Parametric optimization of a neutral system with two delays and PD-controller

• Autorzy: Duda J.
• Języki publikacji: EN

Abstrakty

EN

In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined.

Słowa kluczowe

EN

parametric optimization; Lyapunov functional; time delay system; neutral system

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2013
• Tom: Vol. 23, no. 2
• Strony: 131--143
• Opis fizyczny: Bibliogr. 15 poz., wzory

Twórcy

autor

Duda J.

• AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, Department of Automatics. al. Mickiewicza 30, 30-159 Krakow, Poland

Bibliografia

• [1] J. Duda: Parametric optimization problem for systems with time delay. PhD thesis AGH University of Science and Technology, Poland, 1986.
• [2] J. Duda: Parametric optimization of neutral linear system with respect to the general quadratic performance index. Archiwum Automatyki i Telemechaniki, 33 (1988), 448-456.
• [3] J. Duda: Lyapunov functional for a linear system with two delays. Control andCybernetics, 39 (2010), 797-809.
• [4] J. Duda: Lyapunov functional for a linear system with two delays both retarded and neutral type. Archives of Control Sciences, 20 (2010), 89-98.
• [5] J. Duda: Lyapunov functional for a system with k-non-commensurate neutral time delays. Control and Cybernetics, 39 (2010), 1173-1184.
• [6] J. Duda: Parametric optimization of neutral linear system with two delays with P-controller.Archives of Control Sciences, 21 (2011), 363-372.
• [7] H. Górecki, S. Fuksa, P. Grabowski and A. Korytowski: Analysis and Synthesis of Time Delay Systems, John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore, (1989).
• [8] J. Hale and S. Verduyn Lunel: Introduction to Functional Differential Equations, New York, Springer, (1993).
• [9] E. F. Infante and W. B. Castelan: A Liapunov Functional For a Matrix Difference-Differential Equation. J. Differential Equations, 29 (1978), 439-451.
• [10] V. L. Kharitonov: Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. Int. J. of Control, 78 (2005), 783-800.
• [11] V. L. Kharitonov: Lyapunov matrices for a class of neutral type time delay systems. Int. J. of Control, 81 (2008), 883-893.
• [12] V. L. Kharitonov and E. Plischke: Lyapunov matrices for time-delay systems. Systems & Control Letters, 55 (2006), 697-706.
• [13] V. L. Kharitonov and A. P. Zhabko: Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39 (2003), 15-20.
• [14] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Publishers Dordrecht, 1991.
• [15] Yu. M. Repin: Quadratic Lyapunov functionals for systems with delay. Prikl. Mat. Mekh., 29 (1965), 564-566.