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Nonlinear General Integral Control Design via Equal Ratio Gain Technique

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http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52827#.VKn7FsnQrzE

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This paper proposes two kinds of nonlinear general integral controllers, that is, one is generic and another is practical, for a class of uncertain nonlinear system. By extending equal ratio gain technique to a canonical interval system matrix and using Lyapunov method, theorems to ensure regionally as well as semi-globally asymptotic stability are established in terms of some bounded information. Moreover, for the practical nonlinear integral controller, a real time method to evaluate the equal ratio coefficient is proposed such that its value can be chosen moderately. Theoretical analysis and simulation results demonstrated that not only nonlinear general integral control can effectively deal with the uncertain nonlinear system but also equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.
Cite this paper
Liu, B. (2014) Nonlinear General Integral Control Design via Equal Ratio Gain Technique. International Journal of Modern Nonlinear Theory and Application, 3, 256-266. doi: 10.4236/ijmnta.2014.35028. 
 

[1] Khalil, H.K. (2007) Nonlinear Systems. 3rd Edition, Electronics Industry Publishing, Beijing, 449-453, 551.
[2] Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Linear System Theory. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3174-3177.
[3] Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Sliding Mode Technique. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3178-3181.
[4] Liu, B.S., Li, J.H. and Luo, X.Q. (2014) General Integral Control Design via Feedback Linearization. Intelligent Control and Automation, 5, 19-23. http://dx.doi.org/10.4236/ica.2014.51003
[5] Liu, B.S., Luo, X.Q. and Li, J.H. (2014) General Integral Control Design via Singular Perturbation Technique. International Journal of Modern Nonlinear Theory and Application, 3, 173-181. http://dx.doi.org/10.4236/ijmnta.2014.34019
[6] Liu, B.S., Luo, X.Q. and Li, J.H. (2013) General Concave Integral Control. Intelligent Control and Automation, 4, 356-361. http://dx.doi.org/10.4236/ica.2013.44042
[7] Liu, B.S., Luo, X.Q. and Li, J.H. (2014) General Convex Integral Control. International Journal of Automation and Computing, 11, 565-570. http://dx.doi.org/10.1007/s11633-014-0813-6
[8] Liu, B.S. (2014) Constructive General Bounded Integral Control. Intelligent Control and Automation, 5, 146-155.
http://dx.doi.org/10.4236/ica.2014.53017
[9] Liu, B.S. (2014) On the Generalization of Integrator and Integral Control Action. International Journal of Modern Nonlinear Theory and Application, 3, 44-52. http://dx.doi.org/10.4236/ijmnta.2014.32007
[10] Liu, B.S. (2014) Equal Ratio Gain Technique and Its Application in Linear General Integral Control. International Journal of Modern Nonlinear Theory and Application.                                   eww150105lx
[11] Gajic, Z. (1995) Lyapunov Matrix Equation in System Stability and Control. Mathematics in Science and Engineering, 195, 30-31.eww150105lx
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