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Research Papers

# Application of Semi-Active Inerter in Semi-Active Suspensions Via Force Tracking

[+] Author and Article Information
Michael Z. Q. Chen

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam, Hong Kong, China
e-mail: mzqchen@hku.hk

Yinlong Hu

College of Energy and Electrical Engineering,
Hohai University,
Nanjing 211100, China

Chanying Li

Academy of Mathematics and Systems Sciences,
Beijing 100190, China

Guanrong Chen

Department of Electronic Engineering,
City University of Hong Kong,
Pokfulam, Hong Kong China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 7, 2015; final manuscript received April 1, 2016; published online May 25, 2016. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 138(4), 041014 (May 25, 2016) (11 pages) Paper No: VIB-15-1158; doi: 10.1115/1.4033357 History: Received May 07, 2015; Revised April 01, 2016

## Abstract

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by online control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed in this paper. Two parts are required in the force-tracking strategy: a target active control law and a proper algorithm to adjust the inertance and the damping coefficient online to track the target active control law. The target active control law is derived based on the state-derivative feedback control methodology in the “reciprocal state-space” (RSS) framework, which has the advantage that it is straightforward to use the acceleration information in the controller design. The algorithm to adjust the inertance and the damping coefficient is to saturate the active control force between the maximal and the minimal achievable suspension forces of the semi-active suspension. Both a quarter-car model and a full-car model are considered in this paper. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection, and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.

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## Figures

Fig. 1

Hydraulic inerter in Ref. [26]: (a) a prototype in National Taiwan University—Department of Mechanical Engineering and (b) working principle

Fig. 2

Conceptual block diagram of a semi-active inerter

Fig. 3

Quarter-car model: (a) active suspension and (b) semi-active suspension with a semi-active inerter and a semi-active damper

Fig. 4

Control diagram of a quarter-car model

Fig. 7

Differences of the RM⋅J performance between increasing 10 kg bmax and increasing 100 Ns/m cmax. “ΔRM⋅J>0” means increasing 10 kg bmax improves RM⋅J performance more than increasing 100 Ns/m cmax and vice versa.

Fig. 8

Bump test: (a) sprung mass acceleration, (b) suspension deflection, (c) tire deflection, and (d) suspension force

Fig. 5

(a) Comparison of the overall performance RM⋅J with respect to different static stiffnesses and bandwidths and (b) the percentage improvement over the Semi-D suspension. Thecircles, the diamonds, and the triangles denote the Semi-ID suspensions where the bandwidth of the semi-active inerter is 5 Hz, 10 Hz, and 30 Hz, respectively; the bandwidth of the semi-active damper is uniformly 30 Hz; and the bandwidth of semi-active inerter for the Semi-I suspension is 30 Hz.

Fig. 6

Overall performance RM⋅J and RMS force-tracking error ue with respect to different cmax and bmax. The inner figure is the RMS force-tracking error ue with respect to cmax and bmax. The outer figure is the overall performance RM⋅J with respect to cmax and bmax.

Fig. 9

Frequency responses: (a) sprung mass acceleration, (b) suspension deflection, and (c) tire deflection

Fig. 10

The full-car model

Fig. 11

Control diagram of the full-car model

Fig. 12

(a) Comparison of the overall performance RM⋅J with respect to different static stiffnesses (kf and kr) and (b) the percentage improvement over the Semi-D suspension

Fig. 13

Comparison of performance with different static stiffnesses (kf and kr): (a) total RMS sprung mass acceleration, (b) total RMS suspension deflection, (c) total RMS tire deflection, and (d) total RMS force-tracking error

Fig. 14

(a) Comparison of the overall performance RM⋅J with respect to different speeds and (b) the percentage improvement over the Semi-D suspension

Fig. 15

Suspension performance with respect to different vehicle speeds when kf=kr=80 kN/m: (a) overall performance, (b) total RMS sprung mass acceleration, (c) total RMS suspension deflection, and (d) total RMS tire deflection

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