Rate-independent linear damping in vehicle suspension systems

Abstract

Over the past few decades, several semi-active controllers have been proposed for vehicle suspension systems. Skyhook and groundhook controllers are well-studied and very effective in isolating vibrations. However, these controllers mitigate either the sprung or unsprung mass response at the expense of the other. Moreover, there is no sensor to directly measure the absolute velocity of components in the suspension system (and estimates are subject to error), making it challenging to implement skyhook and groundhook controllers in practical cases. To overcome these limitations, there is a need for a type of damping that mitigates both sprung and unsprung mass responses and also can be implemented using simple local sensors. This paper proposes the use of rate-independent linear damping (RILD) for vehicle suspension systems. RILD provides direct control over displacement; beneficial for low-frequency dynamic systems such as suspension systems that are subject to high frequency vibrations (relative to the system fundamental natural frequency). RILD directly attenuates displacement responses with low damping forces, producing low acceleration responses. The RILD damping force is proportional to the displacement advanced in phase π/2 radians, which makes it noncausal. In this study, a modal causal filter-based approach is proposed to mimic the ideal noncausal response of the RILD model. Acceleration measurements of the sprung mass are used with a Kalman filter to estimate the displacements needed for the algorithm. Numerical analyses were conducted to demonstrate performance of the proposed model in matching noncausal RILD responses. Additionally, the advantages of the proposed model over well-known skyhook and groundhook controllers are studied.