Robust PID controller design for rigid uncertain spacecraft using Kharitonov theorem and vectored particle swarm optimization

  • Authors

    • Supanna S. Kumar
    • C Shreesha
    • N K. Philip
    https://doi.org/10.14419/ijet.v7i2.21.11825

    Received date: April 21, 2018

    Accepted date: April 21, 2018

    Published date: April 20, 2018

  • Attitude control, kharitonov theorem, rigid spacecraft, robust optimization, uncertain system.

  • Abstract

    This paper presents a robust Proportional Integral Derivative controller design methodology for three axis attitude control of a rigid spacecraft with parametric uncertainty using a combination of Kharitonov theorem and vectored particle swarm optimization based approaches. A controller is designed for each of the three axes using a systematic graphical approach. Here, a plot of the stability boundary loci in the integral gain versus proportional gain parameter plane, for the specified gain and phase margins for each of the Kharitonov interval plants is used to determine the region representing the set of all PID controllers that satisfy the desired performance and stability requirements. Vectored particle swarm optimization technique is used to determine the optimized proportional and integral gain values. The spacecraft attitude control system is simulated using Matlab-Simulink tool which shows that the designed controller provides stability, robustness, good reference pointing and disturbance rejection for perturbations within the specific bounds.

  • References

    1. Åström KJ & Hägglund T, PID Controllers: Theory, Design and Tuning, 2nd ed. Research Triangle Park, North Carolina, US: Instrument Society of America, (1995).
    2. Matušů R & Prokop R, “Computation of robustly stabilizing PID controllers for interval systems”, SpringerPlus, Vol.5, (2016).
    3. Matušů R, Prokop R & Prokopova Z, “Simple tuning of PI controllers for interval plants”, Manuf. Ind. Eng., Vol.11, No.2, (2012), pp.44-47.
    4. Tan N & Kaya I, “Computation of stabilizing PI controllers for interval systems”, Proceedings of the 11th Mediterranean Conference on Control and Automation, (2003).
    5. Závacká J & Bakošová M, “Robust controller design for a laboratory process with uncertainties”, Proceedings of the 18th International Conference on Process Control, (2011).
    6. Závacká J, Bakošová M & Vaneková K, “Control of systems with parametric uncertainties using a robust PI controller”, AT&P Journal, (2007), pp.84-87.
    7. Sidi MJ, Spacecraft Dynamics and Control: A Practical Engineering Approach, New York: Cambridge University Press, (1997).
    8. Chen YP & Lo SC, “Sliding-mode controller design for spacecraft attitude tracking maneuvers”, IEEE Trans. Aerosp. Electron. Syst., Vol.29, No.4, (1993), pp.1328-1333.
    9. Jiang B, Hu Q & Friswell MI, “Fixed-time attitude control for rigid spacecraft with actuator saturation and faults”, IEEE Trans. Control Syst. Technol., Vol.24, No.5, (2016), pp.1892-1898.
    10. Lu K & Xia YQ, “Adaptive attitude tracking control for rigid spacecraft with finite-time convergence”, Automatica, Vol.49, No.12, (2013), pp.3591-3599.
    11. Tiwari PM, Janardhanan S & Nabi M, “Rigid spacecraft attitude tracking using finite time sliding mode control”, Third International Conference on Advances in Control and Optimization of Dynamical Systems, (2014).
    12. Tiwari PM, Janardhanan S & Nabi M, “Rigid spacecraft attitude control using adaptive integral second order sliding mode”, Aerospace Science and Technology, Vol.42, (2015), pp.50-57.
    13. Lu K, Xia Y, Fu M & Yu C, “Adaptive finite-time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints”, Int. J. Robust Nonlinear Control, Vol.26, No.1, (2016), pp.28-46.
    14. Lu K, Xia Y, Yu C & Liu H, “Finite-time tracking control of rigid spacecraft under actuator saturations and faults”, IEEE Trans.Autom. Sci. Eng., Vol.13, No.1, (2016), pp.368-381.
    15. Derman HÖ, “3-Axis attitude control of a geostationary satellite”, The Middle East Technical University, (1999).
    16. Bang H, Lee JS & Eun YJ, “Nonlinear attitude control of a rigid spacecraft by feedback linearization”, J. Mech. Sci. Technol., Vol.18, No.2, (2004), pp.203-210.
    17. Hespanha JP, Linear Systems Theory, Princeton, New Jersey: Princeton University Press, (2009).
    18. Chen Z & Huang J, “Attitude tracking and disturbance rejection of rigid spacecraft by adaptive control”, IEEE Trans. Autom. Control., Vol.54, No.3, (2009), pp.600-605.
    19. Shi JF, Ulrich S & Allen A, “Spacecraft adaptive attitude control with application to space station free-flyer robotic capture”, AIAA Guidance, Navigation, and Control Conference, Kissimmee, (2015), pp.1-23.
    20. Sheng S & Sun C, “An adaptive attitude tracking control approach for an unmanned helicopter with parametric uncertainties and measurement noises”, Int. J. Control Autom., Vol.14, No.1, (2016), pp.217-228.
    21. Zou A, de Ruiter AHJ & Kumar KD, “Finite-time attitude tracking control for rigid spacecraft with control input constraints”, IET Control Theory and Applications, Vol.11, No.7, (2017), pp.931-940.
    22. Li Y, Zhaowei S & Dong Y, “Time efficient robust PID plus controller for satellite attitude stabilization control considering angular velocity and control torque constraint”, Journal of Aerospace Engineering, Vol.30, No.5, (2017).
    23. Huang YJ & Wang YJ, “Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem”, ISA Trans, Vol.39, No.4, (2000), pp.419-431.
    24. Eberhart R & Kennedy J, “A new optimizer using particle swarm theory”, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, (1995).
    25. Remya S, Priya CK & Priyanka CP, “PID controller design using particle swarm optimization for servo actuation system of reusable launch vehicle”, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering,Vol.4, No.8, (2015), pp.7226-7236.
    26. Kumar A & Gupta R, “Compare the results of tuning of PID controller by using PSO and GA technique for AVR system”, Intern. J. Adv. Res. Comput. Engin. Technol., Vol.2, No.6, (2013), pp.2130-2138.
    27. AL-MulaHumadi R, Abbas N & Hammadi W, “PID parameters optimization using adaptive PSO algorithm for a DCSM position control”, International Journal of Electrical Engineering and Technology, Vol.4, No.4, (2013), pp.1-13.
    28. Ahmadzadeh R, “Particle Swarm Optimization (Vectorized Code)”. (2014).
    29. Sarma S, Kulkarni AK, Venkateswaralu A, Natarajan P & Malik NK, “Spacecraft dynamics modeling and simulation using Matlab-Simulink”,Third National Conference on Mathematical Techniques Emerging Paradigms for Electronics and IT Industries, (2010).

  • Downloads

  • How to Cite

    S. Kumar, S., Shreesha, C., & K. Philip, N. (2018). Robust PID controller design for rigid uncertain spacecraft using Kharitonov theorem and vectored particle swarm optimization. International Journal of Engineering and Technology, 7(2.21), 9-14. https://doi.org/10.14419/ijet.v7i2.21.11825