Skip to main content
SpringerLink
Log in

Finite time sliding mode control for agile rigid satellite with CMG actuators using fast high-order sliding mode observer

  • Original Paper
  • Published:
Aerospace Systems Aims and scope Submit manuscript

Abstract

This paper proposes a finite-time stable chattering-free output feedback control method for rigid satellites equipped with single gimbal control moment gyro (SGCMG) actuators, considering dynamic uncertainties and external disturbances. The dynamics of a rigid satellite are first represented using the modified Rodrigues parameter (MRP) explanation, and then transformed into Lagrangian state space affine form. Because of cost or technical restrictions, angular velocity data are not always accessible for practical application. So angular velocity is considered to be unmeasurable. In order to avoid increasing mathematical calculations and designing separate observers to estimate external disturbances and system states with finite time convergence, a fast third-order sliding mode state observer has been used to simultaneously estimate disturbances and system states. The main part of the proposed controller is also composed of the fast non-singular terminal sliding mode method, which is a combination of linear sliding mode and terminal sliding mode and guarantees finite-time stability and elimination of chattering phenomenon. For the computation of inverse of Jacobian matrix, off-diagonal singularity robust steering algorithm has been used that capable of escaping any kind of singularities. The stability of the proposed method and the simulation results of the proposed method have been presented and compared with the results of the methods available in the literature, which shows the efficiency of the method proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability

“Not applicable” here.

Abbreviations

SMC:

Sliding mode control

TSMC:

Terminal sliding mode control

NTSMC:

Nonsingular terminal sliding mode

FNTSMC:

Fast Nonsingular terminal sliding mode

HOSMO:

High-order sliding mode observer

TOSMO:

Third-order sliding mode observer

CMG:

Control Moment Gyro

\({\mathcal{R}}^{{\text{n}}}\) :

\({\text{n}}\)-Dimensional Euclidean space

LSM:

Linear sliding mode

TSS:

Terminal sliding surface

NTSS:

Nonsingular terminal sliding surface

FNTSS:

Fast Nonsingular terminal sliding surface

SOSMO:

Second-order sliding mode observer

FTOSMO:

Fast third-order sliding mode observer

MRP:

Modified Rodrigues Parameters

\(V\) :

Lyapunov function

\(\sigma\) :

Modified Rodrigues Parameters (\({\text{rad}}\))

\({\sigma }_{d}\) :

Desired MRP (\({\text{rad}}\))

\({\sigma }_{e}\) :

Attitude error in term of MRP (\({\text{rad}}\))

\(\omega\) :

Angular velocity (\({\text{rad}}/{\text{s}}\))

\({\omega }_{d}\) :

Desired Angular velocity (\({\text{rad}}/{\text{s}}\))

\({\omega }_{e}\) :

Angular velocity error (\({\text{rad}}/{\text{s}}\))

\({S}^{*}\) :

Skew-symmetric matrix [–]

\({\text{J}}\) :

Satellite’s positive definite inertia matrix (\({\text{kg}}.{{\text{m}}}^{2}\))

\({J}_{0}\) :

Nominal value of the inertia matrix (\({\text{kg}}.{{\text{m}}}^{2}\))

\(\delta J\) :

The uncertainty of inertia matrix (\({\text{kg}}.{{\text{m}}}^{2}\))

\(d\left(t\right)\) :

External disturbances (\({\text{N}}.{\text{m}}\))

\({\text{u}}\) :

Control torques generated by satellite’s actuators (\({\text{N}}.{\text{m}}\))

\({H}_{s}\) :

Satellite's angular momentum (\({\text{kg}}.{{\text{m}}}^{2}/s\))

\({h}_{cmg}\) :

Angular momentum of the total CMG actuators(\({\text{kg}}.{{\text{m}}}^{2}/s\))

\({\delta }_{i}\) :

Angle of the gimbal

\(A\left(\delta \right)\) :

Jacobian matrix

\(\theta\) :

Pyramid skew angle in pyramid mounting arrangement of CMGs

\({M}_{\rm ext}\) :

External disturbances (\({\text{N}}.{\text{m}}\))

\({\Delta }_{D}\) :

Upper bound of lumped uncertainty

\({\overline{\Delta } }_{D}\) :

Lumped uncertainty derivative upper bound

\({\widehat{\Delta }}_{D}\) :

Estimated lumped uncertainty upper bound

\({s}_{L}\) :

Linear sliding surface

\({s}_{T}\) :

Terminal sliding surface

\({\lambda }_{i}\) :

FNTSS coefficients

\(\alpha ,\beta\) :

FNTSS power coefficients

\({\kappa }_{1},{\kappa }_{2}\) :

Coefficients of sliding surface function

\({\epsilon }_{s}\) :

Saturation function parameter

\(\eta ,\mu\) :

Coefficients of control inputs function

\(\rho\) :

Design parameter for \({\Delta }_{D}\) adaptation

\(\vartheta\) :

Adaptive parameter for stability analysis

\({\zeta }_{i}\) :

FTOSMO Gaines

\({\varvec{\Omega}}\) :

FTOSMO fast section parameter

\({\widehat{x}}_{i}\) :

Estimated states of system

\(z\) :

FTOSMO augmented variable

\({h}_{0}\) :

Constant angular momentum of CMG

\({m}_{A}\) :

Singularity index of Jacobian matrix

References

  1. Shao S, Zong Q, Tian B, Wang F (2017) Finite-time sliding mode attitude control for rigid spacecraft without angular velocity measurement. J Franklin Inst 354(12):4656–4674

    Article  MathSciNet  Google Scholar 

  2. Guo Y, Huang B, Guo JH, Li AJ, Wang CQ (2019) Velocity-free sliding mode control for spacecraft with input saturation. Acta Astronaut 1(154):1–8

    Article  Google Scholar 

  3. Zhang K, Duan GR, Ma MD (2019) Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements. J Franklin Inst 356(4):1991–2014

    Article  MathSciNet  Google Scholar 

  4. Yuan L, Ma G, Li C, Jiang B (2017) Finite-time attitude tracking control for spacecraft without angular velocity measurements. J Syst Eng Electron 28(6):1174–1185

    Article  Google Scholar 

  5. Hu Q, Jiang B (2017) Continuous finite-time attitude control for rigid spacecraft based on angular velocity observer. IEEE Trans Aerosp Electron Syst 54(3):1082–1092

    Article  MathSciNet  Google Scholar 

  6. Malekzadeh M, Sadeghian H (2019) Attitude control of spacecraft simulator without angular velocity measurement. Control Eng Pract 84(3):72–81

    Article  Google Scholar 

  7. Shtessel Y, Edwards C, Fridman L, Levant A (2014) Sliding mode control and observation. Springer, New York, New York

    Book  Google Scholar 

  8. Liu J, Wang X (2012) Advanced sliding mode control for mechanical systems. Springer, Berlin

    Google Scholar 

  9. Yu X, Feng Y, Man Z (2020) Terminal sliding mode control–An overview. IEEE Open J Ind Electron Soc 25(2):36–52

    Google Scholar 

  10. Utkin V, Poznyak A, Orlov Y, Polyakov A (2020) Conventional and high order sliding mode control. J Frank Inst 357(15):10244–10261

    Article  MathSciNet  Google Scholar 

  11. Fridman L, Moreno JA, Bandyopadhyay B, Kamal S, Chalanga A (2015) Continuous nested algorithms: the fifth generation of sliding mode controllers. In: Yu X, Efe MÖ (eds) Recent advances in sliding modes: from control to intelligent mechatronics. Springer, Cham, pp 5–35

    Chapter  Google Scholar 

  12. Feng Y, Han F, Yu X (2014) Chattering free full-order sliding-mode control. Automatica 50(4):1310–1314

    Article  MathSciNet  Google Scholar 

  13. Dey S, Giri DK, Gaurav K (2021) Laxmi V (2021) Robust nonsingular terminal sliding mode attitude control of satellites. J Aerosp Eng 34:06020003

    Article  Google Scholar 

  14. Guo Y, Huang B, Song SM, Li AJ, Wang CQ (2019) Robust saturated finite-time attitude control for spacecraft using integral sliding mode. J Guid Control Dyn 42:440–446

    Article  Google Scholar 

  15. Gao H, Lv Y, Nguang SK, Ma G (2018) Finite-time attitude quantised control for rigid spacecraft. Int J Syst Sci 49:2328–2340

    Article  MathSciNet  Google Scholar 

  16. Yadegari H, Beyramzad J, Khanmirza E (2022) Magnetorquers-based satellite attitude control using interval type-II fuzzy terminal sliding mode control with time delay estimation. Adv Space Res 69(8):3204–3225

    Article  Google Scholar 

  17. Tiwari PM, Janardhanan S, un Nabi M (2016) Attitude control using higher order sliding mode. Aerosp Sci Technol 54:108–113

    Article  Google Scholar 

  18. Nguyen VC, Vo AT, Kang HJ (2020) A non-singular fast terminal sliding mode control based on third-order sliding mode observer for a class of second-order uncertain nonlinear systems and its application to robot manipulators. IEEE Access 23(8):78109–78120

    Article  Google Scholar 

  19. Nguyen VC, Vo AT, Kang HJ (2021) A finite-time fault-tolerant control using non-singular fast terminal sliding mode control and third-order sliding mode observer for robotic manipulators. IEEE Access 16(9):31225–31235

    Article  Google Scholar 

  20. Van M, Kang HJ, Suh YS, Shin KS (2013) Output feedback tracking control of uncertain robot manipulators via higher-order sliding-mode observer and fuzzy compensator. J Mech Sci Technol 27(8):2487–2496

    Article  Google Scholar 

  21. Bani Younes A, Mortari D (2019) Derivation of all attitude error governing equations for attitude filtering and control. Sensors 19(21):4682

    Article  Google Scholar 

  22. Younes AB, Mortari D, Turner JD, Junkins JL (2014) Attitude error kinematics. J Guid Control Dyn 37(1):330–336

    Article  Google Scholar 

  23. Crassidis JL, Markley FL (1996) Sliding mode control using modified Rodrigues parameters. Jo Guid Control Dyn 19:1381–1383

    Article  Google Scholar 

  24. Crassidis JL, Markley FL (1996) Attitude estimation using modified Rodrigues parameters. In: Flight Mechanics/Estimation Theory Symposium

  25. Khirsaria NM, Kumar SR (2021) Nonlinear spacecraft attitude control design using modified rodrigues parameters. In: 2021 Seventh Indian Control Conference (ICC) 2021 Dec 20, pp 105–110. IEEE

  26. Beyramzad J, Daneshjou K, Khanmirza E (2023) Design a finite-time chattering free attitude controller for rigid spacecraft’s without angular velocity measurement using interval type-II fuzzy logic nonsingular terminal sliding mode and nonlinear extended state observer. In: 21st International Conference of Iranian Aerospace Society 27-29 Feb 2023. pp 1–8

  27. Tiwari PM, Janardhanan SU, un Nabi M (2015) Rigid spacecraft attitude control using adaptive integral second order sliding mode. Aerosp Sci Technol 42:50–57

    Article  Google Scholar 

  28. Sofyalı A, Jafarov EM, Wisniewski R (2018) Robust and global attitude stabilization of magnetically actuated spacecraft through sliding mode. Aerosp Sci Technol 1(76):91–104

    Article  Google Scholar 

  29. Leve FA, Hamilton BJ, Peck MA (2015) Spacecraft momentum control systems. Springer

    Book  Google Scholar 

  30. Richie DJ, Lappas VJ, Prassinos G (2009) A practical small satellite variable-speed control moment gyroscope for combined energy storage and attitude control. Acta Astronaut 65(11–12):1745–1764

    Article  Google Scholar 

  31. Papakonstantinou C, Lappas V, Kostopoulos V (2021) A gimballed control moment gyroscope cluster design for spacecraft attitude control. Aerospace 8(9):273

    Article  Google Scholar 

  32. Mony A, Hablani HB, Paranjape AA (2022) Angular-momentum-based sizing of control moment gyro cluster for an agile spacecraft. J Guid Control Dyn 45(9):1627–1643

    Article  Google Scholar 

  33. Richie DJ, Lappas VJ, Wie B (2009) Practical steering law for small satellite energy storage and attitude control. J Guid Control Dyn 32(6):1898–1911

    Article  Google Scholar 

  34. Courie IA, Jenie YI, Poetro RE (2018) Simulation of satellite attitude control using Single Gimbal Control Moment Gyro (SGCMG) system. J Phys Conf Ser 1130(1):012003

    Article  Google Scholar 

  35. Valk L, Berry A, Vallery H (2018) Directional singularity escape and avoidance for single-gimbal control moment gyroscopes. J Guid Control Dyn 41(5):1095–1107

    Article  Google Scholar 

  36. Wie B (2005) Singularity escape/avoidance steering logic for control moment gyro systems. J Guid Control Dyn 28(5):948–956

    Article  Google Scholar 

  37. Wang L, Chai T, Zhai L (2009) Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics. IEEE Trans Industr Electron 56(9):3296–3304

    Article  Google Scholar 

  38. Yu S, Yu X, Shirinzadeh B, Man Z (2005) Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11):1957–1964

    Article  MathSciNet  Google Scholar 

  39. Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9–10):924–941

    Article  MathSciNet  Google Scholar 

  40. Van M, Ge SS, Ren H (2016) Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control. IEEE Trans Cybern 47(7):1681–1693

    Article  Google Scholar 

Download references

Funding

The authors did not receive support from any organization for the submitted work. The authors declare they have no financial interests.

Author information

Authors and Affiliations

  1. Satellite Research Institute, Sharif University of Technology, Tehran, Iran

    Narges Nazari

  2. Control Engineering Department, Shahid Beheshti University, Tehran, Iran

    Hossein Moladavoudi

  3. Iran University of Science and Technology, Tehran, Iran

    Jalil Beyramzad

Authors
  1. Narges Nazari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Moladavoudi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jalil Beyramzad
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by [Narges Nazari], [Jalil Beyramzad] and [Hossein Moladavoudi]. The first draft of the manuscript was written by [Jalil Beyramzad] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Conceptualization: [Narges Nazari]; Methodology: [Jalil Beyramzad]; Formal analysis and investigation: [Narges Nazari]; Writing—original draft preparation: [Jalil Beyramzad]; Writing—review and editing: [Hossein Moladavoudi],

Corresponding author

Correspondence to Narges Nazari.

Ethics declarations

Conflict of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazari, N., Moladavoudi, H. & Beyramzad, J. Finite time sliding mode control for agile rigid satellite with CMG actuators using fast high-order sliding mode observer. AS (2024). https://doi.org/10.1007/s42401-024-00283-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42401-024-00283-4

Keywords

Search

Navigation