In this paper we will consider asymptotic stabilization using both static and dynamic variable structure controllers for the active control of mechanical vibrations. The proposed approach is mainly based on geometric input-output linearization, and is applied to a mechanical system with one degree of freedom, which uses an electro-hydraulic actuator. Computer simulations are used to show that the dynamic variable structure control system proposed exhibits robust behavior in the face of external disturbances and parameter variations.
Aeyels, D. , 1988, “Some remarks on the stability of nonlinear systems by smooth feedback,” in Perspectives in Control Theory, B. Jakubczyk , K.Malanowsky and W.Respondek (Eds), Proceedings of the Sielpia Conference, Sielpia, Poland , pp. 1–11.
2.
Alleyne, A. and Hedrick, J.K. , 1995, “ Nonlinear adaptive control of active suspensions ,” Vehicle System Dynamics3(1), 94–101 .
3.
Alleyne, A. , Neuhaus, P. , and Hedrick, J.K. , 1993, “ Application of nonlinear control theory to electronically controlled suspensions ,” Vehicle System Dynamics22, 309–320 .
4.
Beard, A.M. , Shubert, D.W. , and Von Flotow, A.H. , 1994, “ A practical product implementation of an active/passive vibration isolation system ,” in Proceedings of ASME Active Control of Vibration and Noise 75, pp. 485–492 .
5.
Bender, E.K. , 1990, “ Optimum linear preview control with application to vehicle suspensions ,” ASME Journal of Basic Engineering75, 485–492 .
6.
Fisher, D. and Isermann, R. , 2004, “ Mechatronic semi-active and active vehicle suspensions ,” Control Engineering Practice12(11), 1353–1366 .
7.
Gaspar, P. , Szaszi, I. , and Bokor, J. , 2003, “ Design of robust controllers for active vehicle suspension using the mixed synthesis ,” Vehicle System Dynamics40(4), 193–228 .
8.
Huang, S. J. and Chao, H. C. , 2000, “ Fuzzy logic controller for a vehicle active suspension system ,” IMechE Journal of Automobile Engineering214(D1), 1–12 .
9.
Isidori, A. , 1989, Nonlinear Control Systems, Springer-Verlag, Berlin .
10.
Kim, C. and Ro, P. I. , 1998, “ A sliding mode controller for vehicle active suspension systems with nonlinearities ,” IMechE Journal of Automobile Engineering212(D), 79–92 .
11.
Kim, C. , Ro, P. I. , and Kim, H. , 1999, “ Effect of the suspension structure on equivalent suspension parameters ,” IMechE Journal of Automobile Engineering213(D), 457–470 .
12.
Llanes-Santiago, O. and Sira-Ramirez, H. , 2000, “Control activo de vibraciones mecánicas mediante platitud diferencial,” in Memorias XII Congreso Latinoamericano de Control Automático, Cali, Colombia , Vol. 1, pp. 829–834.
13.
Llanes-Santiago, O. , Esandi, M.T. , and Sira-Ramirez, H. , 1993, “ Adaptive chattering-free sliding mode control of nonlinear uncertain systems ,” in Proceedings of the 2nd European Control Conference, Groningen The Netherlands, Vol. 2, pp. 829–834 .
14.
Nijmeijer, H. and Van der Schaft, A. , 1990, Nonlinear Dynamical Control Systems, Springer-Verlag, NewYork .
15.
Park, J. H. and Kim, Y. S. , 1999, “ An H∞ controller for active suspension and its robustness based on a full-car model ,” in Proceedings of 14th World Congress of IFAC, Beijing, China, pp. 503–508 .
16.
R'os-Bolivar, M. and Llanes-Santiago, O. , 2000, “Control of vibration via second order sliding mode control,” in 6th International Workshop on Variable Structure Systems, VSS’2000, Sidney, Australia .
17.
Sam, Y. , Osman, J.H. , and Ghani, M.R. , 2004, “ A class of proportional-integral sliding mode control with application to active suspension system ,” Systems & Control Letters51(3/4), 217–224 .
18.
Schinkel, M. , Wang, Y. , and Hunt, K. , 2002, “ Control of uncertain and parameter-variant piecewise linear systems ,” International Journal of Control75(16/17), 1368–1375 .
19.
Sira-Ramirez, H. , 1988, “ Differential geometric methods in variable structure control ,” International Journal of Control48(4), 1359–1392 .
20.
Sira-Ramirez, H. and Llanes-Santiago, O. , 1992, “ An extended system approach to dynamical pulse-frequency-modulation control of nonlinear systems ,” in Proceedings of the 31st IEEE Conference on Decision and Control, Tucson, AZ, Vol. 1, pp. 2376–2380 .
21.
Slotine, J. J. E. and Li, W. , 1991, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, New Jersey .
22.
Spentzas, K. N. and Kanarachos, S. A. , 2002, “ A neural network approach to the design of vehicle's non-linear hybrid suspension system ,” IMechE Journal of Engineering Manufacture216(B5), 833–838 .
23.
Sunwoo, M. and Cheak, K. C. , 1991, “ Investigation of adaptive control approaches for vehicle active suspension systems ,” in Proceedings of the American Control Conference, pp. 1542–1547 .
24.
Sunwoo, M. , Cheak, K. C. , and Huang, N. J. , 1991, “ Model reference adaptive control for vehicle active suspension systems ,” IEEE Transactions on Industrial Electronics38(3), 217–222 .
25.
Thompson, A. G. , 1970, “ Design of active suspension ,” Proceedings of the Institution of Mechanical Engineers185(36), 553–563 .
26.
Thomson, W. T. , 1981, Theory of Vibration with Applications, Prentice-Hall, Englewood Cliffs, New Jersey .
27.
Ting, C. S. and Kung, F. C. , 1995, “ Design of fuzzy controller for active suspension system ,” Mechatronics5(4), 365–383 .
28.
Tomizuka, M. , 1976, “ Optimum linear preview control with applications to vehicle suspensions ,” ASME Journal of Dynamic Systems Measurement and Control98, 309–315 .
29.
Wilson, D. , Sharp, R. S. , and Hassan, S.A. , 1986, “ The application of linear optimal control theory to the design of active automotive suspensions ,” Vehicle System Dynamics15, 105–118 .
30.
Yeh, E. C. and Tsao, Y. J. , 1991, “ A fuzzy preview control scheme of active suspension for rough road ,” International Journal of Vehicle Design100, 166–180 .
