Online adaptive PID tracking control of an aero-pendulum using PSO-scaled fuzzy gain adjustment mechanism


This article is centered on the development of a robust position control and disturbance compensation strategy for a mechatronic aero-pendulum using the soft computing paradigm. The pendulum arm is rotated about its pivot via the thrust generated by two coaxial contra-rotating motorized propellers installed at its free end. The tracking error in arm’s angular position is fed to a multi-loop feedback controller. The proportional–integral–derivative (PID) controller, in the outer loop, stabilizes the arm at the reference position. The reference current control signals generated by the PID position controller are fed to two PI controllers, in the inner loop, that are responsible for regulating the current consumption of each motorized propeller. Initially, the fixed PID controller gains are evaluated by selecting the optimal value of the system’s closed-loop pole using the particle swarm optimization (PSO) algorithm. However, to mitigate the inefficacies of fixed gain controller and further enhance the system’s robustness against bounded exogenous disturbances and damping against oscillations, the closed-loop pole is dynamically adjusted via fuzzy inference system, after every sampling interval. The fuzzy membership functions are calibrated offline via PSO algorithm. The superior time optimal control behavior rendered by the proposed controller is validated by comparing its performance with fixed gain controller via credible real-time experiments.

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  1. Aguas X, Revelo J, Paredes I, Cuaycal A, Herrera M (2018) Integral-optimal sliding mode control for vertical take-off and landing system. In: 2018 international conference on information systems and computer science. Quito, Ecuador, pp 29–35.

  2. Al-Gizi AJH (2018) A particle swarm optimization, fuzzy PID controller with generator automatic voltage regulator. Soft Comput.

    Article  Google Scholar 

  3. Antão R, Mota A, Martins RE (2018) Model-based control using interval type-2 fuzzy logic systems. Soft Comput 22:607–620.

    Article  MATH  Google Scholar 

  4. Bhatti OS, Mehmood-ul-Hasan K, Imtiaz MA (2015) Attitude control and stabilization of a two-wheeled self-balancing robot. Control Eng Appl Inf 17:98–104

    Google Scholar 

  5. Bhatti OS, Tariq OB, Manzar A, Khan OA (2018) Adaptive intelligent cascade control of a ball-riding robot for optimal balancing and station-keeping. Adv Robot 32:63–76.

    Article  Google Scholar 

  6. Bouzid Y, Siguerdidjane H, Bestaoui Y (2017) Nonlinear internal model control applied to VTOL multi-rotors UAV. Mechatron 47:49–66.

    Article  Google Scholar 

  7. Capello E, Park H, Tavora B, Guglieri G, Romano M (2015) Modeling and experimental parameter identification of a multicopter via a compound pendulum test rig. In: 2015 workshop on research, education and development of unmanned aerial systems. Cancun, Mexico, pp 308–317.

  8. Carpio-Alemán M, Orozco-Tupacyupanqui W, Betancur-Betancur M (2016) Design and simulation of a fuzzy controller for Vertical Take off and Landing (VTOL) systems. In: IEEE international autumn meeting on power, electronics and computing. Ixtapa, Mexico, pp 1–6.

  9. Chen T, Shen Q, Su P et al (2016) Fuzzy rule weight modification with particle swarm optimisation. Soft Comput 20:2923–2937.

    Article  Google Scholar 

  10. Djoewahir A, Tanaka K, Nakashima S (2013) Adaptive PSO-based self-tuning PID controller for ultrasonic motor. Int J Innov Comput Inf Control 9:3903–3914

    Google Scholar 

  11. Enikov ET, Campa G (2012) Mechatronic aeropendulum: demonstration of linear and nonlinear feedback control principles with MATLAB/simulink real-time windows target. IEEE Trans Educ 55:538–545.

    Article  Google Scholar 

  12. Farmanbordar A, Zaeri N, Rahimi S (2011) Stabilizing a driven pendulum using DLQR control. In: Fifth Asia modelling symposium. Kuala Lumpur, Malaysia, pp 123–126.

  13. Farooq U, Gu J, El-Hawary ME, Luo J, Asad MU (2015) Observer based fuzzy LMI regulator for stabilization and tracking control of an aeropendulum. In: IEEE 28th Canadian conference on electrical and computer engineering. Halifax, Canada, pp 1508–1513.

  14. Giorgi MGD, Donateo T, Ficarella A, Fontanarosaa D, Morabito AE, Scalincia L (2017) Numerical investigation of the performance of contra-rotating propellers for a remotely piloted aerial vehicle. Energy Procedia 126:1011–1018.

    Article  Google Scholar 

  15. Gültekin Y, Tascioglu Y (2011) Pendulum positioning system actuated by dual motorized propellers. In: 6th international advanced technologies symposium. Elazig, Turkey, pp 6–9

  16. Habib G, Miklos A, Enikov ET, Stepan G, Rega G (2017) Nonlinear model-based parameter estimation and stability analysis of an aero-pendulum subject to digital delayed control. Int J Dynam Control 5:629–643.

    MathSciNet  Article  Google Scholar 

  17. Jahed M, Farrokhi M (2013) Robust adaptive fuzzy control of twin rotor MIMO system. Soft Comput 17:1847–1860.

    Article  Google Scholar 

  18. Jeyalakshmi V, Subburaj P (2016) PSO-scaled fuzzy logic to load frequency control in hydrothermal power system. Soft Comput 20:2577–2594.

    Article  Google Scholar 

  19. Jeyasenthil R, Choi SB, Purohit H, Jung D (2019) Robust position control and disturbance rejection of an industrial plant emulator system using the feedforward-feedback control. Mechatron 57:29–38.

    Article  Google Scholar 

  20. Job MM, Jose PSH (2015) Modeling and Control of Mechatronic Aeropendulum. In: Proceedings of IEEE 2nd international conference on innovations in information embedded and communication systems. Coimbatore, India, pp 1–5.

  21. Kalat AA (2018) A robust direct adaptive fuzzy control for a class of uncertain nonlinear MIMO systems. Soft Comput.

    Article  MATH  Google Scholar 

  22. Kole A (2015) Design and stability analysis of adaptive fuzzy feedback controller for nonlinear systems by Takagi-Sugeno model-based adaptation scheme. Soft Comput 19:1747–1763.

    Article  MATH  Google Scholar 

  23. Mohammadbagheri A, Yaghoobi M (2011) A new approach to control a driven pendulum with PID method. In: 13th international conference on computer modelling and simulation. Cambridge, UK, pp 207–211.

  24. Mohammadi Asl R, Mahdoudi A, Pourabdollah E et al (2019) Combined PID and LQR controller using optimized fuzzy rules. Soft Comput 23:5143–5155.

    Article  Google Scholar 

  25. Muehlebach M, D’Andrea R (2017) The flying platform—a testbed for ducted fan actuation and control design. Mechatron 42:52–68.

    Article  Google Scholar 

  26. Nabipour M, Razaz M, Seifossadat SGH, Mortazavi SS (2016) A novel adaptive fuzzy membership function tuning algorithm for robust control of a PV-based dynamic voltage restorer (DVR). Eng Appl Artif Intell 53:155–175.

    Article  Google Scholar 

  27. Quanser (2009) QNET Practical control guide. Document No. 851, Revision 1.1, pp 55–66

  28. Quanser (2011) QNET VTOL user manual, vol 1, p 27

  29. Raj R, Mohan BM (2018) Modeling and analysis of the simplest fuzzy PID controller of Takagi-Sugeno type with modified rule base. Soft Comput 22:5147–5161.

    Article  MATH  Google Scholar 

  30. Rodríguez-Molina A, Villarreal-Cervantes MG, Aldape-Pérez M (2019) An adaptive control study for the DC motor using meta-heuristic algorithms. Soft Comput 23:889–906.

    Article  Google Scholar 

  31. Saleem O, Mahmood-ul-Hasan K (2018) Adaptive collaborative speed control of PMDC motor using hyperbolic secant functions and particle swarm optimization. Turkish J Elect Eng Comput Sci 26:1612–1622.

    Article  Google Scholar 

  32. Saleem O, Mahmood-ul-Hasan K (2019) Robust stabilisation of rotary inverted pendulum using intelligently optimised nonlinear self-adaptive dual fractional-order pd controllers. Int J Syst Sci 50:1399–1414.

    MathSciNet  Article  Google Scholar 

  33. Saleem O, Hassan H, Khan A, Javaid U (2017) Adaptive fuzzy-PD tracking controller for optimal visual-servoing of wheeled mobile robots. Control Eng Appl Inf 19:58–68

    Google Scholar 

  34. Saleem O, Abbas F, Khan MU, Imtiaz MA, Khalid S (2018) Adaptive collaborative position control of a tendon-driven robotic finger. Control Eng Appl Inf 20:87–99

    Google Scholar 

  35. Saleem O, Shami UT, Mahmood-ul-Hasan K, Abbas F, Mahmood S (2019) Robust-optimal output-voltage control of buck converter using fuzzy adaptive weighted combination of linear feedback controllers. Control Eng Appl Inf 21:43–53

    Google Scholar 

  36. Sun J, Li B, Wen CY, Chen CK (2018) Design and implementation of a real-time hardware-in-the-loop testing platform for a dual-rotor tail-sitter unmanned aerial vehicle. Mechatron 56:1–15.

    Article  Google Scholar 

  37. Uyar E, Akdogan T, Keskin O, Mutlu L (2012) Position control of a seesaw like platform by using a thrust propeller. In: 12th IEEE international workshop on advanced motion control. Sarajevo, Bosnia-Herzegovina, pp 1–6.

  38. Xu JX, Guo ZQ, Lee TH (2014) Design and implementation of integral sliding-mode control on an underactuated two-wheeled mobile robot. IEEE Trans Ind Electron 61:3671–3681.

    Article  Google Scholar 

  39. Yang SF, Chou JH (2009) A mechatronic positioning system actuated using a micro DC-motor-driven propeller–thruster. Mechatron 19:912–926.

    Article  Google Scholar 

  40. Yuan Y, Chen R, Li P (2019) Trim investigation for coaxial rigid rotor helicopters using an improved aerodynamic interference model. Aerosp Sci Technol 85:293–304.

    Article  Google Scholar 

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Correspondence to Omer Saleem.

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Saleem, O., Rizwan, M., Zeb, A.A. et al. Online adaptive PID tracking control of an aero-pendulum using PSO-scaled fuzzy gain adjustment mechanism. Soft Comput 24, 10629–10643 (2020).

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  • Aero-pendulum
  • Proportional–integral–derivative control
  • Self-tuning control
  • Fuzzy inference system
  • Particle swarm optimization