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Page 2 of 15 Cui et al. Complex Eng Syst 2023;3:3 I http://dx.doi.org/10.20517/ces.2022.57

1. INTRODUCTION
As the focus on driving experience increases, research into vehicle steering systems has also gained attention.
Traditional hydraulic power steering (HPS) systems provide assistance torque through an engine and offer a
clear road feel, but have the disadvantage of high energy consumption. Electric power steering (EPS) systems
provide adjustable assistance torque through a motor and have lower energy consumption, but the power-
assisted range of EPS systems is narrow, limiting their application in vehicles with heavy front axle loads.
Electric-hydraulic power steering (EHPS) systems combine the advantages of both systems, providing better
road feel and lower energy consumption. Thus, EHPS systems have been widely used in commercial vehicles.

In recent years, research into EHPS systems has mainly focused on the control aspect [1–6] . Neural network
control algorithms have been applied to the steering assist control of EHPS systems to improve the driver’s
[7]
experience . Kim et al. proposed a design method for the steering motor speed of EHPS systems based
[8]
on driver perception, which improved the driver’s steering road feel and eliminated the catch-up effect .
Lin et al. proposed a slip frequency control method for the steering motor of EHPS systems to effectively
[9]
improve the response speed and accuracy of the steering motor . Ye et al. simplified the EHPS system and
introduced the H2/H∞ control method to control the power assistance, which improves the anti-interference
performance of the steering system [10] . Hur et al. analyzed the characteristics of the interior permanent-
magnet synchronous motor of EHPS systems and proposed precise control and real-time response control
methods for the motor [11] .

However, current research rarely focuses on the steering experience of EHPS systems, and the optimization of
the overall EHPS system is rarely reported. The evaluation indexes of EHPS systems involve not only steering
flexibility and road feel, but also steering economy and other aspects with coupled effects [12–14] . Therefore, the
optimization of the EHPS system is essentially a multi-objective optimization problem (MOP).

Traditional multi-objective optimization algorithms usually set different weights for different indicators and
sum them, thus transforming multi-objective optimization into single-objective optimization [15] . However,
these optimization algorithms show poorer performance in solving too many optimization objectives and non-
convex optimization problems, and are prone to falling into local optima [16] . As such, a number of intelligent
optimization algorithms, such as non-dominated sorting genetic algorithm (NSGA) and NSGA-II, have been
proposed and applied to satellite design and other fields [17,18] . Additionally, the collaborative optimization
(CO) method can effectively solve complex optimization problems, with the obvious advantages of simplifying
system decoupling and achieving parallel computation [19–21] . The complex optimization model is divided into
several subsystems according to the optimization objectives, and the coupling variables in the subsystems are
coordinated by the consistency constraint [22] . This is convenient for concurrent design, which is consistent
with the modern industrial design structure [23–25] .

In this paper, steering road feel, steering sensitivity, and steering energy loss are taken as evaluation indexes.
Considering the coupling factors of each subsystem, the multi-objective collaborative optimization method of
the EHPS system is explored.

Therestofthepaperisorganizedasfollows. ThedynamicmodeloftheEHPSsystemisestablishedinSection2,
and the three evaluation indexes of the steering system are derived for the first time. Section 3 establishes the
multi-objective collaborative optimization model of the EHPS system and shows the multi-objective optimiza-
tion results. Conclusions are given in Section 4.