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Vol: 51(65) No: 2 / June 2006         Data-based Modeling Approaches Applied to a Nonlinear Subsystem of an Air Intake Manifold J. G. Linden Control Theory and Applications Centre, Coventry University, Priory Street, CV1 5FB, Coventry, UK N. Meyer Control Theory and Applications Centre, Coventry University, Priory Street, CV1 5FB, Coventry, UK B. Vinsonneau Control Theory and Applications Centre, Coventry University, Priory Street, CV1 5FB, Coventry, UK K. J. Burnham Control Theory and Applications Centre, Coventry University, Priory Street, CV1 5FB, Coventry, UK, phone: +44-24-7688-8972, e-mail: k.burnham@coventry.ac.uk Keywords: automotive, bilinear systems, multiple models, parameter estimation, regularization. Abstract This paper surveys several black-box modeling approaches in order to replicate a part of the dynamic behavior of an automotive air intake manifold system. Linear and bilinear, time-invariant and time-varying modeling structures are investigated. In addition, multiple models with different blending techniques and operating point dependent models are compared; the latter utilize a mapping between input and model parametrization using polynomial approximations. To overcome possible ill-conditioning problems during the parameter estimation, and to obtain ‘smoother’ estimates in the time-varying case, use is made of a form of on-line Tikhonov regularization, which penalizes the deviation of the first derivative. The proposed approaches, leading to the realization of time-varying models utilizing both linear and bilinear structures with operating point dependent model parameters, are considered to have a wide applicability range. References [1] Y.-W. Kim, G. Rizzoni and V. Utkin, “Automotive engine diagnosis and control via nonlinear estimation”, IEEE Control Systems, no. 2, pp. 84-99, 1988. [2] D.G. Copp, “Modelling and control of automotive air-fuel ratio systems”, Ph.D. dissertation, Coventry University, Coventry, U.K., 1998. [3] J.A.F. Vinsonneau, “`Fault detection and modelling for an automotive system”, Ph.D. dissertation, Coventry University, U.K., 2003. [4] R.R. Mohler, Bilinear Control Processes, Academic Press, New York, 1973. [5] J.G. Linden, “Regularisation techniques and cautious least squares in parameter estimation for model based control”, Master's thesis, Coventry University, U.K., 2005. [6] A. Dunoyer, “Bilinear self-tuning control and bilinearisation with application to non-linear industrial systems”, Ph.D. dissertation, Coventry University, U.K., 1996. [7] T.A. Johansen, “On Tikhonov regularization, bias and variance in nonlinear system identification”, Automatica, vol. 33, no. 3, pp. 441-446, 1997. [8] T.A. Johansen, “Identification of non-linear systems using empirical data and prior knowledge: an optimization approach”,' Automatica, vol. 32, no. 3, pp. 337-356, March 1996. [9] A. Neumaier, “Solving ill-conditioned and singular linear systems: a tutorial on regularization”, SIAM, vol. 40, pp. 636-666, 1994. [10] J. Sjöberg, T. McKelvey and L. Ljung, “On the use of regularization in system identification”, Proceedings of 12th IFAC World Congress, Sydney, Australia, 1993, vol. 7, pp. 381-386. [11] G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems”, IEEE Trans. on Acoustics, Speech and Signal Processing, vol. 37, no. 12, pp. 2024-2036, 1989. [12] K.J. Burnham, “Self-tuning control for bilinear systems”, Ph.D. dissertation, Coventry Polytechnic, U.K., 1991. [13] J.G. Linden, B. Vinsonneau and K.J. Burnham, “Review and enhancement of cautious parameter estimation for model based control: a specific realization of regularization”, Proc. 17th Int. Conf. Systems Engineering, Las Vegas, USA, 2005, pp. 112-117.