pith. sign in

arxiv: 1907.06751 · v3 · pith:344OGCMKnew · submitted 2019-07-15 · 📡 eess.SY · cs.SY· math.OC

Development of a General Momentum Exchange Devices Fault Model for Spacecraft Fault-Tolerant Control System Design

Chengfei Yue , Qiang Shen , Xibin Cao , Feng Wang , Cher Hiang Goh , Tong Heng Lee This is my paper

Pith reviewed 2026-05-24 21:11 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.OC
keywords momentum exchange devicesfault modelspacecraft attitude controlreaction wheelscontrol moment gyrosfault-tolerant controlmultiplicative faultscascade structure
0
0 comments X

The pith

A general cascade multiplicative fault model is established for momentum exchange devices in spacecraft.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews potential mechanical faults in the electric motor and variable speed drive components of momentum exchange devices. From this review it constructs a general fault model using a cascade multiplicative structure that can represent multiple fault types. The model supports simulation of six identified working conditions and visualization of device outputs for both reaction wheels and single gimbal control moment gyros. Simulations using the model show control responses under faults and indicate that additive faults degrade accuracy more than multiplicative faults.

Core claim

The authors model momentum exchange devices as a cascade electric motor-variable speed drive system. Potential faults in the mechanical parts are reviewed and summarized, leading to a general fault model in a cascade multiplicative structure. Six types of working conditions are identified and corresponding fault models constructed. Control responses are demonstrated for reaction wheels and single gimbal control moment gyros under the modeled faults, showing that additive faults are more serious than multiplicative faults from the viewpoint of control accuracy. Existing fault-tolerant control strategies are briefly summarized and potential passive and active approaches for gimbal fault are示范.

What carries the argument

Cascade multiplicative structure fault model built from summarized mechanical faults in the EM-VSD system.

If this is right

  • Various fault scenarios can be simulated and their outputs visualized using the general model.
  • Control responses of reaction wheels and single gimbal control moment gyros can be demonstrated under the six modeled conditions.
  • Additive faults are shown to affect control accuracy more severely than multiplicative faults.
  • The model supports brief summary of existing fault-tolerant strategies and demonstration of approaches for gimbal faults.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The multiplicative cascade form may allow easier integration into existing attitude control software for real-time fault accommodation.
  • Extension to include sensor or electrical faults could be tested by adding further multiplicative stages.
  • Hardware validation on a reaction wheel testbed would directly check whether the six conditions match physical failure modes.

Load-bearing premise

That reviewing and summarizing potential faults in the mechanical part of the EM and VSD system provides a sufficiently complete basis for a general multiplicative cascade model that covers all relevant fault behaviors.

What would settle it

Direct comparison of model-generated outputs against recorded fault data from operating momentum exchange devices on spacecraft would show whether the model reproduces observed behaviors.

Figures

Figures reproduced from arXiv: 1907.06751 by Chengfei Yue, Cher Hiang Goh, Feng Wang, Qiang Shen, Tong Heng Lee, Xibin Cao.

Figure 1
Figure 1. Figure 1: Fault model of EM-VSD system Motivated by the aforementioned observations, this paper investigates the potential faults in the EM-VSD system, which are categorized into multiplica￾tive or additive fault through analyzing an EM-VSD model. The momentum exchange devices are considered as being in a cascade mechanical structure, in which an EM-VSD system governs one degree of control freedom and works independ… view at source ↗
Figure 2
Figure 2. Figure 2: BLDC motor 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fault model of electric motor parameter. Then the mathematical fault model can be constructed as: x˙ = Ax + Bu+DTl + fc (t) (7) or x˙ = Ax + Bu+DTl + XXaijxj  ei = (A + ∆A) x + Bu+DTl , (8) where ei is the ith basis vector, and ∆A is the discrepancy of the state-transition matrix caused by parameter faults. Indexes i, j are related to the EM system and can be determined by fault diagnosis. Fault models (… view at source ↗
Figure 5
Figure 5. Figure 5: Unknown 20% Software 6% Mechanical 54% Electrical 20% Failure type Unknown 17% Software error 4% Electronic circuitry 2% Gyro-scope 17% CMG Reaction wheel 4% 6% Momentum wheel 10% XIPS 10% Thruster 14% Oxidiser tank 2% Fuel tank 8% Enviroment 6% Failure impact and component failure for AOCS [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Fault scenarios of RWs 21 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: RW-actuated attitude control result under nominal condition [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: RW-actuated attitude control result under [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: RW-actuated attitude control result under [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: RW-actuated attitude control result under [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: RW-actuated attitude control result under [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Pyramid configuration of the SGCMGs where Eηg = diag[η g 1 , η g 2 , η g 3 , η g 4 ] is the effectiveness matrix of the gimbal loop and Ega = diag[ ˙δo1 , ˙δo2 , ˙δo3 , ˙δo4 ] is the additive bias of the gimbal loop caused by faults. The nominal angular momentum of the rotor is set as 10 Nm and the max￾imum gimbal angular velocity is set as 100 deg/s. The initial gimbal angle is [0, 0, 0, 0]T deg. Conside… view at source ↗
Figure 13
Figure 13. Figure 13: SGCMG-actuated attitude control result under nominal condition [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: SGCMG-actuated attitude control result in the presence of only rotor fault [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: SGCMG-actuated attitude control result in the presence of only gimbal fault [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: SGCMG-actuated attitude control result in the presence of rotor fault and gimbal [PITH_FULL_IMAGE:figures/full_fig_p032_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Potential fault-tolerant control strategies to handle gimbal fault In Fig. 17a, an additive equivalent strategy is adopted and the real gimbal rate ˙δ is expressed by the gimbal rate command ˙δc and a lumped bias f, i.e. ˙δ = ˙δc +f. To estimate the lumped bias, local estimators (LE) can be designed to estimate each component of f with respect to each SGCMG. Then the gimbal 34 [PITH_FULL_IMAGE:figures/fu… view at source ↗
read the original abstract

This paper investigates the mechanism of various faults of momentum exchange devices. These devices are modeled as a cascade electric motor EM - variable speed drive VSD system. Considering the mechanical part of the EM and the VSD system, the potential faults are reviewed and summarized. Thus with a clear understanding of these potential faults, a general fault model in a cascade multiplicative structure is established for momentum exchange devices. Based on this general model, various fault scenarios can be simulated, and the possible output can be appropriately visualized. In this paper, six types of working condition are identified and the corresponding fault models are constructed. Using this fault model, the control responses using reaction wheels and single gimbal control moment gyros under various fault conditions are demonstrated. The simulation results show the severities of the faults and demonstrate that the additive fault is more serious than the multiplicative fault from the viewpoint of control accuracy. Finally, existing fault-tolerant control strategies are brief summarized and potential approaches including both passive and active ones to accommodate gimbal fault of single gimbal control moment gyro is demonstrated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper reviews mechanical faults in the electric motor (EM) and variable speed drive (VSD) components of momentum exchange devices modeled as an EM-VSD cascade. From this review it constructs a general fault model using a cascade multiplicative structure, defines six working conditions with corresponding fault models, simulates the resulting outputs for reaction wheels and single-gimbal control moment gyros, shows that additive faults degrade control accuracy more than multiplicative faults, and briefly surveys existing fault-tolerant control strategies while demonstrating one approach for gimbal faults.

Significance. If the multiplicative cascade form can be shown to exhaustively capture the reviewed faults without unmodeled residuals, the framework would supply a practical simulation tool for visualizing fault effects and testing passive/active FTC designs in spacecraft attitude control. The explicit comparison of additive versus multiplicative severity and the six-condition taxonomy are concrete contributions that could guide controller robustness analysis.

major comments (1)
  1. [Abstract / model-construction section] Abstract and model-construction section: the claim that the cascade multiplicative structure constitutes a 'general' fault model is load-bearing for the central contribution, yet the manuscript provides no explicit mapping showing that every reviewed mechanical fault in the EM-VSD system reduces to multiplicative parameters without residual additive effects, unmodeled electrical dynamics, or structural changes outside the chosen form. The observation that additive faults are more serious than multiplicative ones directly tests whether the multiplicative cascade is exhaustive rather than a modeling convenience.
minor comments (2)
  1. The six working conditions are introduced without a table or explicit enumeration of the corresponding multiplicative parameters; adding such a summary would improve traceability from the fault review to the simulation cases.
  2. Notation for the cascade structure (e.g., how the multiplicative factors combine across EM and VSD stages) should be defined once with a single equation block rather than reintroduced in each simulation subsection.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The major comment raises a valid point about the need for explicit justification of the 'general' claim. We address it point-by-point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / model-construction section] Abstract and model-construction section: the claim that the cascade multiplicative structure constitutes a 'general' fault model is load-bearing for the central contribution, yet the manuscript provides no explicit mapping showing that every reviewed mechanical fault in the EM-VSD system reduces to multiplicative parameters without residual additive effects, unmodeled electrical dynamics, or structural changes outside the chosen form. The observation that additive faults are more serious than multiplicative ones directly tests whether the multiplicative cascade is exhaustive rather than a modeling convenience.

    Authors: We agree that an explicit mapping would strengthen the presentation. The cascade multiplicative structure was derived directly from the reviewed mechanical faults (friction, efficiency loss, torque ripple, etc.) in the EM-VSD system, each of which primarily scales the torque or speed transmission rather than adding offsets or altering system order. We will add a new table in the revised model-construction section that maps every fault reviewed in the paper to the specific multiplicative parameters, noting any residual effects or electrical dynamics left unmodeled. The additive-fault comparison is introduced separately to quantify severity differences for controller design purposes and does not serve as a test of exhaustiveness; the multiplicative form is proposed specifically for the mechanical faults catalogued, while additive terms represent distinct fault classes (e.g., sensor bias). revision: yes

Circularity Check

0 steps flagged

No significant circularity; model derived from external fault review

full rationale

The paper's central step reviews and summarizes mechanical faults in the EM-VSD cascade from the literature, then constructs a multiplicative structure to simulate scenarios. This is a standard modeling choice with no reduction of any claimed result to fitted inputs, self-referential definitions, or load-bearing self-citations. No equations are presented that equate a 'prediction' to its own construction parameters, and the six working conditions are identified directly from the reviewed faults rather than forced by prior author results. The derivation remains self-contained against the reviewed inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the model rests on domain assumptions about EM-VSD fault mechanisms and the adequacy of a multiplicative cascade representation, with no free parameters or invented entities explicitly stated.

axioms (1)
  • domain assumption Potential faults in the mechanical part of the EM and VSD system can be reviewed and summarized to yield a general model.
    Invoked in the transition from fault review to model establishment.

pith-pipeline@v0.9.0 · 5736 in / 1156 out tokens · 17841 ms · 2026-05-24T21:11:21.816081+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    Tsiotras, H

    P. Tsiotras, H. Shen, and C. Hall. Satellite attitude control and power tracking with energy/momentum wheels. Journal of Guidance, Control, and Dynamics, 24(1):23–34, 2001

    work page 2001

  2. [2]

    Q. Shen, D. Wang, S. Zhu, and E. K. Poh. Robust control allocation for spacecraft attitude tracking under actuator faults. IEEE Transactions on Control Systems Technology, 25(3):1068–1075, 2017

    work page 2017

  3. [3]

    B. Wie, D. Bailey, and C. Heiberg. Rapid multitarget acquisition and pointing control of agile spacecraft. Journal of Guidance, Control, and Dynamics, 25(1):96–104, 2002

    work page 2002

  4. [4]

    Ahmed and D

    J. Ahmed and D. S. Bernstein. Adaptive control of double-gimbal control- moment gyro with unbalanced rotor. Journal of guidance, control, and dynamics, 25(1):105–115, 2002

    work page 2002

  5. [5]

    B. Wie, D. Bailey, and C. Heiberg. Singularity robust steering logic for redundant single-gimbal control moment gyros. Journal of Guidance, Con- trol, and Dynamics , 24(5):865–872, 2001. 36

    work page 2001

  6. [6]

    Pleiades system archi- tecture and main performances

    M Alain Gleyzes, Lionel Perret, and Philippe Kubik. Pleiades system archi- tecture and main performances. International Archives of the Photogram- metry, Remote Sensing and Spatial Information Sciences , 39(1):537–542, 2012

    work page 2012

  7. [7]

    Radiometric and geometric analysis of worldview-2 stereo scenes

    D Poli, E Angiuli, and F Remondino. Radiometric and geometric analysis of worldview-2 stereo scenes. International archives of photogrammetry and remote sensing and spatial information sciences , 38(Part 1):15–18, 2010

    work page 2010

  8. [8]

    F. L. Markley and J. L. Crassidis. Fundamentals of spacecraft attitude determination and control, volume 33. Springer, 2014

    work page 2014

  9. [9]

    A. Fekih. Fault diagnosis and fault tolerant control design for aerospace sys- tems: A bibliographical review. In American Control Conference (ACC), 2014, pages 1286–1291. IEEE, 2014

    work page 2014

  10. [10]

    Jiang and X

    J. Jiang and X. Yu. Fault-tolerant control systems: A comparative study between active and passive approaches. Annual Reviews in control , 36(1):60–72, 2012

    work page 2012

  11. [11]

    Murugesan and P.S

    S. Murugesan and P.S. Goel. Fault-tolerant spacecraft attitude control system. Sadhana, 11(1-2):233–261, 1987

    work page 1987

  12. [12]

    Q. Shen, D. Wang, S. Zhu, and E. K. Poh. Finite-time fault-tolerant atti- tude stabilization for spacecraft with actuator saturation. IEEE Transac- tions on Aerospace and Electronic Systems , 51(3):2390–2405, 2015

    work page 2015

  13. [13]

    Noumi and M

    A. Noumi and M. Takahashi. Fault-tolerant attitude control systems for satellite equipped with control moment gyros. In AIAA Guidance, Navi- gation, and Control (GNC) Conference , page 5119, 2013

    work page 2013

  14. [14]

    Zhang, L

    F. Zhang, L. Jin, and S. Xu. Fault tolerant attitude control for spacecraft with sgcmgs under actuator partial failure and actuator saturation. Acta Astronautica, 132:303–311, 2017. 37

    work page 2017

  15. [15]

    B. Bialke. High fidelity mathematical modeling of reaction wheel perfor- mance. In 1998 Annual American Astronautical Socitety Rocky Mountain Guidance and Control Conference on Advances in the Astronautical Sci- ences, pages 483–496, 1998

    work page 1998

  16. [16]

    Rahimi, K

    A. Rahimi, K. D. Kumar, and H. Alighanbari. Fault estimation of satellite reaction wheels using covariance based adaptive unscented kalman filter. Acta Astronautica, 134:159–169, 2017

    work page 2017

  17. [17]

    Y.C. Choi, J. H. Son, and H. S. Ahn. Fault detection and isolation for a small cmg-based satellite: A fuzzy q-learning approach. Aerospace Science and Technology, 47:340–355, 2015

    work page 2015

  18. [18]

    H. A. Toliyat, S. Nandi, S. Choi, and H. Meshgin-Kelk. Electric Machines: Modeling, Condition Monitoring, and Fault Diagnosis . CRC Press, 2013

    work page 2013

  19. [19]

    Kastha and B

    D. Kastha and B. K. Bose. Investigation of fault modes of voltage-fed inverter system for induction motor drive. IEEE Transactions on Industry Applications, 30(4):1028–1038, 1994

    work page 1994

  20. [20]

    Nandi, H

    S. Nandi, H. A. Toliyat, and X. Li. Condition monitoring and fault diag- nosis of electrical motors — a review. IEEE transactions on energy con- version, 20(4):719–729, 2005

    work page 2005

  21. [21]

    D. U. Campos-Delgado, D. R. Espinoza-Trejo, and E. Palacios. Fault- tolerant control in variable speed drives: a survey. IET Electric Power Applications, 2(2):121–134, 2008

    work page 2008

  22. [22]

    Rajagopalan, J

    S. Rajagopalan, J. M. Aller, J. A. Restrepo, T. G. Habetler, and R. G. Harley. Detection of rotor faults in brushless dc motors operating under nonstationary conditions. IEEE Transactions on Industry Applications , 42(6):1464–1477, 2006

    work page 2006

  23. [23]

    Moseler and R

    O. Moseler and R. Isermann. Application of model-based fault detection to a brushless dc motor. IEEE Transactions on industrial electronics , 47(5):1015–1020, 2000. 38

    work page 2000

  24. [24]

    Rajagopalan

    S. Rajagopalan. Detection of rotor and load faults in brushless DC mo- tors operating under stationary and non-stationary conditions . PhD thesis, Georgia Institute of Technology, 2006

    work page 2006

  25. [25]

    Chen and R

    J. Chen and R. J. Patton. Robust model-based fault diagnosis for dynamic systems, volume 3

    work page

  26. [26]

    G. M. Joksimovic and J. Penman. The detection of inter-turn short cir- cuits in the stator windings of operating motors. IEEE Transactions on Industrial electronics, 47(5):1078–1084, 2000

    work page 2000

  27. [27]

    Betin, M

    F. Betin, M. Deloizy, and C. Goeldel. Closed loop control of a stepping motor drivecomparison between pid control, self tuning regulationand fuzzy logic control. EPE Journal, 8(1-2):33–39, 1999

    work page 1999

  28. [28]

    A. Morar. Stepper motor model for dynamic simulation. Acta Elec- trotehnica, 44(2):117–122, 2003

    work page 2003

  29. [29]

    Collacott

    R. Collacott. Mechanical fault diagnosis and condition monitoring. Springer Science & Business Media, 2012

    work page 2012

  30. [30]

    S. K. Pal. Direct drive high energy permanent magnet brush and brushless dc motors for robotic applications. In IEE Colloquium on Robot Actuators, pages 12–1. IET, 1991

    work page 1991

  31. [31]

    S. K. Pal. Design criteria for brushless dc motors with hollow rotor of samarium cobalt for applications above 25000 rpm in vacuum. In Fifth International Conference on Electrical Machines and Drives , pages 115–

    work page

  32. [32]

    R. Fisher. Design and cost considerations for permanent magnet dc motor applications. Power Conversion & Intelligent Motion , 17(7):18–24, 1991

    work page 1991

  33. [33]

    Report of large motor reliability survey of industrial and commercial installations, part i

    Motor Reliability Working Group et al. Report of large motor reliability survey of industrial and commercial installations, part i. IEEE Trans. Industrial Applications, 1(4):865–872, 1985. 39

    work page 1985

  34. [34]

    Isermann

    R. Isermann. Fault-diagnosis applications: model-based condition moni- toring: actuators, drives, machinery, plants, sensors, and fault-tolerant systems. Springer Science & Business Media, 2011

    work page 2011

  35. [35]

    F. A. Leve, B. J. Hamilton, and M. A. Peck. Spacecraft momentum control systems. Springer, 2015

    work page 2015

  36. [36]

    J. Jin, S. Ko, and C. K. Ryoo. Fault tolerant control for satellites with four reaction wheels. Control Engineering Practice, 16(10):1250–1258, 2008

    work page 2008

  37. [37]

    B. Xiao, Q. Hu, and Y. Zhang. Adaptive sliding mode fault tolerant attitude tracking control for flexible spacecraft under actuator saturation. IEEE Transactions on Control Systems Technology, 20(6):1605–1612, 2012

    work page 2012

  38. [38]

    Sasaki and T

    T. Sasaki and T. Shimomura. Fault-tolerant architecture of two parallel double-gimbal variable-speed control moment gyros. In AIAA Guidance, Navigation, and Control Conference , 2016-0090

    work page 2016

  39. [39]

    Schaub and J

    H. Schaub and J. L. Junkins. Singularity avoidance using null motion and variable-speed control moment gyros. Journal of Guidance, Control, and Dynamics, 23(1):11–16, 2000

    work page 2000

  40. [40]

    Yoon and P

    H. Yoon and P. Tsiotras. Singularity analysis of variable speed control moment gyros. Journal of Guidance, Control, and Dynamics , 27(3):374– 386, 2004

    work page 2004

  41. [41]

    Cui and J

    P. Cui and J. He. Steering law for two parallel variable-speed double- gimbal control moment gyros. Journal of Guidance, Control, and Dynam- ics, 37(1):350–359, 2013

    work page 2013

  42. [42]

    Tafazoli

    M. Tafazoli. A study of on-orbit spacecraft failures. Acta Astronautica, 64(2-3):195–205, 2009

    work page 2009

  43. [43]

    X. Cao, C. Yue, M. Liu, and B. Wu. Time efficient spacecraft maneu- ver using constrained torque distribution. Acta Astronautica, 123:320–329, 2016. 40

    work page 2016

  44. [44]

    S. Yin, B. Xiao, S. X. Ding, and D. Zhou. A review on recent development of spacecraft attitude fault tolerant control system. IEEE Transactions on Industrial Electronics, 63(5):3311–3320, 2016

    work page 2016

  45. [45]

    Zhang and J

    Y. Zhang and J. Jiang. Bibliographical review on reconfigurable fault- tolerant control systems. Annual reviews in control, 32(2):229–252, 2008

    work page 2008

  46. [46]

    Yu and J

    X. Yu and J. Jiang. A survey of fault-tolerant controllers based on safety- related issues. Annual Reviews in Control , 39:46–57, 2015. 41

    work page 2015