This paper presents both the theoretical and the experimental approaches of the development of a mathematical model to be used in multi-variable control system designs of an active suspension for a sport utility vehicle (SUV), in this case a light pickup truck. A complete seven-degree-of-freedom model is successfully quickly identified, with very satisfactory results in simulations and in real experiments conducted with the pickup truth. The novelty of the proposed methodology is the use of commercial software in the early stages of the identification to speed up the process and to minimize the need for a large number of costly experiments. The paper also presents major contributions to the identification of uncertainties in vehicle suspension models and in the development of identification methods using the sequential quadratic programming, where an innovation regarding the calculation of the objective function is proposed and implemented.
Results from simulations of and practical experiments with the real SUV are presented, analysed, and compared, showing the potential of the method.
RaoM. V. C.PrahladV.A turnable fuzzy logic controller for vehicle-active suspension systems. Fuzzy Sets Systems, 1997, 85, 1121.
2.
StutzsL. T.RochinhaF. A.A comparison of control strategies for magnetorheological vehicle suspension systems. In Proceedings of the 11th International Symposium on Dynamic problems in mechanics (DINAME XI), Ouro Preto, Minas Gerais, Brazil, 2005.
3.
HaćA.YounI.ChenH. H.Control of suspensions for vehicles with flexible bodies. Part I: active suspensions. Trans ASME, J. Dynamic Systems, Measmt Control, 1996, 118, 508–517.
4.
AckermannJ.Robust control prevents car skidding. IEEE Control Systems Mag., 1997, 17(3), 23–31.
5.
OdenthalD.BünteT.AckermannJ.Nonlinear steering and braking control for vehicle rollover avoidance. In Proceedings of the Fifth European Control Conference (ECC’99), Karlsruhe, Germany, 31 August–3 September 1999.
6.
TsaoY. J.ChenR.The design of an active suspension force controller using genetic algorithms with maximum stroke constraints. Proc. IMechE, Part D: J. Automobile Engineering, 2001, 215(3), 317’327. DOI: 10.1243/0954407011525638.
7.
SimonD. E.AhmadianM.An alternative semi-active control method for sport utility vehicles. Proc. IMechE, Part D: J. Automobile Engineering, 2002, 216(2), 125’139. DOI: 10.1234/0954407021528977.
8.
da CruzJ. J.BittarA.da CostaE. A.SalesR. M.Control and optimization of the electromagnetic suspension operation of a MAGLEV vehicle. In Proceedings of the 17th International Congress on Mechanical engineering (COBEM 2003), São Paulo, Brazil, 10–14 November 2003, ABCM Symposum Series in Mechatromcs, vol. 1, 2004, 150’158. (Barzilian Society of Mechanical Sciences and Engineering, Rio de Janeiro).
9.
YamamuraS.OhnishiK.MasadaE.Theory of control system of electromagnetically levitated bogie truck. Electl Engng Japan, 1979, 99(6), 62–69.
10.
SchittkowskiK.NLQPL: A FORTRAN-subroutine solving constrained nonlinear programming problems. Ann. of Op. Res., 1985, 5, 485–500.
11.
BraytonR. K.DirectorS. W.HachtelG. D.VidigalL.A new algorithm for statistical circuit design based on quasi-Newton methods and function splitting. IEEE Trans Circuits Systems, 1979, 26, 784–794.
12.
ThompsonA. G.An optimal suspension for an automobile on a random road.SAE paper 790478, 1979.
13.
CrivellaroC.Controle robusto de suspensão semiativa para caminhonetes utilizando amortecedores magneto-reológicos. PhD Thesis, Polytechnic School of University of São Paulo, São Paulo, Brazil, 2008.
14.
HaćA.Adaptive control of vehicle suspension. Veh. System Dynamics, 1987, 16, 57–74.
15.
HrovatD.Survey of advanced suspension developments and related optimal control applications. Automatica, 1997, 33(10), 1781–1817.
16.
GillespieT. D.Fundamentals of vehicle dynamics, 1994 (SAE International, Warrendale, Pennsylvania).
17.
SevinE.PilkeyW. D.Optimum shock and vibration isolation. Report, The Shock and Vibration Information Center, US Department of Defense, Washington, DC, USA, 1971.
18.
SmithR. E.Amplitude characteristics of Dearborn test track roadways. Technical Memorandum SRM-82-26,, Ford Motor Company, Dearborn, Michigan, USA, 1982.
IbrahimS. R.MikulcikE. C.A method for the direct identification of vibration parameters from the free response. Shock Vibr. Bulln, 1977, 47(4), 183–198.
21.
VoldH.KundratJ.RocklinG. T.RusselR.A multi-input modal estimation algorithm for minicomputers. SAE paper 820194, 1982.
22.
JuangJ. N.PappaR. S.An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guidance, Control Dynamics, 1985, 8(5), 620–627.
23.
ZhangI.KandaH.BrownD. L.AllemangR. J.A polyreference frequency domain method for modal parameter identification. In Proceedings of the 1985 ASME Design Engineering Technical Conference 1985, paper 85-DET-106 (ASME, New York).
24.
RichardsonM. H.FormentiD. L.Parameter estimation from frequency response measurements using rational fraction polynomials. In Proceedings of the First International Conference on Modal analysis, 1982, pp. 167–180.
25.
VoldH.Orthogonal polynomials in the polyreference method. In Proceedings of the 11th International Conference on Modal Analysis, Leuven, Belgium, 1986.
26.
Van der AuweraerH.LeuridanJ. M.Multiple input orthogonal polynomial parameter estimation. Mech. System Signal Processing, 1987, 1 (3), 259–272.
27.
ShihC. Y.TsuciY. G.AllemangR. J.BrownD. L.A frequency domain global parameter estimation method for multiple reference frequency response measurements. Mech. System Signal Processing, 1988, 2(4), 349–365.
28.
ShihC. Y.TsuciY. G.AllemangR. J.BrownD. L.A frequency domain global parameter estimation method for multiple reference frequency response measurements. In Proceedings of the 6th International Modal Analysis Conference, Orlando, Florida, 1988, pp. 389–396.
29.
WilliamsR.CrowleyJ. R.VoldH.The multivariate modal indicator function in modal analysis. In Proceedings of the Third International Conference on Modal Analysis, Orlando, Florida, 28–31 January 1985.
30.
CrivellaroC.AlvesS.Phenomenological model of a magneto-rheological damper for semi-active suspension control design and simulation. SAE paper 2006-01-2520, 2006.
31.
CrivellaroC.TamaiE. H.DonhaD. C.Four-wheel vehicle suspension modeling for control system development. In Proceedings of the 18th International Congress of Mechanical Engineering (COBEM2005), Ouro Preto, Minas Gerais, Brazil, 6–11 November 2005.
32.
BiggsM. C.Constrained minimization using recursive quadratic programming. Toward global optimization (Eds (DixonL. C. W.SzergoG. P.), 1975, pp. 341–349 (North-Holland, Amsterdam).
33.
HanS. P.A globally convergent method for nonlinear programming. J. Optimization Theory Applic., 1977, 22(3), 297–309.
34.
PowellM. J. D.The convergence of variable metric methods for nonlinearly constrained optimization calculations. In Nonlinear programming 3 (Eds MangasarianO. L.MeyerR. R.RobinsonS. M.), 1978, pp. 27–63 (Academic Press, London).
35.
PowellM. J. D.A fast algorithm for nonlinearly constrained optimization calculations. In Numerical analysis (Ed. WatsonG. A.), Lecture Notes in Mathematics, 630, 1978, pp. 144–157 (Springer, New York).
PowellM. J. D.Variable metric methods for constrained optimization. In Mathematical programming: the state of the art (Eds BachemA.GrotschelM.KorteB.), 1983, pp. 288–311 (Springer Berlin).
38.
FletcherR.Practical methods of optimization, 1987 (John Wiley, New York).
