×

zbMATH — the first resource for mathematics

Nonlinear \(L_{2}\) control of a laboratory helicopter with variable speed rotors. (English) Zbl 1114.93024
Summary: This paper considers the problem of a nonlinear \(L_{2}\)-disturbance rejection design for a laboratory twin-rotor system. Since the rotor blades present fixed angle of attack, control is achieved by using the rotor speeds as control variables. This mechanical device features highly nonlinear strongly coupled dynamics. The control is developed considering a reduced order model of the rotors obtained by application of a time-scale separation principle, including integral terms on the tracking error to cope with persistent disturbances. An explicit suboptimal solution to the associated partial differential (HJBI) equation is applied. This yields global asymptotical stability for the reduced system. The controller exhibits the structure of a partial feedback linearization with an external nonlinear PID. The paper proposes systematic tuning procedure allowing independent weights for each degree of freedom. The methodology has been tested by experimental results using a laboratory helicopter.

MSC:
93B11 System structure simplification
93B20 Minimal systems representations
93D20 Asymptotic stability in control theory
93C95 Application models in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Avila Vilchis, J.C.; Brogliato, B.; Dzul, A.; Lozano, R., Nonlinear modelling and control of helicopters, Automatica, 39, 1583-1596, (2003) · Zbl 1029.93046
[2] Craig, J.J., Introduction to robotics. mechanics and control, (1989), Addison-Wesley Publishing Company Reading, MA · Zbl 0711.68103
[3] García-Sanz, M.; Elso, J.; Eñaga, I., Control del angulo de cabeceo de un helicoptero Como benchmark de diseño de controladores, Revista iberoamericana de automatica e informatica industrial (RIAI), 3, 2, (2006)
[4] Khalil, H.K., Asymptotic stability of a class of nonlinear multiparameter singularly perturbed systems, Automatica, 17, 797-804, (1981) · Zbl 0485.93053
[5] Kung, Ch.; Yang, C.; Chiou, D.; Luo, Ch., Nonlinear \(H_\infty\) helicopter control, (), 4468-4473
[6] López-Martinez, M. (2005). Nonlinear control of systems with two independent rotors. Ph.D. thesis, University of Seville, Department of System Engineering and Automation. Spain.
[7] López-Martinez, M.; Ortega, M.G.; Rubio, F.R., An \(H_\infty\) controller of the twin rotor laboratory equipment, ()
[8] López-Martinez, M.; Díaz, J.M.; Ortega, M.G.; Rubio, F.R., Control of a laboratory helicopter using switched 2-step feedback linearization, ()
[9] Mullhaupt, Ph.; Srinivasan, B.; Lévine, J.; Bonvin, D., A toy more difficult to control than the real thing, (), 253-258
[10] Mullhaupt, Ph.; Srinivasan, B.; Lévine, J.; Bonvin, D., Cascade control of the toycopter, ()
[11] Ortega, M.G.; Vargas, M.; Vivas, C.; Rubio, F.R., Robustness improvement of a nonlinear \(H_\infty\) controller for robot manipulators via saturation functions, Journal of robotic systems, 22, 8, 421-437, (2005) · Zbl 1133.70316
[12] Postlethwaite, I.; Smerlas, A.; Walker, D.J.; Gubbels, A.W.; Baillie, S.W.; Strange, M.E., \(H_\infty\) control of the NRC Bell 205 fly-by-wire helicopter, Journal of the American helicopter society, 44, 4, (1999)
[13] Reinier, J.; Balas, G.J.; Garrard, W.L., Flight control design using robust dynamic inversion and time-scale separation, Automatica, 32, 1, 1493-1504, (1996) · Zbl 0871.93037
[14] van der Schaft, A., \(L_2\)-gain and passivity techniques in nonlinear control, (2000), Springer Berlin · Zbl 0937.93020
[15] Walker, D.J.; Postlethwaite, I., Advanced helicopter flight control using two-degree-of-freedom \(H_\infty\) optimization, Journal of guidance, control, and dynamics, 19, 2, (1996) · Zbl 0850.93632
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.