In this study we present a fuzzy robust control design which combines H∞ control performance with Tagagi-Sugeno (T-S) fuzzy control for the control of delayed nonlinear structural systems under external excitations. We design a nonlinear fuzzy controller based on parallel distributed compensation schemes. The controller design problem is reformulated as a linear matrix inequality (LMI) problem as derived from the Lyapunov theory. This robust method is designed to overcome the modeling error that can occur between delayed nonlinear structural systems with T-S fuzzy models. Given the fuzzy-model-based H∞ control and the stability conditions, the stability of a delayed nonlinear structural system under external excitation is ensured. Furthermore, the delayed nonlinear structural system is equipped with a tuned mass damper designed according to the first mode of frequency. The feedback gain of the fuzzy controller is found via the Matlab LMI toolbox. The proposed method is then applied to a delayed nonlinearly tuned mass damper system. The simulation results show that not only is the proposed method able to stabilize delayed nonlinear structural systems, but also has strong robustness in terms of preventing modeling errors and external excitations.
Aldemir, U. and Bakioglu, M., 2001, "Active structural control based on the prediction and degree of stability," Journal of Sound and Vibration247, 561-576.
2.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. , 1994, Linear Matrix Inequalities In System And Control Theory, Studies in Applied Mathematics (SIAM), Philadelphia, PA.
3.
Cao, H. and Li, Q.S., 2004, "New control strategies for active tuned mass damper systems ," Computers & Structures82, 2341-2350.
4.
Chen, B.S., Tseng, C.S., and Uang, H.J., 1999, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Transactions on Fuzzy Systems7, 571-585.
5.
Chen, C.W., Lin, C.L., Tasi, C.H., Chen, C.Y., and Yeh, K., 2007a, "A novel delay-dependent criteria for time-delay T-S fuzzy systems using fuzzy Lyapunov method," International Journal on Artificial Intelligence Tools, 16, 545-552.
6.
Chen, C.W., Yeh, K., Chiang, W.L., Chen, C.Y., and Wu, D.J., 2007b, "Modeling, H∞ control and stability analysis for structural systems using Takagi-Sugeno fuzzy model," Journal of Vibration and Control13, 1519-1534.
7.
Chen, B., Liu, X.P., and Tong, S.C., 2007c, "New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay," Fuzzy Sets and Systems158, 2209-2224.
8.
Chen, B.S., Tseng, C.S., and Uang, H.J., 2000, "Mixed H2 / H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach," IEEE Transactions on Fuzzy Systems8, 249-265.
9.
Chen, C.W., Chiang, W.L., Tasi, C.H., Chen, C.Y., Wang, M.H.L., 2006, "Fuzzy Lyapunov method for stability conditions of nonlinear systems," International Journal on Artificial Intelligence Tools15, 163-171.
10.
Chen, C.W., 2009, "Modeling and control for nonlinear structural systems via a NN-based approach," Expert Systems with Applications36, 4765-4772.
11.
Chen, C.Y., Hsu, R.C., and Chen, C.W., 2005, "Fuzzy logic derivation of neural network models with time delays in subsystems," International Journal on Artificial Intelligence Tools14, 967-974.
12.
C.W. Chen, Ken Yeh and F.R. Liu, 2009, "Adaptive fuzzy sliding mode control for seismically excited bridges with lead rubber bearing isolation," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems17(5), 705-727.
13.
Chen, C.W., Chiang, W.L., and Hsiao, F.H., 2004, "Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems," Mathematics and Computers in Simulation66, 523-537.
14.
C.Y. Chen, J.W. Lin, W.I. Lee, and C.W. Chen, 2010, "Fuzzy control for an oceanic structure: A case study in time-delay TLP system"Journal of Vibration and Control16(1), 147-160.
15.
Chen, P.C., Chen, C.W., and Chiang, W.L., 2009, "GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems," Expert Systems with Applications36, 5872-5879.
16.
Chen, P.C., Chen, C.W., and Chiang,W.L.2008, "GA-based fuzzy sliding mode controller for nonlinear systems," Mathematical Problems in Engineering, DOI: 10.1155/2008/325859.
17.
Chen, X.J., Sun, Z.Q., and He, Y.Y., 1998, "Analysis and design of fuzzy controller and fuzzy observer ," IEEE Transactions on Fuzzy Systems6, 41-51.
18.
Feng, G., Chen, C.-L., Sun, D., and Zhu, Y., 2005, "H∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities," IEEE Transactions on Fuzzy Systems13, 94-103.
19.
Frahm, H., 1911. Device for damping vibrations of bodies. US patent 989-958.
20.
Ghaboussi, J. and Joghataie, A., 1995, "Active control of structures using neural networks," ASCE Journal of Engineering Mechanics121, 555-567.
21.
Guerra, T.M. and Vermeriren, L., 2001, "Control law for Takagi-Sugeno fuzzy models," Fuzzy Sets and Systems120, 95-108.
22.
Horn, R. and Johnson, C., 1991, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK.
23.
Hsiao, F.H., Chen, C.W., Wu, Y.H., and Chiang, W.L., 2005a, "Fuzzy controllers for nonlinear interconnected TMD systems with external force," Journal of The Chinese Institute of Engineers28, 175-181.
24.
Hsiao F.H., Chen C.W., Liang Y.W., Xu S.D. and Chiang W.L., 2005b, "T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays," IEEE Transactions on Circuits & Systems-I52, 1883- 1893.
25.
Hsiao, F.H., Hwang, J.D., Chen, C.W., and Tsai, Z.R., 2005c, "Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control," IEEE Transactions on Fuzzy Systems, 13, 152- 163.
26.
Hsieh, T.-Y., Wang, M.H.L., Chen, C.-W., Chen, C.-Y., Yu, S.-E., Yang, H.-C., and Chen, T.-H., 2006, "A new viewpoint of s-curve regression model and its application to construction management," International Journal on Artificial Intelligence Tools15, 131-142.
27.
Li, H.J. and Hu, S.L.J., 2002, "Tuned mass damper design for optimally minimizing fatigue damage," Journal of Engineering Mechanics126, 703-707.
28.
Li, J., Wang, H.O., Niemann, D., and Tanaka, K., 2000, "Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems: An LMI approach," Information Sciences123, 201-221.
29.
Li, X. and de Souza, C.E., 1997, "Criteria for robust stability and stabilization of uncertain linear systems with state delay," Automatica33,1657-1662.
30.
Limanond, S. and Si, J., 1998, "Neural-network-based control design: An LMI approach ," IEEE Transactions on Neural Networks9, 1422-1429.
31.
Lu, L.T., Chiang, W.L., Tang, J.P., Liu M.Y., and Chen, C.W., 2003, "Active control for a benchmark building under wind excitations ," Journal of Wind Engineering and Industrial Aerodynamics91, 469-493.
32.
Ma, X.J., Sun, Z.Q., and He, Y.Y., 1998, "Analysis and design of fuzzy controller and fuzzy observer ," IEEE Transactions on Fuzzy Systems6, 41-51.
33.
Nagashima, I., Maseki, R., Asami, Y., Hirai, J., and Abiru, H., 2001,"Performance of hybrid mass damper system applied to a 36-storey high-rise building," Earthquake Engineering and Structural Dynamics121, 1615- 1637.
34.
Rao, M.M. and Datta, T.K., 2005, "Predictive active control of building frames with a solo neurocontroller," Journal of Vibration and Control11, 627-641.
35.
Takagi, T. and Sugeno, M., 1985, "Fuzzy identification of systems and its applications to modeling and control," IEEE Transactions on Systems, Man, and Cybernetics15, 116-132.
36.
Tanaka, K., and Sano, M., 1994, "A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer," IEEE Transactions on Fuzzy Systems, 2, 119-134.
37.
Tanaka, K. and Sugeno, M., 1992, "Stability analysis and design of fuzzy control systems ," Fuzzy Sets and Systems45, 135-156.
38.
Tanaka, K., Hori, T., and Wang, H.O., 2003, "A multiple Lyapunov function approach to stabilization of fuzzy control systems," IEEE Transactions on Fuzzy Systems11, 582-589.
39.
Tanaka, K., Ikeda, T., and Wang, H.O., 1996, "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities," IEEE Transactions on Fuzzy Systems4, 1-13.
40.
Tsai, C.H., Chen, C.W., Chiang, W.L., and Lin, M.L., 2008, "Application of geographic information system to the allocation of disaster shelters via fuzzy models," Engineering Computations25, 86-100.
41.
Wang, H.O., Tanaka, K., and Griffin, M.F., 1996, "An approach to fuzzy control of nonlinear systems: stability and design issues," IEEE Transactions on Fuzzy Systems4, 14-23.
42.
Wang, H.O., Tanaka, K., and Griffin, M.F., 1995, "Parallel distributed compensation of nonlinear systems by Takagi and Sugeno’s fuzzy model," in Proceedings of 4th IEEE International Conference on Fuzzy Systems, Yokohama, Japan, March 20-24, pp. 531-538.
43.
Wang, J.F. and Lin, C.C., 2005, "Seismic performance of multiple tuned mass dampers for soil-irregular building interaction system," International Journal of Solids and Structures42, 5536-5554.
44.
Wang, J.F., Lin, C.C., and Chen, B.L., 2003, "Vibration suppression for high speed railway bridges using tuned mass dampers," International Journal of Solids and Structures40, 465-491.
45.
Wang, L.K., Leung, F.H.F., and Tam, P.K.S., 1996, "Fuzzy model-based controller for inverted pendulum," Electron. Letters32, 1683-1685.
46.
Xu, S.Y. and Lam, J., 2005, "Robust H ∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers," IEEE Transactions on Fuzzy Systems13, 82-93.
47.
Yang, J.N., Wu, J.C., and Agrawal A.K., 1995a, "Sliding mode control for nonlinear and hysteretic structures ," Journal of Engineering Mechanics-ASCE121, 1330-1339.
48.
Yang, J.N., Wu, J.C., Kawashima, K., and Unjoh, S., 1995b, "Hybrid control of seismic-excited bridge structures ," Earthquake Engineering and Structural Dynamics24, 1437-1451.
49.
Yeh, K., Chen, C.Y., and Chen, C.W., 2008, "Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method," Applied Mathematics and Computation205, 568-577.
50.
Yeh, K. and Chen, C.W.2010 "Stability analysis of interconnected fuzzy systems using the fuzzy Lyapunov method," Mathematical Problems in Engineering- An Open Access Journal, DOI: 10.1155/2010/734340.
51.
Zadeh, L.A., 1965, "Fuzzy sets," Information and Control8, 338-353.
