Modified Clipped-LQR Method for Semi-Active Vibration Reduction Systems with Hysteresis

Abstract:

Smart materials are being applied more and more widely in semi-active vibration reduction systems. Actuators built with their use are characterized by nonlinearities and hysteretic effects. Their omission in mathematical descriptions may lead to deterioration of the vibration reduction systems. For that reason, it is important to take into account these negative phenomena associated with the actuators at the controller synthesis stage. One method for determining the control laws in semi-active vibration reduction systems that is frequently discussed in academic literature is “Clipped-LQR”. The present paper proposes modification of that method to allow inclusion in the controller synthesis of the hysteretic properties and other nonlinearities of an actuator. The method developed was verified by determining the controller for the semi-active suspension of a machine operator’s seat. A magnetorheological damper was used as an actuator. The dynamic properties of the foam covering of the operator’s seat were included in model. Simulation tests were performed on the vibration reduction system and function of vibration transmissibility was determined. The semi-active vibration reduction system tested was compared to a passive system. The considerations presented herein relate to the semi-active suspension of a machine operator’s seat, and the method presented may be applied to other controlled systems with many degrees of freedom.

• Periodical: Solid State Phenomena (Volume 177)
• Pages: 10-22
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.177.10
• Online since: July 2011
• Authors: Marek Sibielak, Waldemar Rączka, Jarosław Konieczny
• Keywords: Clipped LQR, Magnetoreological (MR) Damper, Semiactive Seat Suspension

References

[1] W. Rączka, M. Sibielak, J. Konieczny: Smart vibration isolation systems with shape memory alloy, proceedings of 7th International Carpathian Control Conference (Czech Republic, 2006).

[2] M. Sibielak: Identification of hysteresis operator for a controllable damper with piezoelectric actuator, proceedings 7th Conference on Active noise and vibration control methods : Wigry, Poland, (2005).

[3] W. Rączka: Mechanics and Control, AGH University of Science and Technology Krakow, Vol. 22 (2003), p.389–394.

[4] W. Rączka: Hydraulika a Pneumatika Vol. 7 (2005), p.40–42.

[5] W. Rączka: Testing of a spring with controllable stiffness, Mechanics, AGH University of Science and Technology. Commission on Applied Mechanics of Polish Academy of Sciences. Cracow vol. 25 (2006), p.79–86.

[6] C.M. Harris: Shock and Vibration Handbook (McGraw-Hill, New York, 1987).

[7] C.H. Hansen, S. Snyder: Active Control of Noise and Vibration (Spon Press, London, 1997).

[8] J. Kowal, J. Pluta, J. Konieczny, A. Kot: Energy recovering in active vibration isolation system – results of experimental research, J. of Vibration and Control Vol. 14 no. 7 (2008) p.1075–1088.

DOI: 10.1177/1077546308088980

[9] J. Konieczny, J. Kowal: Full active vehicle suspension – experimental data, Proceedings, ACTIVE, Canada (2009).

[10] L.R. Miller: Tuning passive, semi-active, and fully active suspension systems, Proceeding of the 27th Conference on Decision and Control, Austin, TX, (1988).

DOI: 10.1109/cdc.1988.194694

[11] D.C. Karnopp, M.J. Crosby, R.A. Harwood: J. of Eng. for Industry Vol. 96 (1974), p.619–626.

[12] D.C. Karnopp: J. of Dynamic Systems, Measur., and Control Vol. 112 (1990), p.448–455.

[13] X. Wu, M.J. Griffin: J. of Sound and Vibration Vol. 203 (5) (1997), p.781–793.

[14] Y. Liu, T.P. Waters, M.J. Brennan: J. of Sound and Vibration Vol. 280 (2005), p.21–39.

[15] Z. Gosiewski, A. Mystkowski: Mech. Systems and Signal Processing Vol. 22, (2008) pp.1297-1303.

[16] S. Hurlebaus, L. Gaul: Mech. Systems and Signal Processing Vol. 20 (2006), p.255–281.

[17] J. Konieczny, W. Rączka, M. Sibielak: Experimental investigation of the semi-active vibration isolation system, proceedings 9th Conference on Active noise and vibration control methods, Poland, (2009).

[18] M. Zapateiro, N. Luo, H. R. Harimi: Solid State Phen. Vols. 147-149 (2009), pp.839-844.

[19] B. Sapiński: Solid State Phenomena Vols. 147-149 (2009), pp.819-824.

[20] E.J. Krasnicki: Shock and Vibration Bulletin Vol. 50 (1980), p.69–76.

[21] J. Alanoly, S. Sankar: J. of Sound and Vibration Vol. 126 (1) (1988), p.145–156.

[22] J. Alanoly, S. Sankar: J. of Mechanisms, Transmissions and Automation in Design Vol. 109 (1987), p.242–247.

DOI: 10.1115/1.3267444

[23] J.S. Lane, A.A. Ferri, B.S. Heck: Design Engineering Division Vol. 49, (1992), p.165.

[24] T. Pinkaew, Y. Fujino: Engineering Structures Vol. 23 (2001), p.850–856.

[25] S. E. Lyshevski: Optimal control of nonlinear continuous-time systems: design of bounded controllers via generalized nonquadratic functional, Proceedings of American control conference, (1998) (p.205–209).

DOI: 10.1109/acc.1998.694659

[26] R. Beard, G. Saridis, J. Wen: Automatica Vol. 33(12), (1997), p.2159–2177.

[27] R. Beard, G. Saridis, J. Wen: J. of Optimi. Theory and Appl. Vol. 96(3), (1998), p.589.

[28] E. Guglielmino, T. Sireteanu, C.W. Stammers, G. Ghita, M. Giuclea: Semi-active Suspension Control, Springer (2008).

DOI: 10.3397/1.3110986

[29] S. M. Savaresi, Ch. Poussot-Vassal, C. Spelta, O. Sename, L. Dugart: Semi-active suspension control design for vehicles (Elsevier, NY 2010 ).

DOI: 10.1016/b978-0-08-096678-6.00006-7

[30] En RongWang, Xiao Qing Ma, S Rakhela and C Y Su: Modelling the hysteretic characteristics of a magnetorheological fluid damper, Proc. Instn Mech. Engrs Vol. 217.

[31] M. Sibielak: Optimal control smart systems, proceedings 8th Conference on Active noise and vibration control methods, Poland, (2007).

[32] G. Yang, B.F. Spencer Jr, J. D. Carlson, M. K. Sain: Eng. Struct., Vol. 24, (2002), pp.309-323.

[33] J. Konieczny: Modelling of the electrohydraulic full active vehicle suspension, Engineering Transactions, (2008) Vol. 56, iss. 3 pp.247-268.

[34] J. Konieczny, J. Kowal: A pole placement controller for active vehicle suspension, Archives of Control Sciences, (2005) Vol. 15, iss. 1 pp.97-116.

[35] K. Jaracz, J. Pluta, M. Sibielak: Testing the Electrohydraulic Servo Driver Sensitivity to Supply Pressure Changes. Proceedings of 5rd International Carpathian Control Conference Zakopane, Poland, May 25-28, (2004) pp.433-438.

[36] J. Pluta, W. Rączka, M. Sibielak: Optimision of Parameters of an Electrohydraulic Serwomechanism Controller. Proceedings of 4rd International Carpathian Control Conference Slovak Republic. May 26-29, (2003) pp.556-561.

[37] J. Kwaśniewski, A. Piotrowska, W. Rączka, M. Sibielak: The mathematical model of a hydrostatic transmission for controller design. Proceedings Conference of the Modelling and Simulation. Palm Spring, California, USA (2003) pp.275-280.

[38] Sk. Faruke Ali, A. Ramaswamy: J. Dynamic Systems, Measur. And Control Vol. 131 (2009).