Frequency domain $ H_{\infty} $ control design for active suspension systems

Jamal Mrazgua; El Houssaine Tissir; Mohamed Ouahi

doi:10.3934/dcdss.2021036

Article Contents

2022, Volume 15, Issue 1: 197-212. Doi: 10.3934/dcdss.2021036

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Frequency domain $ H_{\infty} $ control design for active suspension systems

1.
University of Sidi Mohammed Ben Abdellah, Department of Physics, Faculty of Sciences Dhar El Mehraz, LISAC, BP 1796, Fes-Atlas, Morocco
2.
University of Sidi Mohammed Ben Abdellah, Engineering, Systems and Applications, Laboratory National School of Applied Sciences (ENSA), Fez, Morocco

^* Corresponding author: Jamal Mrazgua
^* Corresponding author: Jamal Mrazgua

Received: July 31, 2020

Revised: January 31, 2021

Early access: March 2021

Published: January 2022

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Abstract

A methodology for fault-tolerant-control(FTC) is proposed that compensates actuator failures in active suspension systems (ASS). This methodology is based on a Frequency Domain approach that represents failures using a scale factor to optimize the ASS and improve ride comfort. The controller design is carried out using off-the-shelf tools based on linear matrix inequalities (LMIs), guaranteeing asymptotic stability, compensating the effect of actuator faults, and ensuring certain $ H_{\infty} $ performance. In the context of ASS, the performance guarantees correspond to ride comfort in the presence of road disturbances. To validate the approach, controllers are developed and tested in simulation for a quarter-car model: the results illustrate the effectiveness of the proposed approach.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Quarter-car model with an active suspension

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Figure 2. Bump response of sprung mass acceleration

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Figure 3. Bump response of suspension deflection

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Figure 4. Bump response of tyre deflection

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Figure 5. Transfer function

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Figure 6. Force of the actuator

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Table 1. Quarter-Car Model Parameters

$ m_{s} $	Suspended mass
$ m_{u} $	Unsupported mass
$ c_{s} $	Damping of the suspension system
$ k_{s} $	Stiffness of the suspension system
$ c_{t} $	Damping of the pneumatic tyre
$ k_{t} $	Compressibility of the pneumatic tyre
$z_{s} $	Displacement of the sprung mass
$ z_{u} $	Displacement of unsprung mass
$ \delta^ {f} (t) $	Fault-tolerant-control

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Table 2. Quarter-Car Model Parameters

$ m_{s} $	$ m_{u} $	$ k_{s} $	$ k_{t} $	$ c_{s} $	$ c_{t} $
320	40	18	200	1	10
kg	kg	KN/m	KN/m	KNs/m	Ns/m

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