Title: Particle swarm optimisation application in designing sliding-mode and proportional-derivative fuzzy logic controllers on multi-body dynamic vehicle model

Authors: Ngoc Dai Pham; Viet Thang Vu

Addresses: Department of Automotive Engineering, Faculty of Transportation Engineering, Ho Chi Minh City University of Technology (HCMUT) – Vietnam National University Ho Chi Minh City, 268 Ly Thuong Kiet Street, Dien Hong Ward, Ho Chi Minh City, Vietnam ' Department of Automotive Engineering, Faculty of Transportation Engineering, Ho Chi Minh City University of Technology (HCMUT) – Vietnam National University Ho Chi Minh City, 268 Ly Thuong Kiet Street, Dien Hong Ward, Ho Chi Minh City, Vietnam

Abstract: The study uses a multi-body dynamic (MBD) model built with MATLAB Simscape/Simmechanics to simulate the 2DOF quarter-vehicle system's responses during the optimisation of the structure as well as the controllers. The study applied the Pareto optimisation method in simultaneously determining elastic and damping elements' parameters of the bus suspension system by PSO to optimise at the same time the vehicle body's acceleration (acc) and suspension's relative displacement (rel). The study proposed a new design method for proportional derivative fuzzy logic (PD-FLC) and decoupled algorithm sliding-mode (DA-SMC) control systems on vehicle suspension when the membership functions' positions' parameters E/NS-PS, DE/NS-PS of the FLC set and the sliding surface's parameters η and k of the SMC set are simultaneously optimised by PSO. The active suspension system is more effective than the passive system in reducing displacement (over 40%) and vehicle body acceleration (over 17%).

Keywords: sliding-mode control; fuzzy logic control; particle swarm optimisation; multi-objective optimisation; 2DOF quarter-vehicle; multi-body dynamic; MBD.

DOI: 10.1504/IJVP.2026.152850

International Journal of Vehicle Performance, 2026 Vol.12 No.2, pp.214 - 238

Received: 03 Mar 2025
Accepted: 14 Oct 2025
Published online: 13 Apr 2026 *

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