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Abstract

A switched-control technique for fluid distribution systems is presented. It is based on a compartment model of the distribution network consisting of a number of interconnected reservoirs. The unforced flows among reservoirs and environment only depend (non-linearly) on the stored water levels (state variables), which are also influenced by the water demands (disturbances) and by the forced flows of the water pumped into or out of the reservoirs (controlled variables). The control objective is to drive the system to the equilibrium state and keep it there. This goal can be achieved by means of a state-feedback control, which entails switching the controlled inputs among given values according to the current system state. Necessary and sufficient stabilizability conditions are provided. The global asymptotic stability of the overall control system is proved by resorting to a suitable control-Lyapunov function. An experiment is worked out to show the performance of the adopted control policy.

Keywords

Lyapunov functions stability state feedback switched control water distribution networks.

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References

Antsaklis, P. and Nerode, A., editors. 1998: Special issue on hybrid control systems. IEEE Transactions on Automatic Control 43, 457-587.

Biscos, C. , Mulholland, M. , Le Lann, M.V. , Buckley, C.A. and Brouckaert, C.J. 2003: Optimal operation of water distribution networks by predictive control using MINLP. Water SA 29, 393-404.

Blanchini, F. and Miani, S. 2007: Set-theoretic methods in control. Birkhäuser, Systems & Control Series: Foundations & Applications.

Blanchini, F. , Miani, S. and Ukovich, W. 2000: : Control of production-distribution systems with unknown inputs and system failures. IEEE Transactions on Automatic Control 45, 1072-81.

Blanchini, F. , Rinaldi, F. and Ukovich, W. 1997: : Least inventory control of multi-storage systems with non-stochastic unknown input. IEEE Transactions on Robotics and Automation 13, 633-45.

Branicky, M.S. 1998: : Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control 43, 475-82.

Cembrano, G. , Wells, G. , Quevedo, J. , Perez, R. and Argelaguet, R. 2000: : Optimal control of a water distribution network in a supervisory control system. Control Engineering Practice 8, 1177-88.

DeCarlo, R.A. , Branicky, M.S. , Pettersson, S. and Lennartsson, B. 2000: : Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of IEEE 88, 1069-82.

De Poli, G. and Viaro, U. 1980: : Design and control of optimal water distribution systems . Ricerche di Automatica 11, 111-31.

10.

Geem, Z.W. 2006: : Optimal cost design of water distribution networks using harmony search. Engineering Optimization 38, 259-77.

11.

Johansson, K.H. , Egerstedt, M. , Lygeros, J. and Sastry, S. 1999: : On the regularization of Zeno hybrid automata. Systems & Control Letters 38, 141-50.

12.

Koroleva, O.I. and Krstic, M. 2004: Approximate solutions to nonlinear fluid networks with periodic inputs. Proceedings of the American Control Conference, Boston, MA, 3, 2284-89.

13.

Larson, R.E. and Keckler, W.G. 1969: Applications of dynamic programming to the control of water resource systems. Automatica 5, 15-26.

14.

Liberzon, D. 2003: Switching in system and control. Birkhäuser, Systems & Control Series: Foundations & Applications.

15.

Martinez, F. , Hernandez, V. , Alonso, J.M. , Rao, Z. and Alvisi, S. 2007: : Optimizing the operation of the Valencia water distribution network. Journal of Hydroinformatics 9, 65-78.

16.

Mercangöz, M. and Doyle, F.J. III 2007: Distributed model predictive control of an experimental four-tank system. Journal of Process Control 17, 297-308.

17.

Moss, F.H. and Segall, A. 1982: An optimal control approach to dynamic routing in networks . IEEE Transactions on Automatic Control 27, 329-39.

18.

Shamir, U. 1979: Optimization in water distribution systems engineering . Mathematical Programming Study 11, 65-84.

19.

Sun, Z. and Ge, S. 2005: Switched linear systems control and design. Springer, Communications and Control Engineering Series.

20.

Terra, M.H. , dos Reis, J.A.T. , Chaudhry, F.H. and Schiavetto de Souza, R. 2002: Control of transients in water distribution networks by H∞ control. Journal of the Brazilian Society of Mechanical Sciences 24, 286-92.

21.

Trawicki, D. and Urbowska, W. 2007: Hybrid optimization algorithms for control of water distribution systems. Proceedings of 11th IFAC/ IFORS/IMACS/IFIP Symposium Large Scale Complex Systems Theory and Applications, Gdansk, paper no. 32 (CD-ROM).

22.

Ulanicki, B. , Kahler, J. and See, H. 2007: Dynamic optimization approach for solving an optimal scheduling problem in water distribution systems. Journal of Water Resources Planning and Management 133, 23-32.

23.

Wang, J. 2007: Switched-control strategies for optimized operation of DWDS. Proceedings of 11th IFAC/IFORS/IMACS/IFIP Symposium Large Scale Complex Systems Theory and Applications, Gdansk, paper no. 67 (CD-ROM).

24.

Wang, J. and Brdys, M.A. 2006: Optimal operation of water distribution systems under full range of operating scenarios. Proceedings of 6th UKACC International Control Conference, Glasgow , paper no. 112 (CD-ROM).

Switched control of fluid networks

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