Volume 18 Issue 5
Oct.  2021
Turn off MathJax
Article Contents
Liang-Cheng Cai. Simultaneous Stabilization of Port-Hamiltonian Systems Subject to Actuation Saturation and Input Delay. International Journal of Automation and Computing, vol. 18, no. 5, pp.849-854, 2021. https://doi.org/10.1007/s11633-015-0928-4
 Citation: Liang-Cheng Cai. Simultaneous Stabilization of Port-Hamiltonian Systems Subject to Actuation Saturation and Input Delay. International Journal of Automation and Computing, vol. 18, no. 5, pp.849-854, 2021.

# Simultaneous Stabilization of Port-Hamiltonian Systems Subject to Actuation Saturation and Input Delay

##### doi: 10.1007/s11633-015-0928-4
• Corresponding author: Liang-Cheng Cai  received the Ph. D. degree in the control theory and engineering from the Central South University, China in 2013. Since 2013, he is with Department of Electrical Engineering, Southwest Jiaotong University, China.
His research interests include control, motors, inverter and simulation.
E-mail: caispss@163.com
(Corresponding author)
• Accepted Date: 2015-04-08
• Publish Online: 2015-11-06
• Publish Date: 2021-10-01
• This paper investigates the simultaneous stabilization of Port-Hamiltonian (PH) systems subject to actuation saturation (AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay. Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.

• Recommended by Associate Editor Yuan-Qing Xia
•  [1] A. van der Schaft. $L_2$-gain and Passivity Techniques in the Nonlinear Control, London, Great Britain: Springer-Verlag, 2000. [2] D. A. Dirksz, J. M. A. Scherpen. Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica, vol. 48, no. 6, pp. 1045-1056, 2012. [3] F. Castaños, G. Dmitry, V. Hayward, H. Michalska. Implicit and explicit representations of continuous-time port-Hamiltonian systems. Systems & Control Letters, vol. 62, no. 3, pp. 324-330, 2013. http://www.sciencedirect.com/science/article/pii/S0167691113000261 [4] T. C. Ionescu, A. Astolfi. Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems. Automatica, vol. 49, no. 8, pp. 2424-2434, 2013. [5] L. C. Cai, Y. He, M. Wu. On the effects of desired damping matrix and desired Hamiltonian function in the matching equation for Port-Hamiltonian systems. Nonlinear Dynamics, vol. 72, no. 1-2, pp. 91-99, 2013. [6] M. Schöberl, A. Siuke. Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators. Automatica, vol. 50, no. 2, pp. 607-613, 2014. [7] M. Seslija, J. M. A. Scherpen, A. van der Schaft. Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems. Automatica, vol. 50, no. 2, pp. 369-377, 2014. [8] R. Ortega, A. van der Schaft, B. Maschke, G. Escobar. Interconnection and damping assignment passivity-based control of Port-controlled Hamiltonian systems. Automatica, vol. 38, no. 4, pp. 585-596, 2002. [9] R. Ortega, E. García-Canseco. Interconnection and damping assignment passivity-based control: A Survey. European Journal of Control, vol. 10, no. 5, pp. 432-450, 2004. [10] R. Ortega, A. van der Schaft, F. Castanos, A. Astolfi. Control by interconnection and standard passivity-based control of port-Hamiltonian systems. IEEE Transactions on Automatic Control, vol. 53, no. 11, pp. 2527-2542, 2008. [11] A. Donaire, S. Junco. On the addition of integral action to port-controlled Hamiltonian systems. Automatica, vol. 45, no. 8, pp. 1910-1916, 2009. [12] A. Astolfi, R. Ortega, A. Venkatraman. A globally exponentially convergent immersion and invariance speed observer for machanical systems with non-holonomic constraints. Automatica, vol. 46, no. 1, pp. 182-189, 2010. [13] A. Venkatraman, R. Ortega, I. Sarras, A. van der Schaft. Speed observation and position feedback stabilization of partially linearizable mechanical systems. IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1059-1074, 2010. [14] A. Donaire, T. Perez. Dynamic positioning of marine craft using a port-Hamiltonian framework. Automatica, vol. 48, no. 5, pp. 851-856, 2012. [15] T. S. Hu, Z. L. Lin. Control Systems with Actuator Saturation: Analysis and Design, Boston, USA: Birkhauser, 2001. [16] Z. R. Xi, G. Feng, D. Z. Cheng, Q. Lu. Nonlinear decentralized saturated controller design for power systems. IEEE Transactions on Control System Technology, vol. 11, no. 4, pp. 539-547, 2003. [17] A. R. Wei, Y. Z. Wang. Stabilization and $H_{\infty}$ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica, vol. 46, no. 12, pp. 2008-2013, 2010. [18] R. Pasumarthy, C. Y. Kao. On stability of time-delay Hamiltonian systems. In Proceeding of the American Control Conference, IEEE, St. Louis, USA, pp. 4909-4914, 2009. [19] W. W. Sun. Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation. Applied Mathematics and Computation, vol. 217, no. 23, pp. 9625-9634, 2011. [20] R. M. Yang, Y. Z. Wang. Finite-time stability analysis and $H_{\infty}$ control for a class of nonlinear time-delay Hamiltonian systems. Automatica, vol. 49, no. 2, pp. 390-401, 2013. [21] L. C. Cai, Y. He, M. Wu. Energy-shaping for Hamiltonian control systems with time delay. Journal of Control Theory and Application, vol. 11, no. 3, pp. 436-441, 2013. [22] Y. Z. Wang, G. Feng, D. Z. Cheng. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica, vol. 43, no. 3, pp. 403-415, 2007. [23] A. R. Wei, Y. Z. Wang, X. M. Hu. Parallel simultaneous stabilization of a set of port-controlled Hamiltonian systems subject to actuator saturation. Journal of Systems Science and Complexity, vol. 24, no. 1, pp. 120-139, 2011. [24] Z. R. Xi, D. Z. Cheng. Passivity-based stabilization and $H_{\infty}$ control of the Hamiltonian control systems with dissipation and its applications to power systems. International Journal of Control, vol. 73, no. 18, pp. 1686-1691, 2000. [25] Q. Lu, Y. Sun. Nonlinear Control and Power Systems, Beijing, China: Scientific Press, 1993.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures(3)  / Tables(2)

用微信扫码二维码

分享至好友和朋友圈