Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform
SUMMARYA three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective...
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| Veröffentlicht in: | International journal of robust and nonlinear control Jg. 23; H. 12; S. 1360 - 1392 |
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Bognor Regis
Blackwell Publishing Ltd
01.08.2013
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| Abstract | SUMMARYA three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three‐time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed‐loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three‐time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright © 2012 John Wiley & Sons, Ltd. |
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| AbstractList | SUMMARY A three-time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three-time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed-loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three-time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright [copy 2012 John Wiley & Sons, Ltd. A three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three‐time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed‐loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three‐time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright © 2012 John Wiley & Sons, Ltd. SUMMARYA three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three‐time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed‐loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three‐time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright © 2012 John Wiley & Sons, Ltd. SUMMARY A three-time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three-time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed-loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three-time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright © 2012 John Wiley & Sons, Ltd. [PUBLICATION ABSTRACT] |
| Author | Esteban, S. Gordillo, F. Aracil, J. |
| Author_xml | – sequence: 1 givenname: S. surname: Esteban fullname: Esteban, S. email: Correspondence to: S. Esteban, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Sevilla, 41092, Spain., sesteban@us.es organization: Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092, Sevilla, Spain – sequence: 2 givenname: F. surname: Gordillo fullname: Gordillo, F. organization: Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, 41092, Sevilla, Spain – sequence: 3 givenname: J. surname: Aracil fullname: Aracil, J. organization: Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, 41092, Sevilla, Spain |
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| Cites_doi | 10.1049/ip‐cta:19949624 10.1016/S1697-7912(08)70172-9 10.1016/0167‐6911(86)90116‐7 10.1109/TCST.2009.2028549 10.1137/1.9780898719185 10.2514/2.4830 10.1049/ip-cta:19971638 10.2514/6.2001-4257 10.1007/BFb0007175 10.2514/3.20016 10.1109/ACC.2001.946348 10.1016/j.sysconle.2005.09.019 10.1007/BF01599620 10.1109/TAC.1985.1104064 10.1016/S1474-6670(17)66062-2 10.4050/JAHS.48.3 10.1016/0167-6911(85)90022-2 10.2514/6.2008-6564 10.1016/0005-1098(84)90069-4 10.1109/TAC.1984.1103586 10.1109/TAC.1987.1104564 10.2514/3.19972 10.2514/3.21715 10.2514/3.20932 10.3182/20080706-5-KR-1001.00962 10.2514/1.8978 10.1016/j.automatica.2006.10.013 10.2514/2.4794 10.1109/CCA.1999.806163 10.2514/3.20822 10.2514/2.4029 10.1109/ICNN.1997.614409 10.2514/6.2005-6236 10.1109/AEROCS.1993.720939 10.2514/6.2008-6566 10.1137/1.9781611971118 10.2514/3.56651 10.1109/TCST.2007.912242 10.2514/2.4142 10.1109/TAC.1978.1101728 |
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DOI: 10.2514/2.4794. 1984; 20 2008; 6564 1987; 32 2008; 6566 1996; 19 2002; 9 1985; 5 2011 1997; 20 2010; 18 2006; 55 1987; 90 1985; 8 2008; 16 2008 1995 2006 1984; 29 2008; 5 1994 1993 1992; 15 1995; 18 2002 1999; 1 1991 2001; 24 2005; 28 1997; 4 1978 1999 1977 2000; 4281 2001 1986; 7 1978; 23 2001; 4 1994; 141 1986; 5 2002; 144 2003; 48 1985; 30 2007; 43 2005; 6236 e_1_2_10_46_1 e_1_2_10_21_1 e_1_2_10_44_1 e_1_2_10_42_1 e_1_2_10_40_1 e_1_2_10_2_1 e_1_2_10_4_1 e_1_2_10_18_1 e_1_2_10_53_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_39_1 e_1_2_10_8_1 e_1_2_10_14_1 e_1_2_10_37_1 e_1_2_10_13_1 e_1_2_10_34_1 e_1_2_10_11_1 e_1_2_10_32_1 e_1_2_10_30_1 e_1_2_10_51_1 Johnson W (e_1_2_10_49_1) 1994 Leishman J (e_1_2_10_48_1) 2006 Naidu D (e_1_2_10_23_1) 2002; 9 e_1_2_10_29_1 e_1_2_10_27_1 e_1_2_10_25_1 e_1_2_10_24_1 e_1_2_10_45_1 e_1_2_10_22_1 e_1_2_10_43_1 e_1_2_10_20_1 e_1_2_10_41_1 Michel A (e_1_2_10_31_1) 1977 Khalil H (e_1_2_10_9_1) 2002 e_1_2_10_52_1 e_1_2_10_3_1 e_1_2_10_19_1 e_1_2_10_5_1 e_1_2_10_17_1 e_1_2_10_38_1 e_1_2_10_7_1 e_1_2_10_15_1 e_1_2_10_36_1 e_1_2_10_12_1 e_1_2_10_35_1 e_1_2_10_10_1 e_1_2_10_33_1 e_1_2_10_50_1 e_1_2_10_28_1 e_1_2_10_26_1 e_1_2_10_47_1 |
| References_xml | – reference: Leishman J. Principles of Helicopter Aerodynamics. Cambridge University Press: New York, NY, 10011-4211, USA, 2006. – reference: Abed E. Strong D-stability. Systems & Control Letters 1986; 7(3):207-212. DOI: 10.1016/0167-6911(86)90116-7. – reference: Kokotović P, Bensoussan A, Blankenship G. Singular Perturbations and Asymptotic Analysis in Control Systems, Vol. 90. Springer-Verlag: Berlin, Germany, 1987. – reference: Michel A, Miller R. Qualitative Analysis of Large Scale Dynamical Systems. Academic Press Inc (London) LTD: Oval Road, London NW1, England, 1977. – reference: Naidu D, Calise A. Singular perturbations and time scales in guidance and control of aerospace systems: a survey. Journal of Guidance, Control and Dynamics 2001; 24(6):1057-1078. DOI: 10.2514/2.4830. – reference: Ardema M, Rajan N. Separation of time-scales in aircraft trajectory optimization. Journal of Guidance, Control, and Dynamics 1985; 8(2):275-278. DOI: 10.2514/3.19972. – reference: Balakrishnan S, Biega V. Adaptive-critic-based neural networks for aircraft optimal control. Journal of Guidance, Control, and Dynamics 1996; 19(4):893-898. DOI: 10.2514/3.21715. – reference: Naidu D. Singular perturbations and time scales in control theory and applications: an overview. Dynamics of Continuous Discrete and Impulsive Systems Series B 2002; 9:233-278. – reference: López-Martínez M, Ortega M, Vivas C, Rubio F. Nonlinear L2 control of a laboratory helicopter with variable speed rotors. Automatica 2007; 43(4):655-661. DOI: 10.1016/j.automatica.2006.10.013. – reference: Kokotović P, Khalil H, O'reilly J. Singular Perturbation Methods in Control: Analysis and Design. Society for Industrial Mathematics: Philadelphia, PA, USA, 1999. – reference: Sira-Ramírez H, Zribi M, Ahmad S. Dynamical sliding mode control approach for vertical flight regulation in helicopters. IEE Proceedings-Control Theory & Applications 1994; 141(1):19-24. 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| Snippet | SUMMARYA three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based... A three‐time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time... SUMMARY A three-time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based... |
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| SubjectTerms | asymptotic stability helicopter control Helicopters Law Mathematical models mathematical upper bounds nonlinear systems Nonlinearity Pitch angle Reproduction Singular perturbation Stability analysis |
| Title | Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform |
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