The 2D Burgers equation has extensively been considered as a benchmark problem by flow control researchers. The flavour of the problem is its multidimensionality and non-linearity, which are the reasons for making the governing equation a good start for developing a well defined understanding of control of flows. This paper demonstrates that an infinite dimensional observer can be designed, and by the aid of the observer, a simple boundary feedback control can be achieved under severe noise and disturbance scenarios. The results are in good compliance with the theoretical claims.
Aström, K. J. and Hägglund, T. H.1995: PID controllers: theory, design and tuning. ISA The Instrumentation, Systems, and Automation Society.
2.
Blender, R.1991: Iterative solution of nonlinear partial-differential equations. Journal of Physics A: Mathematical and General24, L509-L512.
3.
Boules, A. N. and Eick, I. J.2003: A spectral approximation of the two-dimensional Burgers equation. Indian Journal of Pure & Applied Mathematics34, 299-309.
4.
Burns, J. A., King, B. B. and Zietsman, L. 2002a: On the computation of singular functional gains for linear quadratic optimal boundary control problems. Proceedings of the 3rd Theoretical Fluid Mechanics Meeting, St. Louis, 24-26 June, AIAA, 2002-3074.
5.
Burns, J. A., King, B. B., Rubio, A. D. and Zietsman, L. 2002b: Functional gain computations for feedback control of a thermal fluid. Proceedings of the 3rd Theoretical Fluid Mechanics Meeting, St. Louis, 24-26 June, AIAA, 2002-2992.
6.
Donea, J. and Huerta, A.2003: Finite element methods for flow problemsJohn Wiley & Sons, 252-253.
7.
Efe, M.Ö. and Özbay, H. 2003a: Integral action based Dirichlét boundary control of Burgers equation. Proceedings of the IEEE International Conference on Control Applications (CCA’2003), Istanbul, 23-25 June, 1267-1272.
8.
Efe, M.Ö., Yuan, X., Özbay, H. and Samimy, M. 2004: Interpolating local models of POD using fuzzy decision mechanisms. 9th Mechatronics Forum International Conference,30 August 30-1 September, Ankara, Turkey, 347-356.
9.
Efe, M.Ö. and Özbay, H.2004: Low dimensional modeling and Dirichlét boundary controller design for Burgers equation. International Journal of Control7, 895-906.
10.
Farlow, S. J.1993: Partial differential equations for scientists and engineers. Dover Publications, 317-322.
11.
Hataue, I.1998: Mathematical and numerical analyses of dynamical structure of numerical solutions of two-dimensional fluid equations. Journal of the Physical Society of Japan67, 1895-1911.
12.
Hietarinta, L.2000: Comments on ‘Exact solutions of the teo-dimensional Burgers equation’. Journal of Physics A: Mathematical and General33, 5157-5158.
13.
Hinze, M. and Volkwein, S.2002: Analysis of instantaneous control for Burgers equation. Nonlinear Analysis50, 1-26.
14.
Krstić, M.1999: On global stabilization of Burgers equation by boundary control. Systems and Control Letters37, 123-141.
15.
Liu, W.-J. and Krstić, M.2000: Backstepping boundary control of Burgers equation with actuator dynamics. Systems and Control Letter41, 291-303.
16.
Liu, W.-J. and Krstić, M.2001: Adaptive control of Burgers equation with unknown viscosity. International Journal Adaptive Control and Signal Processing15, 745-766.
17.
McDonough, J. M. and Huang, M. T.2004: A‘poor man’s Navier Stokes equation’: derivation and numerical experiments—the 2-D case. International Journal for Numerical Methods in Fluids44, 545-578.
18.
Nishinari, K., Matsukidaira, J. and Takahashi, D.2001: Two-dimensional Burgers cellular automaton. Journal of the Physical Society of Japan70, 2267-2272.
19.
Park, H. M. and Jang, Y. D.2002: Control of Burgers equation by means of mode reduction. International Journal of Engineering Science38, 785-805.
20.
Sirendaoreji, S. J.1999: Exact solutions of the two-dimensional Burgers equation. Journal of Physics A: Mathematical and General32, 6897-6900.
21.
Vedantham, R.2000: Optimal control of the viscous Burgers equation using an equivalent index method. Journal of Global Optimization18, 255-263.
22.
Wescott, B. L. and Rizwan-uddin. 2001: An efficient formulation of the modified nodal integral method and application to the two-dimensional Burgers equation. Nuclear Science and Engineering139, 293-305.
23.
Zhu, Z.1996: Exact solutions for a two-dimensional KdV-Burgers-type equation. Chinese Journal of Physics34, 1101-1105.
