Experimental and theoretical study of the electrical failures in a fault-tolerant ... fidelity model of the servovalve of a modern fly-by-wire actuator is developed and ...
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Experimental and theoretical study of the electrical failures in a fault-tolerant direct-drive servovalve for primary flight actuators G Di Rito and R Galatolo Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2008 222: 757 DOI: 10.1243/09596518JSCE588 The online version of this article can be found at: http://pii.sagepub.com/content/222/8/757
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Experimental and theoretical study of the electrical failures in a fault-tolerant direct-drive servovalve for primary flight actuators G Di Rito* and R Galatolo Department of Aerospace Engineering, University of Pisa, Pisa, Italy The manuscript was received on 4 March 2008 and was accepted after revision for publication on 8 April 2008. DOI: 10.1243/09596518JSCE588
Abstract: The current paper deals with the study of the electrical failures in fault-tolerant flight actuators, with particular reference to the short circuits of the servovalve coils. A highfidelity model of the servovalve of a modern fly-by-wire actuator is developed and validated through experiments, focusing attention on the characterization of the component dynamics in case of partial and total short circuits of the direct-drive motor coils. The servovalve model is then used to simulate a typical on-ground built-in-test procedure to determine the limit condition for the detection of a partial short circuit. Finally, once different possible combinations of short circuits are injected, the degradation of performances of the whole actuator is characterized through experiments, and the servovalve model is used to justify the test results, highlighting and discussing the effects of the failures on the system dynamics. Keywords: flight control, fault-tolerant actuators, direct-drive servovalve, failure analysis, testing, modelling and simulation
1
INTRODUCTION
Full-authority fly-by-wire flight control systems are nowadays a standard technology solution for advanced military aircraft and for civil transport airliners. To provide the adequate level of safety, the primary flight actuators are designed to be faulttolerant components, so that they must be able appropriately to operate in the event of one or more failures. The capability of the system to tolerate the actuator failures also depends on the flight control computers, which must be able to detect the malfunctions by means of both on-ground and inflight built-in tests [1]. However, as a result of inadequate or impracticable monitoring procedures, a flight actuator can operate with dormant failures, implying an unexpected degradation of the performance and the safety of the aircraft. *Corresponding author: Department of Aerospace Engineering, University of Pisa, via Caruso, Pisa, Italy. email: g.dirito@ing. unipi.it JSCE588 F IMechE 2008
When hydraulic flight actuators with direct-drive servovalve [2, 3] are concerned, dormant failures can be caused by the short circuits in the servovalve coils. Actually, as these faults can involve only a part of the windings, the on-ground built-in-tests cannot detect the malfunction, causing the aircraft to take off with a damaged actuator. The problem is that a partial short circuit could extend to the rest of the coil during the flight, implying a significant degradation of the actuator performances. Although many authors have focused their attention on the study, the modelling, and the dynamic characterization of electrical motors in faulty conditions [4–6], scarce information is available about the modelling and the failure analysis of direct-drive electrical motors for aerospace servovalves. In the current paper, a high-fidelity model of the direct-drive servovalve of a modern fly-by-wire actuator is developed and validated through experiments, focusing attention on the characterization of the component dynamics in short circuits of the motor coils. Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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SYSTEM DESCRIPTION Architecture of the fault-tolerant flight actuator
As shown in Fig. 1, the reference actuator has a tandem cylinder and quadruple electronics, so that the system is capable of tolerating one hydraulic failure and up to two electrical failures. Concerning the direct-drive servovalve, its internal architecture is schematically reported in Fig. 2, where it can be noted that the valve spool movement is obtained by a permanent magnet electric motor with four coils operating in a flux-summed configuration. When no current circulates in the motor coils, the armature (rigidly linked to the valve spool) is centred with respect to its endstrokes, as in this condition the centring spring is unloaded and the magnetic fluxes induced by the permanent magnets provide equal and opposite forces. When the currents are not zero, the magnetic flux induced by the coils causes an unbalanced armature polarization; a magnetic force is therefore generated, and the resulting spool movement allows the actuator to control the hydraulic power.
Fig. 2 Quadruple direct-drive motor for aerospace servovalves
2.2
Electrical failure modes of the direct-drive electrical motor
Five basic operational states can be defined for each of the four motor coils:
Fig. 1 Primary fly-by-wire actuator with tandem cylinder Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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Electrical failures in a fault-tolerant direct-drive servovalve
(a) the normal condition, in which the coil voltage is controlled by the electronic drive, composed of a servo-amplifier performing a closed-loop current control, Fig. 3(a); (b) the partial short circuit, in which the short circuit extends to a limited number of windings, while the rest of the coil is still connected with the electronic drive, Fig. 3(b); (c) the total short circuit, in which a fault results in a direct electrical connection between the coil pins, Fig. 3(c); (d) the hardover, in which the current feedback is failed and the servo-amplifier fixes the coil voltage to its maximum value; (e) the open circuit, in which the coil wire is broken and the current circulation is inhibited. The failure analysis proposed in this paper has been focused on the short circuits, since (as discussed in section 4) they can imply significant fault detection problems as well as a severe degradation of the actuator dynamic behaviour.
3
MODEL OF THE FAULT-TOLERANT DIRECTDRIVE SERVOVALVE
Before discussing the simulation details, it must be outlined that the model of the fault-tolerant directdrive servovalve has been developed as a multistate machine, which is able to simulate the component dynamics in different working conditions (normal; with one or more total short circuits; with one or more partial short circuits). However, for the sake of simplicity, the model will be described with reference to an operating condition in which a partial short circuit is applied to one of the four coils, while the
Fig. 4
759
Scheme of the magnetic flux paths in the directdrive motor in a partial short circuit failure
other three coils are active. This condition allows the basic simulation problems to be highlighted, and the resulting model can be easily adapted when additional (partial or total) short circuits are considered. The model is composed of three sections: one for the calculation of the magnetic fluxes, another for the simulation of the current dynamics, and one for the simulation of the valve spool dynamics.
3.1
Magnetic fluxes in the direct-drive motor
The simulation of the magnetic fluxes has been obtained by means of the magnetic circuit theory [7], using (in the case of one partial short circuit) the magnetic flux scheme reported in Fig. 4. The resulting magnetic circuit (Fig. 5) contains five coils, as the partial short circuit has been simulated by dividing the failed
Fig. 3 Motor coil working condition: (a) normal, (b) partial short circuit, (c) total short circuit JSCE588 F IMechE 2008
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Fig. 5 Equivalent magnetic circuit of the direct-drive motor in a partial short circuit failure
coil into two sections: one (involving Nsc windings) and by the reluctances of the axial gaps (Ral and Rar), totally shorted, and the other ‘normally’ controlled by which depend on the armature position (xs). the servo-amplifier, thus reproducing the failure mode The magnetic field of the motor is thus composed of scheme reported in Fig. 3(c). ten fluxes: a flux that links all the coils and the axial air Each magnet is assumed to be a rare-earth magnet gaps of the armature (Qcn), two fluxes linking the working in the linear range, is modelled as a permanent magnets and the axial air gaps of the magnetomotive force (Wm) in series with a reluctance armature (Qml and Qmr), and seven flux leakages, (Rim) that represents the demagnetization characterrepresenting the secondary magnetic paths related to the permanent magnets (Qmdl and Qmdr) and the motor istics of the material [8]. Each motor coil is modelled as a magnetomotive force (Njij, where Nj is the coils (Qcd j with j 5 1,…,5). number of coil windings and ij is the coil current in Once the armature position and the coil currents are known, the magnetic fluxes can be obtained by invertthe jth coil) in series with the reluctances of the air ing equations (1) and (2), and the magnetic force (Fm) gaps between one coil and another (Rca for the axial path and Rcr for the radial path). Finally, the air gaps can be calculated by applying the virtual work principle [7], differentiating the magnetic field energy (Em) with between the armature and the case are represented by the reluctance of the armature radial clearance (Rrc) respect to the armature position, equations (3) and (4) 9 8 9 38 Wm > 2 > > > > > > > > Wm > > > > > 7> 6 > > > > 0 < z< z< 0 < < Q > > > 7 6 mi rc mi al al ml > = 6 = < W < 7 m 7 Qmdr ~6 ð1Þ < 0 < z< 0 0 mi mi md 7> 6 > > Wm > > > > 7> 6 > > > > 0 5 > Qmdl > 5> > > P > > > > ; > : > > N j ij > ; : { > >
> > > > > =
Ni1
2
> 6 > > 0 ðN {Nsc Þi4 > > > 4 > > > ; : Nsc i5 0 Ni2 Ni3
{ = < 7 7 Qcd3 0 7> > > 7> { Qcd4 > > > > > > > ; : : Rc ðhz1Þ ~Rc NNsc
Em ~ 12 Wm ðQmr zQml zQmdr zQmdl Þ #
761
V j~1, . . . ,5
ð2Þ
ðj=h; j=hz1Þ
ð3Þ
ð7Þ
j~1
Fm ~
3.3
L Em ~f0 ðxs ÞW2m zf1 ðxs ÞWm L xs |
5 X
Nj ij zf2 ðxs Þ
j~1
5 X
!2 N j ij
ð4Þ
Dynamics of the currents
If a partial short circuit is applied to the hth motor coil, the dynamics of the currents is regulated by equations (5) and (6). In particular, equation (5) refers to all the active coils and to the section of the failed coil that is still controlled by the servoamplifier, while equation (6) refers to the shorted section of the failed coil. The resistances of the coils are finally calculated taking into account the number of their windings, equation (7) R c j ij z
5 X
Ljk
k~1
dik zKb x_ s ~Ksa Rs icom j {ij dt
Rc ðhz1Þ ihz1 z
5 X
Lðhz1Þ k
k~1
JSCE588 F IMechE 2008
dik zKb x_ s ~0 dt
ms x€s zCs x_ s zKs xs ~Fm zFf zFfr
ð6Þ
ð8Þ
where ms is the spool mass, Ks is the centring spring stiffness, and Cs includes all the linear damping effects (the viscous friction and the internal damping of the centring spring), while Ff and Ffr respectively represent the flow force and the sliding friction force. Concerning the flow force, it must be outlined that the validation of the servovalve model (section 3.4) has been obtained without flow regulation, so the flow force has not been taken into account in the servovalve model. Regarding the sliding friction, an accurate modelling is necessary to obtain significant results from the simulation of the flight control system built-intests (section 4.1), since they are based on the verification of the valve current-to-displacement static response, which is heavily influenced by the friction effects. Thus, the single-state elastoplastic friction model [10] given by equations (9) to (11) has been used ð9Þ
Ffr ~{Kfr z
z_ ~x_ s {ajx_ s j ð5Þ
ðj=hz1Þ
V j~1, . . . ,5
Assuming that the centring spring is unloaded when the spool is centred (i.e. xs 5 0), the spool displacement dynamics is generally described by equation (8)
j~1
As pointed out by equation (4), the magnetic force can be expressed as a sum of three basic terms. The first one is exclusively attributable to the permanent magnets; it depends on the armature position, and its effect can be viewed as a diminution of the centring spring stiffness. The second term is the most important force contribution; it is linear with the coil currents, and it is produced by the interaction between the magnetic fluxes induced by the currents and the ones induced by the permanent magnets. The third term is exclusively attributable to the coils, but it tends to be important only when high currents are considered [9].
3.2
Valve spool dynamics
z zsl
8 0 > > > < pðjzj{zst Þ a~ sin2 > 2ðzsl {zst Þ > > : 1
ð10Þ
jzj¡zst zst vjzjvzsl
ð11Þ
jzj¢zsl
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where z is the local deformation of the spool contact area, Kfr is the contact stiffness, a is the stick-slip factor, zsl is the local deformation during the slipping motion (assumed to be constant), and zst is the maximum local deformation during the sticking motion (assumed to be zsl/2).
3.4
Experimental validation
The basic problem in the study of the short circuit failure is attributable to the fact that the fault can involve a limited part of the coil, and it is very complex experimentally to reproduce this condition. This leads to the necessity of modelling and simulation for estimating the effects of the failure on the actuator dynamics, but it also implies some kind of uncertainty about the verification of the simulation results. On the other hand, the experimental study of the total short circuits is rather simple to realize, as the faults can be reproduced without performing invasive tests on the component. This aspect was important for the research because parallel experimental activities were carried out on the flight actuator, and others were planned for the future. For these reasons, the validation of the model has been obtained only with reference to the total short circuits, by testing an actual aircraft servovalve with an electronic control unit specifically designed for the artificial injection of the failures [11]. Figure 6 reports the working scheme of one of the four electronic circuitries used for testing the faulttolerant servovalve. Three discrete switches have been inserted: the closing of the switch A results in injecting a total short circuit, while the closing of the switches B and C results in engaging the servoamplifier with the coil.
Fig. 6
Both the static and the dynamic performances of the servovalve have been characterized, by testing the component at different working conditions and without flow regulation. Figure 7 shows the comparison between the current-to-displacement curves obtained using the hardware and the model at different working conditions. Each curve refers to a test in which a sinusoidal low-frequency command signal (¡imax at 0.02Hz) is provided to the direct-drive motor, while the spool displacement and the coil current are measured. It can be noted that the simulation results satisfactorily match the experimental data, both in normal condition and in the case of short circuits. The model is able to reproduce the hysteresis amplitude, which basically depends on the effects of the sliding friction, as well as the overall shape of the current-todisplacement curve, which is essentially attributable to the non-linear relation between the magnetic force and the armature position, equation (4). Figure 8 shows the comparison between the hardware and the model frequency responses of the servovalve with reference to the normal condition and in case of total short circuit failures. The results are obtained by commanding the servovalve with 20 per cent of the maximum current and by defining the output signal as a percentage of the spool full stroke. The model generally matches the experimental data, even if the phase errors tend to increase in the high-frequency range if the failed conditions are concerned. The short circuits lower the steady-state asymptote of the frequency response (coherently with the results shown in Fig. 7) and they also reduce the servovalve bandwidth, which passes from about 5 Hz to about 2.5 Hz when two short circuits occur. The phenomenon depends on the fact that the current generated in the shorted coils is opposite to the ones circulating in the active coils, so that the short circuits act as brakes in the spool dynamics.
Scheme of the servovalve electronic control unit: (a) active coil and (b) shorted coil
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Electrical failures in a fault-tolerant direct-drive servovalve
Fig. 7
Model validation: servovalve current-to-displacement curves at different working conditions
The proposed model provided satisfactory results, but further studies have been planned with the purpose of obtaining a complete validation of the modelling schemes in terms of reliability and the robustness of results (e.g. Monte-Carlo statistical analysis). 3.5
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Numerical characteristics of the model
The servovalve model has been entirely developed in the Matlab-Simulink environment, using the Stateflow charts for the reconfiguration of the model due JSCE588 F IMechE 2008
to failure events. The numerical solution demonstrated to be stable and accurate using the Runge– Kutta method (ODE 4) with an integration step of 18.5 ms. The need of this very small integration step results from the simulation of event-driven dynamics such as the valve sliding friction (section 3.3) and the current dynamics in case of failures. In particular, it must be outlined that, once defined these simulation parameters, it is not possible to simulate the servovalve dynamics introducing partial short circuits with too-small or too-large extensions. This limit depends on the fact that, for both cases, Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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Fig. 8
Model validation: servovalve open-loop frequency responses at different working conditions
the magnetic inductance of one coil would be too small, inducing too-fast current responses and, as a consequence, numerical instability. In the perspective of using the servovalve model for real-time/hardware-in-the-loop applications, a real-time executable code has been obtained by means of the xPC Target tools, and the model results to be suitable for the real-time execution on a common off-the-shelf PC (AMD Athlon 2.1 GHz), even if one PC must be completely dedicated to the servovalve simulation.
4
4.1
FAULT DETECTION PROBLEMS AND ACTUATOR PERFORMANCE DEGRADATION Simulation of the direct-drive servovalve onground built-in-test
In a fly-by-wire aircraft, the correct operational state of each critical subsystem, such as a primary flight actuator, must be assessed by the flight control computers before and during the mission, through check procedures known as built-in-tests. In particular, the basic objective of an on-ground built-intest is the detection of dormant failures, which (depending on the failure type as well as on the system availability requirement) can even lead to
aborted mission. On the other hand, the in-flight built-in-tests aim to detect, isolate, and possibly compensate the failures, to maintain the appropriate levels of safety and performance [1]. The direct-drive servovalve of a primary flight actuator is a critical component of a flight control system, as the aircraft controllability directly depends on the performances of its flight controls, which are strongly influenced by the servovalve dynamics. For this reason, specific on-ground built-in-tests are carried out on the direct-drive servovalve, with the purpose of detecting electrical malfunctions, mechanical seizures, as well as the overall valve performance (e.g. by testing the capability of driving the spool all along its stroke with the minimum tolerable number of active coils). Concerning the electrical failures (section 2.2), the identification of both the hardover and the open circuit is quite reliable and simple to implement, since a comparison between the demand current and the actual one (two signals that are always available in the control electronics) is sufficient. On the other hand, a direct and reliable detection of a short circuit could be obtained only by measuring the current and the pin-to-pin voltage of a coil; however, the latter signal is usually not available in the common implementations [12].
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An alternative approach could be based on the evaluation of the servovalve current-to-displacement response related to the single coils (Fig. 7(b)), but this procedure could imply the possibility of having dormant failures owing to partial faults. This problem has been pointed out by means of the validated model of the servovalve, simulating an onground built-in-test composed of the following steps. Step 1: all the coil currents are set to zero; after that, a test current (iBIT) is sent to the coil 1 and a static measurement of the spool position (xs1 BIT) is recorded; Step(s) 2 (3 and 4): step 1 is repeated commanding the coil 2 (3 and 4); Step 5: if the jth spool position measurement (where j 5 1,…,4) is outside a fixed threshold (i.e. |xs j BIT 2 xs nom| . Dxth), a malfunction is detected in the jth coil; otherwise the servovalve passes the check. The failure coverage provided by this test clearly depends on the position threshold (Dxth): in particular, the larger is the threshold, the bigger is the undetected partial short circuit. Nevertheless, toosmall thresholds cannot be used, because the current-to-displacement response of a direct-drive motor depends on the temperature (the air gaps vary with the thermal dilatation and the magnet properties are temperature dependent [8]), and the component temperature during the built-in-test is not predictable. For example, once assumed iBIT 5 imax (xs nom < 0.4xs max, Fig. 7(b)) and Dxth 5 0.1xs max, Figs 9 and 10 report the results of built-in-test simulations performed with no failures and with increasing extensions of a partial short circuit (involving 20 and 50
Fig. 10
per cent of the total windings). Figure 9 shows the spool displacement responses; it can be noted that, if the fault involves 20 per cent of the coil, the test is not able to detect the malfunction and a dormant failure will result. It can be observed that this fault is not severe and the performance degradation would not be significant, but a small short circuit can rapidly extend. Actually, Fig. 10 shows that the current dynamics in the shorted section of the failed coil is characterized by a transient that is as stronger as the partial short circuit is smaller. Considering that, when the motor works with all the coils, the transients in shorted windings are much higher (the peak value can reach up to 3–4 times the maximum current), a rapid fault extension is expected after a short period of operation. For this reason, the performance degradation of the flight actuator has been characterized with reference to a completely extended failure (a total short circuit) and, as the worst case condition for the two-fail-operative servovalve, to the case of two total short circuits.
4.2
Fig. 9
Simulation of the servovalve built-in-test with a partial short circuit: spool displacement
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Simulation of the servovalve built-in-test with a partial short circuit: current in the shorted coil
Characterization of the actuator performance degradation
The degradation of the flight actuator performances owing to the short circuit failures has been characterized through experiments. As shown by Fig. 11, the flight actuator closedloop control is composed of two position feedbacks, one acting on the servovalve spool (for enhancing the component bandwidth) and the other on the actuator rod. To obtain a basic characterization of the system dynamics, simple proportional controls have been used for both the loops. Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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Fig. 11 Closed-loop control scheme of the flight actuator
Figure 12 reports the closed-loop frequency responses of the flight actuator in different operative conditions. The experiments – performed with a command amplitude of about 1 per cent of the actuator full stroke – highlight that in the normal condition the actuator response is well damped and exhibits a bandwidth (defined at 245u phase delay) of about 5 Hz. If one short circuit is injected, the variation of the actuator dynamics is negligible in the low-frequency range (, 5 Hz), but it tends to be more important at medium–high frequencies (. 10 Hz), as the phase delay and the amplitude attenuation are notably increased. If the actuator
works with two short circuits, the performance degradation becomes significant, as the damping becomes worse, the bandwidth lowers up to 3 Hz and the phase delay is strongly increased (e.g. at 10 Hz, the two failures add about 40u phase delay to the normal actuator response). These phenomena can be justified and discussed with reference to Fig. 13, where the closed-loop frequency responses of the real-aircraft servovalve are compared with those provided by the model. The results, which generally provide a further validation of the model, show the effects of the short circuit failures on the closed-loop dynamics of the servovalve. In particular,
Fig. 12 Degradation of the actuator frequency response owing to short circuit failures Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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Fig. 13
Degradation of the servovalve closed-loop frequency response owing to short circuit failures
the steady-state asymptote of the amplitude response lowers of about 2 dB if two short circuits are injected, which means that, in these conditions, the actuator open-loop gain is reduced of about 20 per cent and, as a consequence, the closed-loop bandwidth lowers. Moreover, Fig. 13 points out that the servovalve bandwidth (30 Hz in the normal condition) lowers up to 10 Hz if two short circuits occur, so that the valve dynamics strictly couples with that of the rod, and additional phase delay results. Finally, it must be mentioned that the frequency responses reported in Fig. 13 have been performed on the isolated servovalve with a command amplitude of 10 per cent of the maximum valve opening, but, in the whole actuator dynamics, the valve commands rapidly tend to saturate if the servovalve response is not fast enough; so additional servovalve phase delay must be taken into account when the actuator works in the failoperative conditions. 4.3
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Failure compensation
The characterization of the actuator performances discussed in section 4.2 has been obtained assuming that no control reconfiguration is applied after the failures. On the other hand, once the effects of the JSCE588 F IMechE 2008
short circuits on the servovalve dynamics are known, compensation techniques similar to the one proposed by the authors in reference [13] or others can be used, significantly reducing the actuator sensitivity to the failures. However, no compensation can be applied if the failure is not detected, and this problem is relevant to the case of short circuits. Actually, during the in-flight built-in-tests, the electrical health state of a servovalve is typically judged [12] by comparing the current signal fed back by the servo-amplifier with a reference value provided by a servo-amplifier model (in-line monitoring) or obtained by a comparison with the signals coming from the other lines (crossline monitoring). Unfortunately, these techniques are not effective for detecting the short circuits. As shown in Fig. 3, the servo-amplifier connected to the failed coil feeds back a current as well as the one connected to the active coil, and, as the commands are the same, the current sensed in the failed line is almost identical to the ones related to the active lines. For these reasons, both the inline and the crossline monitoring are not able to detect the short circuits, and no compensation can be applied. A possible solution can be obtained by an inline monitoring based on an accurate and real-time Proc. IMechE Vol. 222 Part I: J. Systems and Control Engineering
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executable model of the direct-drive servovalve, which should be able to provide a precise correlation between the current commands and the spool position, allowing identification of the number (even if not the location) of short circuits, and to implement the system compensation.
5
CONCLUSION
The dynamics of a fault-tolerant direct-drive servovalve for primary fly-by-wire actuators has been studied – developing and validating through experiments a highfidelity model that is able to simulate the component behaviour in partial and total short circuits to the directdrive motor coils. The model has then been used for simulating a typical on-ground built-in-test procedure, obtaining a servovalve dormant failure related to a short circuit involving the 20 per cent of the windings of a coil. Simulation results also highlighted that the current circulating in the shorted section of a coil can reach values of about 3–4 times the maximum allowable current, thus implying a rapid fault extension after a short period of operation. For this reason, the experimental characterization of the flight actuator performance has been obtained in the case of one and (as the worst case condition) two total short circuits. Experiments highlighted that the short circuits almost halve the actuator bandwidth and also cause a reduction of the response damping. The phenomena have been correlated with the effects of the failures on the isolated servovalve dynamics that reduce both the actuator open-loop gain and the servovalve bandwidth. Finally, the problems related to the in-flight detection and compensation of the short circuits with the traditional monitoring techniques have been discussed, pointing out the potential effectiveness of an inline monitoring based on an accurate and real-time executable model of the direct-drive servovalve dynamics.
4 Trutt, F. C., Santa Cruz, C., Kohler, J. L., and Sottile, J. Prediction of electrical behavior in deteriorating induction motors. IEEE Trans. Ind. Applic., 1993, 29, 1239–1243. 5 Chen, H. and Zhang, C. Analysis of electrical faults for switched reluctance motor driver. In Proceedings of the 3rd World Congress on Intelligent control and automation, 2000, Vol. 1, 666–669. 6 Juricic, J., Moseler, O., and Rakar, A. Model-based condition monitoring of an actuator system driven by a brushless DC motor. Control Engng Practice, 2001, 9, 545–554. 7 Fitzgerald, A. E., Kingsley, C. Jr, and Kusko, A. Electric machinery: the processes devices and systems of electromechanical energy conversion, 3rd edition, 1971 (McGraw-Hill, New York). 8 Campbell, P. The design and application of high energy rare earth permanent magnets. Proceedings of the Electrical Electronics Insulation Conference, 1995, pp. 49–57. 9 Di Rito, G. Experimental validation of theoretical and numerical models of a DDV linear force motor. Proceedings of the 3rd FPNI-PhD Symposium, 2004, pp. 105–114. 10 Dupont, P., Hayward, V., Armstrong, B., and Altpeter, F. Single state elastoplastic friction models. IEEE Trans. Autom. Control, 2002, 47(5), 787–792. 11 Denti, E., Di Rito, G., and Galatolo, R. Real-time hardware-in-the-loop simulation of fly-by-wire flight control systems. 25th International Congress of the Aeronautical Sciences (ICAS), 2006. 12 Bonnice, W. F. and Baker, W. Intelligent fault diagnosis and failure management of flight control actuation systems, NASA Contractor Report 177481, 1988. 13 Di Rito, G. and Galatolo, R. Modelling the dynamics of a direct-drive servovalve for failoperative primary flight control actuators. Proceedings of the 3rd International Conference on Recent advances in aerospace actuation systems and components, 2004, pp. 67–72.
APPENDIX Notation
REFERENCES 1 Pratt, R. W. Flight control systems: practical issues in design and implementation, 2000 (Institution of Engineering and Technology, Stevenage). 2 Miller, F. G. Direct drive control valves and their applications. Proceedings of the IMechE International Conference on Aerospace hydraulics and systems, September 1993, pp. 1–16. 3 Steed, D. J. Direct drive actuation for primary flight control. Proceedings of the IMechE International Conference on Aerospace hydraulics and systems, September 1993, pp. 17–22.
Cs Em Ff Ffr Fm icom j ij j Kb Kfr
spool damping (kg/s) field magnetic co-energy (J) flow force (N) sliding friction force (N) magnetic force (N) current command to the jth coil (A) current circulating in the jth coil (A) index related to the direct-drive servovalve coil back-electromotive force (V s/m) contact stiffness (kg/s2)
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JSCE588 F IMechE 2008
Electrical failures in a fault-tolerant direct-drive servovalve
Ks Ksa Ljk
ms N Nsc Rc j Rs xs z zsl zst
a Qcdj Qcn Qmdl
centring spring stiffness (kg/s2) servo-amplifier gain magnetic inductance of the jth coil related to the current circulation in the kth coil (H) spool mass (kg) total number of coil windings number of shorted coil windings resistance of the jth coil (Ohm) sense resistance (Ohm) spool displacement (m) local deformation of the contact area (m) local deformation during the slipping motion (m) maximum local deformation during the sticking motion (m) stick-slip factor dispersed magnetic flux linked to the jth coil (Wb) net magnetic flux linked to armature and coils (Wb) dispersed magnetic flux linked to the left permanent magnet (Wb)
JSCE588 F IMechE 2008
Qmdr Qml Qmr Wm Ral Rar Rca Rcr
Rmd
Rmi Rrc
769
dispersed magnetic flux linked to the right permanent magnet (Wb) magnetic flux linked to the left permanent magnet (Wb) magnetic flux linked to the right permanent magnet (Wb) magnetomotive force of the permanent magnet (A) magnetic reluctance of the armature axial gap (left side) (A/Wb) magnetic reluctance of the armature axial gap (right side) (A/Wb) magnetic reluctance of the axial dispersion path of a coil (A/Wb) magnetic reluctance of the radial dispersion path of a coil (A/Wb) magnetic reluctance of the dispersion path of the permanent magnet (A/Wb) internal magnetic reluctance of the permanent magnet (A/Wb) magnetic reluctance of the armature radial clearance (A/Wb)
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