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Algebraic H2 Optimal Control Design in an Active Vehicle Suspension Application

Aghil Shavalipour(1*), Sallehuddin Mohd Haris(2), Zulkifli Mohd Nopiah(3)

(1) University Kebangsaan Malaysia, Malaysia
(2) University Kebangsaan Malaysia, Malaysia
(3) University Kebangsaan Malaysia, Malaysia
(*) Corresponding author


DOI: https://doi.org/10.15866/iremos.v8i3.6304

Abstract


A vehicle suspension plays a crucial role in adequately guaranteeing the performance and stability of the vehicle. Uncertainties in parameter values have a profound effect on the suspension performance, which could also result in instability causing loss of control of the vehicle. Suspension design is made even more complicated due to conflicting requirements which necessitate trade-offs between ride comfort, road holding and suspension deflection. Although extensive research have been carried out on the control of active suspension systems, such works by large have focused on optimizing controllers based on a nominal suspension model. These controllers are optimized through numerical computation so as to be sufficiently robust such that system performance is maintained to be within acceptable bounds under certain variation limits from the nominal parameter values. However, performance would degrade if the parameter variations exceed these allowed limits. Since optimization was performed through numerical computation, optimal controller values need to be repeatedly computed to adapt to changing parameter values. In this work, we present a method to perform analytical computation for H2 optimal control of an active suspension. By utilizing the intriguing relationship between the sum of roots and spectral factorization through Gröbner bases, we found the H2 optimal control for an active suspension as an algebraic solution in terms of the sprung mass, which was taken as the varying parameter. Hence, the resulting controller can always be adapted to be optimal for any value of sprung mass.
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Keywords


Algebraic Riccati Equation; Optimal Control; Spectral Factorization; Sum of Roots

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References


S. Türkay and H. Akçay, "A study of random vibration characteristics of the quarter-car model," Journal of sound and vibration, vol. 282, pp. 111-124, 2005.
http://dx.doi.org/10.1016/j.jsv.2004.02.049

H. Du and N. Zhang, "H∞ control of active vehicle suspensions with actuator time delay," Journal of sound and vibration, vol. 301, pp. 236-252, 2007.
http://dx.doi.org/10.1016/j.jsv.2006.09.022

H. Du, N. Zhang, and J. Lam, "Parameter-dependent input-delayed control of uncertain vehicle suspensions," Journal of Sound and Vibration, vol. 317, pp. 537-556, 2008.
http://dx.doi.org/10.1016/j.jsv.2008.03.066

G. Gao and S. Yang, "Semi-active control performance of railway vehicle suspension featuring magnetorheological dampers," in Industrial Electronics and Applications, 2006 1ST IEEE Conference on, 2006, pp. 1-5.
http://dx.doi.org/10.1109/iciea.2006.257097

H. Gao, W. Sun, and P. Shi, "Robust Sampled-Data Control for Vehicle Active Suspension Systems," Control Systems Technology, IEEE Transactions on, vol. 18, pp. 238-245, 2010.
http://dx.doi.org/10.1109/tcst.2009.2015653

H. Anai, S. Hara, M. Kanno, and K. Yokoyama, "Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem," Journal of Symbolic Computation, vol. 44, pp. 703-725, 2009.
http://dx.doi.org/10.1016/j.jsc.2008.04.015

M. Kanno and S. Hara, "Symbolic-numeric hybrid optimization for plant/controller integrated design in H∞ loop-shaping design," Journal of Math-for-Industry (JMI), vol. 4, pp. 135-140, 2012.

K. Zhou, J. C. Doyle, and K. Glover, Robust and optimal control vol. 40: Prentice Hall New Jersey, 1996.

D. A. Bini, B. Iannazzo, and B. Meini, Numerical solution of algebraic Riccati equations vol. 9: Siam, 2012.
http://dx.doi.org/10.1137/1.9781611972092

M. Kanno, K. Yokoyama, H. Anai, and S. Hara, "Solution of algebraic riccati equations using the sum of roots," in Proceedings of the 2009 international symposium on Symbolic and algebraic computation, 2009, pp. 215-222.
http://dx.doi.org/10.1145/1576702.1576733

R. Rajamani, Vehicle dynamics and control: Springer, 2012.
http://dx.doi.org/10.1007/978-1-4614-1433-9

V. Bolotnikov, "Confluent Vandermonde matrices and divided differences over quaternions," Comptes Rendus Mathematique, vol. 353, pp. 391-395, 2015.
http://dx.doi.org/10.1016/j.crma.2015.02.004


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