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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.

#### Keywords

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

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