Previous |  Up |  Next

Article

Keywords:
decoupling control law; geometric control of dynamic systems
Summary:
The geometric control properties of vehicles with active suspensions are analyzed. A special attention is devoted to the problem of disturbance decoupling. Active suspensions of advanced vehicles allow the active rejection of external disturbances exerted on the sprung mass of the vehicle and caused by road surface irregularity. We focus on the road irregularity disturbances with the purpose of isolating the chassis from vibrations transmitted through suspensions. The paper is aimed at the synthesis of a decoupling control law of the regulated outputs, i. e., roll, pitch and chassis height, from the external disturbances. The paper emphasizes that disturbance decoupling can be thought as a structural property of road vehicles with active suspensions. The framework throughout is the geometric approach to the control of dynamic systems. It is shown that a controlled and conditioned invariant subspace exists such that it allows the geometric disturbance localization. The decoupling problem with stability and the algebraic feedback of suspension heights, i. e. the system measurements, are considered. Simulations with real data are included to validate theoretical results. Saturating actuators are also considered in order to model a more realistic case.
References:
[1] Barbagli F., Marro G., Mercorelli, P., Prattichizzo D.: Some results on output algebraic feedback with applications to mechanical systems. In: Proc. 37th IEEE Internat. Conference Decision Control, Tampa, Florida 1998, pp. 3545–3550
[2] Marro G., Barbagli F.: The algebraic output feedback in the light of dual–lattice structures. Kybernetika 35 (1999), 6, 693–706 MR 1747970
[3] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, Englewood Cliffs, N. J. 1992 MR 1149379 | Zbl 0758.93002
[4] Basile G., Marro G.: L’invarianza rispetto ai disturbi studiata nello spazio degli stati. Rendiconti della LXX Riunione Annuale AEI, 1969
[5] Basile G., Marro G.: A state space approach to non–interacting controls. Ricerche Automat. 1 (1970), 1, 68–77
[6] Chen, Ben M.: Solvability conditions for the disturbance decoupling problems with static measurement feedback. Internat. J. Control 68 (1997), 51–60 DOI 10.1080/002071797223721 | MR 1687550
[7] Chen, Ben M., Mareels, Iven M. Y., Zheng,, Yu Fan, Zhang, Cishen: Solutions to disturbance decoupling problem with constant measurement feedback for linear systems. In: Proc. 38th IEEE Internat. Conference Decision Control, 1999, pp. 4062–4067
[8] Hirata T., Koizumi S., Takahashi R.: $H^{\infty }$ control of railroad vehicle active suspension. Automatica 31 (1995), 1, 13–24 DOI 10.1016/0005-1098(94)E0048-M | MR 1312200
[9] Hrovat D.: Optimal active suspension structures for quarter–car vehicle models. Automatica 26 (1990), 5, 845–860 DOI 10.1016/0005-1098(90)90002-Y
[10] Koumboulis F. N., Tzierakis K. G.: Meeting transfer function requirement via static measurement output feedback. J. Franklin Institute – Engineering and Applied Mathematics (1998), 661–677 DOI 10.1016/S0016-0032(96)00144-5 | MR 1615521
[11] Peng H., Tomizuka M.: Control of Front–wheel–steering Rubber Tire Vehicles. Report UCB–ITS–PRR–90–5 of PATH program, Institute of Transportation Studies, University of California at Berkley, Berkeley 1990
[12] Prattichizzo D., Mercorelli P., Bicchi, A., Vicino A.: Geometric disturbance decoupling control of vehicles with active suspensions. In: Proc. IEEE Internat. Conference on Control Applications, Trieste 1998
[13] Prattichizzo D., Mercorelli P., Bicchi, A., Vicino A.: Active suspensions decoupling by algebraic feedback. In: Proc. 6th IEEE Mediterranean Conference on Control and Systems, Sardinia 1998
[14] Rajamani R., Hedrick J. K.: Adaptive observers for active automotive suspensions: theory and experiments. IEEE Trans. Control System Technology 3 (1995), 1, 86–92 DOI 10.1109/87.370713
[15] Ray L. R.: Nonlinear state and tire force estimation for advanced vehicle control. IEEE Trans. Control System Technology 3 (1995), 1, 117–124 DOI 10.1109/87.370717
[16] Rosenbrock H. H.: State–space and Multivariable Theory. Thomas Nelson and Sons Ltd., 1970 MR 0325201 | Zbl 0246.93010
[17] Unyelioglu K. A., Ozguner U., Winkelman J.: A decomposition method for the design of active suspension controllers. In: Proc. 13th 1996 IFAC World Congress, San Francisco 1996
[18] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Springer–Verlag, New York 1979 MR 0569358 | Zbl 0609.93001
[19] Wonham W. M., Morse A. S.: Decoupling and pole assignment in linear multivariable systems: a geometric approach. SIAM J. Control 8 (1970), 1, 1–18 DOI 10.1137/0308001 | MR 0270771 | Zbl 0206.16404
Partner of
EuDML logo