the present disclosure; Figure 1 b shows an axial view of the magnetically geared system of Figure 1 A; Figure 2a shows a first example expected torque model according to the present disclosure; Figure 2b shows a second example expected torque model according to the present disclosure; Figure 2c shows a third example expected torque model according to the present disclosure; Figure 3 shows a plot of actual torque against time for a driven system, showing a plurality of first measurement windows; Figure 4a shows a normalised statistical distribution of residuals obtained under normal operating conditions, during the first measurement windows of Figure 3; Figure 4b shows a normalised statistical distribution of residuals obtained under a first fault condition, during the first measurement windows of Figure 3; Figure 4c shows a normalised statistical distribution of residuals obtained under a second fault condition, during the first measurement windows of Figure 3; Figure 5 shows a further plot of actual torque against time for the driven system, showing a plurality of second measurement windows; Figure 6a shows a normalised statistical distribution of residuals obtained under normal operating conditions, during the plurality of second measurement windows of Figure 5; Figure 6b shows a normalised statistical distribution of residuals obtained under a fault condition, during the plurality of second measurement windows of Figure 5; Figure 7 shows a method according to the present disclosure; Figure 8 shows a controller according to the present disclosure; and Figure 9 shows a cross-sectional view of a magnetically geared system according to a further example of the present disclosure. Like reference numerals are used for like features throughout the drawings. Detailed description Figures 1A and 1B show a magnetically geared system 100 according to an example of the present disclosure. The magnetically geared system 100 is operable as a motor. The system 100 may be for used as a servo motor for a robotic arm or an aircraft control surface, or as a drive motor for a locomotive. However, as the skilled reader will understand, the motor is not limited to these specific applications. The magnetically geared system 100 includes an outer stator 102, a first (inner) rotor 104, and a second (intermediate) rotor 106. The second (intermediate) rotor is positioned radially between the stator 102 and the first rotor 104. The stator 102 comprises a plurality of circumferentially arranged conductive windings 108 and a first plurality of permanent magnets 120, the first rotor 104 comprises a second plurality of circumferentially arranged permanent magnets 110, and the second rotor 106 comprises plurality of circumferentially arranged unmagnetised magnetisable (typically ferromagnetic, e.g. steel) pole pieces 112. One of the first rotor 104 and the second rotor 106 can be connected to an external load (for example, the wheels of a vehicle, a propellor of a boat, etc.). The other of the first rotor and the second rotor is passive, in that it is not connected to a load. In the depicted example, the second rotor is configured for connection to a load, and the first rotor is passive. That is, there is an output shaft 118 coupled to the second rotor 106. There is no shaft coupled to the first rotor 104. The first plurality of permanent magnets 120 produce a first magnetic field, and the second plurality of permanent magnets 110 produce a second magnetic field. The pole pieces 112 modulate the interaction between the first and second magnetic fields, coupling the magnetic fields to produce a geared interaction between the first rotor 104 and the second rotor 106. In the example shown, the first rotor 104 comprises 3 magnetic pole pairs, and the second rotor 106 comprises 21 pole pieces. Accordingly, the second rotor will rotate at a geared (lower) speed than the first rotor, at a gear ratio (Gr) of 1 / 7. Additionally, when the windings 108 of the stator are supplied with a three-phase, 120 degree displaced current, a rotating magnetic field is set up in the system 100. This rotating magnetic field may have the same number of pole pairs as the first magnetic field generated by the first permanent magnets 110. Accordingly, the rotating magnetic field applies an electromagnetic torque to the first rotor, thereby driving rotation of the first rotor 104. Furthermore, because of the magnetic coupling as described above, this in turn will drive rotation of the second rotor 106, at a geared lower speed than the first rotor 104. In Figures 1A and 1B, the drive shaft 118 is attached to the second rotor 106. Accordingly, the rotating magnetic field drives rotation of the drive shaft 118 at the geared, lower speed. Therefore, the example of Figures 1A and 1B is particularly well suited to high-torque applications and / or for use as a servo motor (thanks to the 1 / 7 gear ratio). However, as the reader will understand, in some examples the drive shaft 118 may be attached to the first rotor. Bearings B1 enable the first rotor 104 to rotate relative to the drive shaft 118. Similarly, bearings B2 enable the drive shaft and the second rotor 106 to rotate relative to the stator 102. Magnetically geared system 100 also includes a controller (not shown) configured to implement a method according to Figure 7. Figure 8 schematically illustrates the components of such a controller. According to the present disclosure, the controller uses an instantaneous load angle of the system, the dynamics of the load angle of the system, and a current supplied to the windings 108, to detect and distinguish between different fault conditions. In particular, the load angle of the system, the dynamics of the load angle of the system, and the current supplied to the windings 108, are used to calculate the actual torque on the system. The actual torque on the system is compared with an expected torque of the system (namely a torque that would be expected under healthy operation of the system). By comparing the actual and expected torques, the controller identifies the presence of a fault condition (i.e. detects the presence of a fault), and further distinguishes between different fault conditions (i.e. diagnoses the type of fault). The load angle on the system is calculated based on a rotational displacement between the first rotor 104 and the second rotor 106. In particular, based on equation [1] below, the load angle (0e) on the system can be calculated: = ~ 0R2^R2 [1 ]> where 0ri is the rotational position of the first rotor 104 relative to the stator 102; 0R2 is the rotational position of the second rotor 106 relative to the stator 102; Nri is the number of pole pairs (which may be equal to the number of permanent magnets) on the first rotor 104; and NR2 is the number of pole pieces on the second rotor 106. Therefore, by determining the absolute rotational position of each of the first rotor and the second rotor relative to the stator, the load angle (0e) can be calculated. Additionally, by monitoring the load angle (0e) through measurement of the absolute rotor positions, a second time derivative of the load angle can be calculated at any given point in time. This second time derivative of the load angle (^^) is sometimes referred to herein as the dynamics of the system. The actual torque (Tt) on the system is calculated based on equation [2]: Tl = + + Gr^ Tp [2], where Ji is the inertia of the second rotor 106; Gr is the gear ratio of the magnetic gear; JVR1 is the number of magnetic pole pairs on the first rotor 104; Jm is the inertia of the first rotor 104; TP is the pull out torque of the magnetic gear; and Te is the electrical torque on the system. Ji, Gr, p, Jm, and Tp, are known quantities of the system. Te is given by equation 3: Te=Kt.l [3], where Kt is a known, system-specific constant of the system (defined herein as the motor constant Kt); and I is the magnitude of the current supplied to the windings. In some examples, e.g. where the magnitude of the current I is constant, the only two variables on the system are load angle (0e) and the second derivative of the load angle (^-^)- In such examples, the calculation of actual torque is done based on dtz load angle (0J and the second derivative of the load angle (^). Alternatively to calculating the actual torque as described above, a torque transducer may be used to directly measure an actual torque (Ti) on the system. The torque transducer may, for example, be mounted to the output shaft, or arranged between the second rotor and the output shaft. The expected torque (Texp) on the system is estimated using a predefined model representing the system under normal (e.g. healthy) operating conditions. The model can be determined from laboratory testing, field testing, or simulation. In the case of field testing, the model may be determined during normal operation of the system. The model may even be periodically updated during normal operation of the system. Figures 2a-2c show models representing normal operation of various systems according to the present disclosure. Figures 2a-2b show two different normal operation modes according to a servo motor arrangement according to the present disclosure, namely a servo motor arrangement utilising a servo motor 100 according to Figures 1a and 1b. Figure 2c shows a normal operation mode of a drive motor arrangement according to the present disclosure, namely a drive motor arrangement utilising a drive motor 100 according to Figures 1a and 1b. Figure 2a shows an illustration of a first example expected torque model according to the present disclosure. The first example model represents an example of normal operation of a servo motor apparatus for controlling a robotic arm or an aircraft flight surface. Expected torque (Texp) on the system is directly proportional to the angular position of the output shaft 118. Expected torque (in Nm) is shown on the y-axis, and angular position (in degrees) is shown on the x-axis. Therefore, by measuring the angular position of the output shaft 118 on such a servo system, the expected torque can be calculated using the model of Figure 2a. Figure 2b shows an illustration of a second example expected torque model according to the present disclosure. The second example model represents an example of normal operation of the same servo system as Figure 2a. Expected torque (Texp) on the system is shown against rotation velocity of the output shaft 118. Expected torque (in Nm) is shown on the y-axis, and velocity of the output shaft (in degrees per second) is shown in the x-axis. Therefore, by measuring the angular velocity of the output shaft 118 on such a servo system, the expected torque can be calculated using the model of Figure 2b. Figure 2c shows an illustration of a third example expected torque model according to the present disclosure. The third example model represents normal operation of a drive system for driving a locomotive. Expected torque (Texp) on the system is related to the rotational velocity of the output shaft 118. Expected torque (in Nm) is shown on the y-axis, and velocity of the output shaft (in degrees per second) is shown in the x-axis. Therefore, by measuring the rotational velocity of the output shaft 118 on such a drive system, the expected torque can be calculated using the model of Figure 2c. As the skilled reader will understand, in some examples, the model may be more complex than a simple linear relationship. In any such case, the model will similarly be determined based on laboratory testing, field testing, or simulation. In alternative examples, the expected torque (Texp) on the system 100 may be directly measured at an output component attached to the system, for example at an output component which is connected to a transmission arrangement, wherein the transmission arrangement is itself driven by the system 100. Namely, the expected torque (Texp) on the system 100 may be directly measured by a torque transducer associated with the output component. The torque transducer may thus represent a torque which would be expected to be seen at the output shaft 118 of the system 100 under normal operating conditions, while the actual torque (T{) represents the torque which is actually seen at the output shaft 118. Therefore, where there are fault conditions present in the transmission arrangement, such fault conditions can be detected and diagnosed by comparing the expected torque (Texp) and the actual torque (Ti). At any given point in time, the actual torque (TJ on the system can be calculated based on the load angle, load angle dynamics, and current supplied to the windings (using equations [2] and [3]); and expected torque (Texp) on the system 100 can be calculated based on output rotational position or output rotational velocity, using the model of Figure 2a or the model of Figure 2b (as appropriate), or based on torque measured at an output component driven by the system 100. From the actual torque and the expected torque value, a residual (r) at the given point in time can be calculated using equation [4]: r = Tt - Texp [4], where Tt is the actual torque and Texp is the expected torque. A single residual may be used to detect and diagnose faults. Alternatively, a plurality of residuals may be calculated over a given time period. An average (e.g. mean) of the plurality of residuals may be calculated in order to detect and diagnose faults. Alternatively, the plurality of residuals may be represented as a statistical distribution, and a statistical analysis of the distribution may be used to detect and diagnose faults. For at least the detection of faults, magnitudes of the residuals may be used. That is to say, an average (e.g. mean) may be calculated from the magnitudes of the residuals, or the magnitudes of the plurality of residuals may be represented as a statistical distribution. Diagnosis of the type of fault may also be done using the magnitudes of the residuals, for example using an average or statistical distribution which itself is based on the magnitudes of the residuals. However, in some examples, diagnosis of the type of fault may additionally use the Taw’ residual values, i.e. may also account for the polarity of the residual without applying a magnitude operation to the residuals. For example, by looking at the polarity of one or more residuals, the system can determine whether actual torque is higher or lower than expected. At a high level, it may be determined that the system is under normal operating conditions when the residual(s) is / are under a first threshold value which is predetermined. If the residual(s) is / are over the first threshold, then the system is operating under a fault condition. In order to determine which fault condition is present, further analysis of the residual(s) is done. This will be described in more detail below. The detection and diagnosis of faults for a servo system having a model of expected torque according to Figures 2a and 2b will now be described further. As the skilled reader will understand, the same principles apply equal to detection and diagnosis of faults for a drive system having a model of expected torque according to Figure 2c, or indeed any other system having a measurable expected torque model. For illustrative purposes, a servo system having a model of expected torque according to Figures 2a-2b is described in more detail below. In order to smooth out noisy data, a plurality of residual measurements are typically taken. These may be taken at a plurality of different output angular positions of the system. Figure 3 shows a torque plot for a system which is cycled between 5 different actuator angular positions over the course of about 1.5 seconds. Each angular position has a different associated torque, owing to the model shown in Figure 2a. The y-axis represents the actual torque (TJ of the system, as calculated using equation [2] or measured using a torque transducer. Five zero speed state measurement windows 300 are shown on the graph. These zero speed state windows are time windows at which the system is settled at a given output angular position, and in which the actual torque (Ti) is approximately constant and would be expected to follow the model shown in Figure 2a under normal (e.g. healthy) operating conditions. The residual measurements are taken in these steady-state windows, in order to ensure that it is only torque contributions from angular position, and not torque contributions from transitions between angular positions (which would include a velocity contribution), which are measured. Accordingly, a comparison with the model in Figure 2a can be made. That is to say, residuals can be calculated between the measured / calculated actual torque values, and the expected torque values according to Figure 2a. In an exemplary example, a predetermined plurality of residual measurements are taken in each measurement window 300. For example, ten residual measurements may be taken in each window. These residual measurements are then compiled into a statistical distribution. Figure 4a shows a normalised statistical distribution of residuals obtained from the measurement windows 300 for the system under normal and healthy operating conditions. As shown, all of the residuals are below 0.02Nm. In the instant example, 0.02Nm is set as the first threshold, below which the system is determined to be healthy and above which the system is determined to be operating in a fault condition. Therefore, if a plot as shown in Figure 4a is observed, then the system is determined to be under normal operating conditions. Figures 4b and 4c, on the other hand, show two different fault conditions of the system. Figure 4b shows a normalised statistical distribution of residuals obtained from a system under a first fault condition. Figure 4c shows a normalised statistical distribution of residuals obtained from a system under a second fault condition. As can be seen, it is possible to distinguish between the first fault condition (Figure 4b) and the second fault condition (Figure 4c) by setting a second threshold of 0.16Nm. In particular, if there are residuals present between the first threshold of 0.02Nm and the second threshold of0.16Nm, then the system is under the first fault condition. However, if the residuals are all above the second threshold of 0.16Nm then the system is under the second fault condition. As the skilled reader will understand from Figures 4a-4c, it is therefore possible to determine which fault condition is present by taking a mean average of the residual values and determining where the average lies relative to the two thresholds. Alternatively, it is possible to determine which fault condition is present by comparing a newly generated statistical distribution of residuals to the statistical distribution of residuals shown in Figure 4b and 4c. In the servo motor example (e.g. a servo system following the model of Figure 2a under normal operating conditions), a residual plot resembling Figure 4b may be indicative of a position-dependent parasitic torque being present on the system. This is a first fault condition, and may for example represent a parasitic spring-like force being present somewhere in the system. Conversely, a residual plot resembling Figure 4c may be indicative of a position-independent parasitic torque being present on the system. This is a second fault condition, and may for example represent snagging of a part of the system by a dead weight, such as snagging of an appendage actuated by the servo system by a dead weight. Therefore, it is possible both to detect the presence of a fault condition, and to determine which type of fault condition is present. As the skilled reader will understand, these are just examples of the first and second fault conditions. There may be further fault conditions for the servo motor which are not observable when the servo system is in a zero speed state. For example, a bearing failure in the system may only be observable when the output shaft is moving e.g. at a constant velocity. In order to investigate for such a further error, it may be necessary to separately obtain a statistical distribution of residuals when the system is at constant velocity, rather than being at zero speed. Figure 5 shows the same plot as Figure 3, but this time a plurality of approximately constant velocity measurement windows 500 are shown. These windows represent the transitions between the different fixed position states. These are time windows for which the rotational velocity of the output shaft 118 is non-zero and substantially constant. These constant velocity measurement windows 500 are time windows at which the output shaft 118 is rotating at a constant velocity, and in which the actual torque (7)) would be expected to follow the model of Figure 2b if the system is under normal operating conditions. Therefore, by taking measurements in these measurement windows 500, a comparison with the model of Figure 2b can be made. That is to say, residuals can be calculated between the measured / calculated actual torque values and the expected torque values according to Figure 2b. In an exemplary example, a predetermined plurality of residual measurements are taken in each measurement window 500. For example, 10 residual measurements may be taken in each window. These residual measurements are then compiled into a statistical distribution. Figure 6a shows a normalised statistical distribution of residuals obtained from measurement windows 500 for the system under normal and healthy operating conditions. As shown, all of the residuals are below 0.04Nm. In the instant example, 0.04Nm is set as the threshold, below which the system is determined to be healthy and above which the system is determined to be operating in a fault condition. Therefore, if a plot as shown in Figure 6a is observed, then the system is under normal operating conditions. Figure 6b, on the other hand, shows a residual plot corresponding to a fault condition of the system. Figure 6b in particular shows a normalised statistical distribution of residuals obtained from a system under a further (e.g. third) fault condition. As can be seen, it is possible to distinguish between the normal operation and the further fault condition by setting a threshold of 0.04Nm. This fault condition may correspond to bearing degradation in the system. In the above description, we have outlined the technical principles underlying the present invention, namely the use of residuals between actual and expected torque, and the comparison of these residuals to different residual statistical distributions in order to detect and diagnose fault conditions within a magnetically geared system. Based on the foregoing technical understanding, a method of detecting and diagnosing fault conditions according to the present disclosure will now be described. Figure 7 shows a method 700 of detecting and diagnosing fault conditions in a magnetic motor 100 as shown in Figures 1a and 1b. At step 702, the motor 100 is caused to cycle through a plurality of operational states, each operational state having a respective measurement window associated therewith. The plurality of operational states may be a plurality of fixed angular position states, e.g. as illustrated in Figure 3; or a plurality of constant velocity states, e.g. as illustrated in Figure 5. In another example, the plurality of operational states may be a plurality of constant acceleration or deceleration states. At step 704, a plurality of actual torque measurements / calculations are made in each of the measurement windows. Actual torque is either calculated using equations [2] and [3] based on the instantaneous load angle on the system, the second derivative of the load angle on the system, and the magnitude of the current supplied to the windings; or measured using the torque transducer. At step 706, an expected torque value is determined for each measurement window. Expected torque value is determined based on either the angular position of the output shaft 118, or the angular velocity of the output shaft 118, and based on a model which relates the angular position or rotational velocity to the expected torque on the system (e.g. the model of Figure 2a, Figure 2b, or Figure 2c, as appropriate). Alternatively, an expected torque value is measured at an output component which is driven by the system 100 via a transmission coupled to the system 100. At step 707, a residual is calculated between each actual torque measurement / calculation and the expected torque value for the corresponding measurement window. The calculated residuals are then compiled into a statistical distribution of residuals. At step 708, the statistical distribution of the residuals, or an average of the residuals, is compared with a first threshold. If the statistical distribution of the residuals, or the average of the residuals, is below a first threshold, then it is determined at step 710 that the system is under normal operating conditions. If the statistical distribution of the residuals, or the average of the residuals, is above the first threshold, then it is determined at step 712 that the system is in a fault condition. An alert may at this point be generated. At step 714, based on the system being in a fault condition, the statistical distribution of the residuals, or the average of the residuals, is optionally analysed to determine which of a first fault condition and a second fault condition is present. The analysis may comprise comparing the average of the residuals to a second threshold, determining that a first fault condition is present if the average is between the first threshold and the second threshold; and determining that a second fault condition is present if the average is above the second threshold. Alternatively, the analysis may comprise comparing the statistical distribution of the residuals to a first predefined residual distribution, and to a second predefined residual distribution. If the statistical distribution matches or resembles the first statistical distribution, it may be determined that the system is under the first fault condition. If the statistical distribution matches or resembles the second statistical distribution, it may be determined that the system is under the second fault condition. If it is determined that the first fault condition is present, a first command is issued at step 716. The first command may comprise alerting a system user to the first fault condition. Additionally, or alternatively, the first command may comprise implementing a first corrective action based on the first fault condition. If it is determined that the second fault condition is present, a second command is issued at step 718. The second command may comprise alerting a system user to the second fault condition. Additionally, or alternatively, the first command may comprise implementing a second corrective action based on the second fault condition. Optionally, after step 710, the method of steps 702-708 may be repeated for a different plurality of operational states. For example, if steps 702-708 were performed based on a plurality of fixed angular position measurement windows, steps 702-708 may be repeated for a plurality of constant velocity measurement windows. The method may be performed upon startup of the motor 100, or periodically during operation of the motor 100, or on demand. Figure 8 shows a controller for implementing the method of Figure 7. Figure 8 shows a schematic and simplified representation of a controller (computer apparatus 800) which can be used to perform methods described herein, either alone, in combination with other computer apparatuses or as part of a network or a “cloud” computing arrangement. The computer apparatus 800 comprises various data processing resources such as a processor 802 (in particular, a hardware processor) coupled to a central bus structure. Also connected to the bus structure are further data processing resources such as memory 804. A display adapter 806 connects a display device 808 to the bus structure. One or more input adapters 810 may connect a user-input device 812, such as a keyboard and / or a mouse to the bus structure. A sensor 811 may also input to the input device adapter 810. The sensor 811 may for example comprise the torque transducer. The input device adapter 810 may comprise an analogue to digital (ADC) converter, the ADC converter configured to receive an analogue output the torque transducer as an input thereto, and configured to provide a digital output to the processor 802, the digital output being based on the analogue input. One or more communications adapters 814 are also connected to the bus structure to provide connections to other computer systems 800 and other networks. In operation, the processor 802 of computer system 800 executes a computer program comprising computer-executable instructions that may be stored in memory 804. When executed, the computer-executable instructions may cause the computer system 800 to perform one or more of the methods described herein. The results of the processing performed may be displayed to a user via the display adapter 806 and display device 808. User inputs for controlling the operation of the computer system 800 may be received via the user-input device adapters 810 from the user-input devices 812. It will be apparent that some features of computer system 800 shown in Figure 8 may be absent in certain cases. For example, one or more of the plurality of computer apparatuses 800 may have no need for display adapter 806 or display device 808. This may be the case, for example, for particular server-side computer apparatuses which are used only for their processing capabilities and do not need to display information to users. Similarly, user input device adapter 810 and user input device 812 may not be required. In its simplest form, computer apparatus 800 comprises processor 802 and memory 804. Figure 9 shows a cross-sectional view of a magnetically geared system 900 according to a further example of the present disclosure, which differs from the system 100 of Figure 1A but is interchangeably useable in place of the system 100 of Figure 1 A. In particular, the system 900 of Figure 9 also includes a controller (not shown) configured to implement a method according to Figure 7. Figure 8 schematically illustrates the components of such a controller. The magnetically geared system 900 is operable as a motor. However, whereas the system 100 of Figure 1A is arranged such that the stator, first rotor, and second rotors are concentric, the second rotor 906 in the system 900 is axially offset from the stator 902. Accordingly, the system 900 is split into a motor drive portion 900A at a first axial end thereof and a magnetic gear portion 900B at a second axial end thereof. The first portion 900A is rotationally coupled to the second portion 900B by an elongated first rotor 904. A first end of the first rotor 904 (the end located in the motor drive portion 900A) is coupled to a second end of the firs rotor 904 (the end located in the magnetic gear portion 900B) by a mediating shaft 901. The system 900 may be for used as a servo motor for a robotic arm or an aircraft control surface, or as a drive motor for a locomotive. However, as the skilled reader will understand, the motor is not limited to these specific applications. The magnetically geared system 900 includes an outer stator 902, a first rotor 904, and a second rotor 906. The first rotor 904 is positioned radially inside of the stator 902, and radially inside of the first rotor 906. The stator 902 comprises a plurality of circumferentially arranged conductive windings 908. A first plurality of permanent magnets 920 are provided around the second rotor 906. The first rotor 904 comprises a second plurality of circumferentially arranged permanent magnets 910, and the second rotor 906 comprises plurality of circumferentially arranged unmagnetised magnetisable (typically ferromagnetic, e.g. steel) pole pieces 912. The second rotor 906 is connected to an external load (for example, the wheels of a vehicle, a propellor of a boat, etc.). The first rotor 904 is passive, in that it is not connected to a load. The first plurality of permanent magnets 920 produce a first magnetic field, and the second plurality of permanent magnets 910 produce a second magnetic field. The pole pieces 912 modulate the interaction between the first and second magnetic fields, coupling the magnetic fields to produce a geared interaction between the first rotor 904 and the second rotor 906. Additionally, when the windings 908 of the stator are supplied with a three-phase, 120 degree displaced current, a rotating magnetic field is set up in the system 900. This rotating magnetic field may have the same number of pole pairs as the first magnetic field generated by the first permanent magnets 910. Accordingly, the rotating magnetic field applies an electromagnetic torque to the first rotor, thereby driving rotation of the first rotor 904. Furthermore, because of the magnetic coupling as described above, this in turn will drive rotation of the second rotor 906, at a geared lower speed than the first rotor 904. The drive shaft 918 is attached to the second rotor 906. Accordingly, the rotating magnetic field drives rotation of the drive shaft 918 at the geared, lower speed. Bearings B1 enable the first rotor 904 to rotate relative to the drive shaft 918. Similarly, bearings B2 enable the drive shaft 918 and the second rotor 906 to rotate relative to the stator 902. The described arrangements and methods are merely exemplary, and it will be appreciated by a person skilled in the art that various modifications can be made without departing from the scope of the appended claims. More generally, it should be appreciated that the number of steps shown in the figures is not intended to be limiting. Steps may be repeated as often as necessary and certain steps may be omitted. The computer apparatus discussed above may be a local computer or a server. While various specific combinations of components and method steps have been described, these are merely examples. Components and method steps may be combined in any suitable arrangement or combination. Components and method steps may also be omitted to leave any suitable combination of components or method steps. The described methods may be implemented using computer executable instructions. A computer program product or computer readable medium may comprise or store the computer executable instructions. The computer program product or computer readable medium may comprise a hard disk drive, a flash memory, a read-only memory (ROM), a CD, a DVD, a cache, a random-access memory (RAM) and / or any other storage media in which information is stored for any duration (e.g., for extended time periods, permanently, brief instances, for temporarily buffering, and / or for caching of the information). A computer program may comprise the computer executable instructions. The computer readable medium may be a tangible or non-transitory computer readable medium. The term “computer readable” encompasses “machine readable”. In an implementation, the modules, components and other features described herein can be implemented as discrete components or integrated in the functionality of hardware components such as ASICS, FPGAs, DSPs or similar devices. The singular terms “a” and “an” should not be taken to mean “one and only one”. Rather, they should be taken to mean “at least one” or “one or more” unless stated otherwise. The word “comprising” and its derivatives including “comprises” and “comprise” include each of the stated features, but does not exclude the inclusion of one or more further features.

Claims

1. A method of operating a magnetically coupled system, the magnetically coupled system comprising:a stator comprising a plurality of windings arranged to generate a rotating magnetic field;a first rotor comprising a plurality of permanent magnets having an associated second magnetic field;a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor;at least one sensor arranged to detect a rotational state of the system; anda controller configured to monitor the magnetically geared system;the method comprising:calculating, based on the detected rotational state of the system, an actual torque on the system;determining, based on at least one operating parameter of the system, an expected torque on the system;determining that the system is under normal operating conditions when a residual between the actual torque and the expected torque is below a first predetermined threshold.

2. A method according to claim 1, further comprising:determining that the system is under a first fault condition when the residual is above the first threshold and has a first characteristic; anddetermining that the system is under a second fault condition when the residual is above the first threshold and has a second characteristic which is different from the first characteristic.

3. A method according to claim 1 or claim 2, further comprising, based on the detected rotational state of the system, calculating a load angle of the system;wherein the actual torque on the system is calculated based on the calculated load angle.

4. A method according to claim 3, wherein the at least one sensor comprises a first rotational sensor arranged to detect a rotational position of the first rotor relative to the stator, and a second rotational sensor arranged to detect a rotational position of the second rotor relative to the stator.

5. A method of operating a magnetically coupled system, the magnetically coupled system comprising:a stator comprising a plurality of windings arranged to generate a rotating magnetic field;a first rotor comprising a plurality of permanent magnets having an associated second magnetic field;a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor;a torque transducer; anda controller configured to monitor the magnetically geared system;the method comprising:determining, based on an output from the torque sensor, an actual torque on the system;determining, based on at least one operating parameter of the system, an expected torque on the system;determining that the system is under normal operating conditions when a residual between the actual torque and the expected torque is below a first predetermined threshold.

6. A method according to claim 5, further comprising: determining that the system is under a first fault condition when the residual is above the first threshold and has a first predetermined characteristic; anddetermining that the system is under a second fault condition when the residual is above the first threshold and has a second predetermined characteristic that is different from the first characteristic.

7. A method according any preceding claim, wherein the expected torque on the system is calculated based on the operating parameter and on a predetermined model which relates the operating parameter to expected torque.

8. A method according to claim 2 or claim 6, wherein the first characteristic comprises the residual being between the first threshold and a second threshold; and the second characteristic comprises the residual being greater than the second threshold.

9. A method according to claim 2 or claim 6, wherein the method comprises calculating a residual between the actual torque and the expected torque; wherein the system is determined to be under normal operating conditions when the residual is below the first threshold; wherein the system is determined to be under the first fault condition when the residual has a first predetermined shape; and wherein the system to be under the second fault condition when the residual has a second predetermined shape which is different from the first predetermined shape.

10. A method according to claim 2, 6, 8 or 9, wherein the first fault condition is indicative of accumulated system degradation.

11. A method according to claim 2, 6, 8, 9 or 10, wherein the second fault condition is indicative of an instantaneous fault.

12. A method according to claim 2 or claim 6, further comprising:when the first fault condition is present, issuing a first command; and when a second fault condition is present, issuing a second command;wherein the first command is for a first corrective or abortive measure to be implemented; and wherein the second command is for a second corrective measure that is different from the first corrective measure to be implemented.

13. A method according to any preceding claim, wherein the calculation of the actual and expected torques on the system is performed when the system is in a zero speed state; or wherein the calculation of the actual and expected torques on the system is performed when the system is in a constant velocity state; or whereinthe calculation of the actual and expected torques on the system is performed when the system is in an acceleration or deceleration condition.

14. A method according to claim 13, wherein the calculation of the actual and expected torques on the system is performed once the current supplied into the coils has been in the zero speed state for at least a predetermined period of time.

15. A method according to any preceding claim, wherein a plurality of actual and expected torque measurements are taken in order to accumulate a statistical distribution of residuals.

16. A method according to claim 15, wherein the method further comprises calculating a statistical determinant from the statistical distribution of residuals.

17. A method according to any preceding claim, wherein the second rotor comprises a plurality of pole pieces.

18. A method according to any preceding claim, wherein the stator further comprises a plurality of permanent magnets having an associated first magnetic field.

19. A method according to any preceding claim, wherein the system further comprises an output shaft coupled to the second rotor.

20. A system comprising:a stator comprising a plurality of windings arranged to generate a rotating magnetic field;a first rotor comprising a plurality of permanent magnets having an associated second magnetic field;a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor;at least one sensor arranged to detect a rotational state of the system; and a controller configured to monitor the magnetically geared system;wherein the controller is further configured to implement a method according to any preceding claim, when dependent upon claim 1.

21. A system comprising:a stator comprising a plurality of windings arranged to generate a rotating magnetic field;a first rotor comprising a plurality of permanent magnets having an associated second magnetic field;a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor;a torque transducer; anda controller configured to monitor the magnetically geared system;wherein the controller is further configured to implement a method according to any preceding claim, when dependent upon claim 5.

22. A computer-readable medium having instructions stored thereon which, when executed by a processor, cause the processor to implement a method according to any of claims 1 to 19.

23. A method of operating a magnetically coupled system, the magnetically coupled system comprising:a stator comprising a plurality of windings arranged to generate a rotating magnetic field;a first rotor comprising a plurality of permanent magnets having an associated second magnetic field;a second rotor through which the rotating magnetic field and the second magnetic field are coupled, whereby rotation of the first rotor is magnetically coupled to rotation of the second rotor;at least one sensor arranged to detect a rotational state of the system; anda controller configured to monitor the magnetically geared system;the method comprising:calculating, based on the detected rotational state of the system, a first torque on the system;calculating, based on a magnitude of the current supplied to the windings, a second torque on the system;determining that the system is under normal operating conditions when a residual between the first torque and the second torque is below a predetermined threshold.

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