Sage Journals: Discover world-class research

Abstract

In this paper, we investigated the design of robust controllers for a class of nonlinear uncertain systems with bounded inputs, which have not yet been thoroughly discussed. Based on the variable structure system theory, we developed a novel stable sliding mode control scheme for this class of systems. A key feature of this control scheme is the introduction of a new generalized error as a complement to the conventional generalized error to form a meaningful error measure so that a new sliding mode controller incorporated with a two-input one-output fuzzy controller can be constructed to improve the reaching behavior of the system during the reaching phase as well as the tracking precision while in the boundary layer. The nonlinear bench mark problem, TORA, was used as an example to demonstrate the effectiveness of the design. Simulation results showed that, as compared with various available controllers in literature, much better responses to any initial conditions and to single-frequency sinusoidal disturbances can be obtained.

Keywords

Variable structure systems sliding mode controllers fuzzy controllers TORA

Get full access to this article

View all access options for this article.

References

Baik, I. C. , Kim, K. H. , Kim, H. S. , Moon, G. W. and Youn, M. J. , 1996, “Robust nonlinear speed control of PM synchronous motor using boundary layer integral sliding control with sliding load torque observer”, in IEEE PESC 96 Record., pp. 1242-1247.

Bartolini, G. and Pydynowski, P. , 1996, “An improved chattering free VSC scheme for uncertain dynamical systems,” IEEE Transactions on Automatic Control 41, 1220-1226.

Bartolini, G. , Ferrara, A. , and Usai, E. , 1997, “Applications of a sub-optimal discontinuous control algorithm for uncertain second order systems,” International Journal of Robust and Nonlinear Control 7, 299-319.

Bartonili, G. , Ferrara, A. , and Usai, E. , 1998, “Chattering avoidance by second order sliding mode control,” IEEE Transactions on Automatic Control 43, 241-246.

Bupp, R. T. , Berstein, D. S. , and Coppola, V. T. , 1995, “A benchmark problem for nonlinear control design: problem statement, experimental testbed, and passive nonlinear compensation,” in Proceedings of American Control Conference, Seattle, WA, pp. 4363-4367.

Bupp, R. T. , Bernstein, D. S. , and Coppola, V. T. , 1996, “Experimental implementation of integrator backstepping and passive nonlinear controllers on the RTAC testbed,” in IEEE Conference on Control Applications, Dearborn, MI, pp. 279-284.

Chern, T. L. , and Wu, Y. C. , 1993, “Design of brushless DC position servo systems using integral variable structure approach,” IEEE Electronic Power Applications 140, 27-34.

Diong, B. M. , 1997, “A sliding mode control approach to the benchmark problem for nonlinear control design,” in Proceedings IECON 97, pp. 68-72.

Escobar, G. , Ortega, R. , and Sira-Ramirez, H. , 1999, “Output feedback global stabilization of a nonlinear benchmark system using a saturated passivity-based controller,” IEEE Transactions on Control Systems Technology 7, 289-293.

10.

Filev, D. P. , and Yager, R. R. , 1993, “Three models of fuzzy logic controllers,” Cybernetics and Systems 24, 91-114.

11.

Gao, W. , and Hung, J. C. , 1993, “Variable structure control of nonlinear systems: a new approach,” IEEE Transactions on Industrial Electronics 40, 45-55.

12.

Hwang, G. C. , and S. C. Li , 1992, “A stability approach to fuzzy control design for nonlinear systems,” Fuzzy Sets and Systems 48, 279-287.

13.

Jankovic, M. , Fontaine, D. , and Kokotovic, P. V. , 1996, “TORA example: cascade- and passivity-based control designs,” IEEE Transactions on Control Systems Technology 4, 292-297.

14.

Jiang, Z. P. , Hill, D. J. , and Guo, Y. , 1998, “Stabilization and tracking via output feedback for the nonlinear benchmark system,” Automatica 34, 907-915.

15.

Jiang, Z. P. , and Kanellakopoulos, I. , 1999, “Global output-feedback tracking for a benchmark nonlinear system,” in IEEE Conference on Decision and Control, Phoenix, Arizona, pp. 4802-4807.

16.

Kawaji, S. , and Matsunaga, M. , 1991, “Fuzzy control of VSS type and its robustness,” in Proceedings 3rd IFSA Congress, Brussels, pp. 81-88.

17.

Lee, J. H. , Ko, J. S. , Chun, S. K. , Lee, J. J. , and Youn, M. J. , 1992, “Design of continuous sliding mode controller for BLDDM with prescribed tracking performance,” Conference Record, IEEE PESC 92, pp. 770-775.

18.

Levant, A. , 1993, “Sliding order and sliding accuracy in sliding mode control,” International Journal of Control 58, 1247-1263.

19.

Palm, R. , 1998, “Fuzzy sliding mode control”, in C. Bonivento , C. Fantuzzi and R. Rovatti (ed.), Fuzzy Logic Control Advances in Methodology, Singapore, World Scientific, pp. 75-109.

20.

Slotine, J.-J. E. , 1984, “Sliding controller design for non-linear systems,” International Journal of Control 40, 421-434.

21.

Slotine, J-J. E. and Li, W. , 1991, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ.

22.

Sira-Ramirez, H. , 1992, “On the sliding mode control of nonlinear systems,” Systems and Control Letters 19, 303-312.

23.

Wan, C.-J. , Bernstein, D.S. , and Coppola, V. T. , 1994, “Global stabilization of the oscillating eccentric rotor,” in Proceeding of IEEE Conference on Decision and Control, Orlando, FL, pp. 4024-4029.

A Novel Fuzzy Sliding Mode Control Scheme for Nonlinear Systems with Bounded Inputs

Abstract

Keywords

Get full access to this article

References