Model-free controller with an observer applied in real-time to a 3-DOF helicopter

In this paper, a model-free controller with an observer is presented for a class of uncertain continuous-time multiinput-multioutput nonlinear dynamic systems. The proposed model-free control law consists of 2 parts: the first part is a linear control term used to specify the dynamics of the closed loop system, and the second part is a compensator of the effects of uncertainties and external disturbances. The compensator is synthesized from an estimator of the effects of uncertainties and disturbances based on the Lyapunov approach. In order to estimate the unavailable states of the controlled system, a linear state observer is designed. All of the signals in the closed-loop system are proved to be uniformly ultimately bounded using the Lyapunov stability theory. The effectiveness and feasibility of the proposed control strategy are examined in a real-time application for a helicopter with 3 degrees of freedom.

Model-free controller with an observer applied in real-time to a 3-DOF helicopter

In this paper, a model-free controller with an observer is presented for a class of uncertain continuous-time multiinput-multioutput nonlinear dynamic systems. The proposed model-free control law consists of 2 parts: the first part is a linear control term used to specify the dynamics of the closed loop system, and the second part is a compensator of the effects of uncertainties and external disturbances. The compensator is synthesized from an estimator of the effects of uncertainties and disturbances based on the Lyapunov approach. In order to estimate the unavailable states of the controlled system, a linear state observer is designed. All of the signals in the closed-loop system are proved to be uniformly ultimately bounded using the Lyapunov stability theory. The effectiveness and feasibility of the proposed control strategy are examined in a real-time application for a helicopter with 3 degrees of freedom.

___

  • 1] Fliess M, Join C. Intelligent PID controllers. In: 16th Mediterranean Conference on Control and Automation; 25–27 June 2008; Ajaccio-Corsica, France. pp. 326–331.
  • [2] Michel L, Join C, Fliess M, Sicard P, Ch´eriti A. Model-free control of dc/dc converters. In: 12th IEEE Workshop on Control and Modeling for Power Electronics; 28–30 June 2010; Boulder, CO, USA. pp. 1–8.
  • [3] Coelho LDS, Coelho AAR. Model-free adaptive control optimization using a chaotic particle swarm approach. Chaos Soliton Fract 2009; 41: 2001–2009.
  • [4] Kim JH, Lewis FL. Model-free H∞ control design for unknown linear discrete-time systems via Q-learning with LMI. Automatica 2010; 46: 1320–1326.
  • [5] Coelho LDS, Pessˆoa MW, Sumar RR, Coelho AAR. Model-free adaptive control design using evolutionary-neural compensator. Expert Syst Appl 2010; 37: 499–508.
  • [6] Qi G, Chen Z, Yuan Z. Model-free control of affine chaotic systems. Phys Lett A 2005; 344: 189–202.
  • [7] Han J. From PID to active disturbance rejection control. IEEE T Ind Electron 2009; 56: 900–906.
  • [8] Zheng Q, Gao LQ, Gao Z. On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics. In: Proceedings of the 46th IEEE Conference on Decision and Control; 12–14 December 2007; New Orleans, LA, USA. pp. 12–14.
  • [9] L´eonard F, Martini A, Abba G. Robust nonlinear controls of model-scale helicopters under lateral and vertical wind gusts. IEEE T Contr Syst T 2012; 20: 154–163.
  • [10] Morsli S, Tayeb A, Mouloud D, Abdelkader S. A robust adaptive fuzzy control of a unified power flow controller. Turk J Electr Eng Co 2012; 20: 87–98.
  • [11] Boulkroune A, Tadjine M, Msaad M, Farza M. Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction. Fuzzy Set Syst 2010; 161: 797–820.
  • [12] Chen HY, Huang SJ. Learning control of robot manipulators in the presence of additive disturbances. P I Mech Eng I-J Sys 2010; 224: 669–677.
  • [13] Tatlicio˘glu E. Learning control of robot manipulators in the presence of additive disturbances. Turk J Electr Eng Co 2011; 19: 705–714.
  • [14] Apkarian J. 3D Helicopter Experiment Manual. Markham, Canada: Quanser Consulting, 1998.
  • [15] Fradkov AL, Andrievsky B, Peaucelle D. Estimation and control under information constraints for LAAS helicopter benchmark. IEEE T Contr Syst T 2010; 18: 1180–1187.
  • [16] Rios H, Rosales A, Ferreira A, Davila A. Robust regulation for a 3-DOF helicopter via sliding-Modes control and observation techniques. In: 2010 American Control Conference; 30 June–2 July 2010; Baltimore, MD, USA. pp. 4427–4432.
  • [17] Rios H, Rosales A, Davila A. Global non-homogeneous quasi-continuous controller for a 3-DOF helicopter. In: 11th International Workshop on Variable Structure Systems; 26–28 June 2010; Mexico City, Mexico. pp. 475–480.
  • [18] Liu Z, Choukri Elhaj Z, Shi H. Control strategy design based on fuzzy logic and LQR for 3-DOF helicopter model. In: International Conference on Intelligent Control and Information Processing; 13–15 August 2010; Dalian, China. pp. 262–266.
  • [19] Hao L, Yao Y, Geng L, Yisheng Z. Robust LQR attitude control of 3-DOF helicopter. In: Proceedings of the 29th Chinese Control Conference; 29–31 July 2010; Beijing, China. pp. 529–534.
  • [20] Kiefer T, Graichen K, Kugi A. Trajectory tracking of a 3DOF laboratory helicopter under input and state constraints. IEEE T Contr Syst T 2010; 18: 944–952.
  • [21] Kutay AT, Calise AJ, Idan M, Hovakimyan N. Experimental results on adaptive output feedback control using a laboratory model helicopter. IEEE T Contr Syst T 2005; 13: 196–202.
  • [22] Zhou F, Li D, Xia P. Research of fuzzy control for elevation attitude of 3-DOF Helicopter. In: 2009 International Conference on Intelligent Human-Machine Systems and Cybernetics; 26–27 August 2009; Hangzhou, Zhejiang, China. pp. 367–370.
  • [23] Yang L, Zhang L, Li Q. Design and application of fuzzy sliding mode control in the 3-DOF helicopter. In: International Workshop on Intelligent Systems and Applications; 23–24 May 2009; Wuhan, China, pp. 1–5.
  • [24] Witt J, Boonto S, Werner H. Approximate model predictive control of a 3-DOF helicopter. In: Proceedings of the 46th IEEE Conference on Decision and Control; 12–14 December 2007; New Orleans, LA, USA. pp. 4501–4506.
  • [25] Xiuyan W, Changli Z, Zongshuai L. Robust H-infinity tracing control of 3-DOF helicopter model. In: 2010 International Conference on Measuring Technology and Mechatronics Automation; 13–14 March 2010; Changsha, China. pp. 279–282.
  • [26] Marques de Carvalho FG, Hemerly EM. Adaptive elevation control of a three degrees-of-freedom model helicopter using neural networks by state and output feedback. ABCM Symposium Series in Mechatronics 2008; 3: 106–113.
  • [27] Ishitobi M, Nishi M, Nakasaki K. Nonlinear adaptive model following control for a 3-DOF tandem-rotor model helicopter. Control Eng Pract 2010; 18: 936–943.
  • [28] Shan J, Liu HT, Nowotny S. Synchronised trajectory-tracking control of multiple 3-DOF experimental helicopters. IEE P-Contr Theor AP 2005; 152: 683–692.