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Cui et al. Complex Eng Syst 2023;3:3 I http://dx.doi.org/10.20517/ces.2022.57 Page 7 of 15

Table 1. The basic parameter of EHPS system
Name Value Name Value
m/kg 4495 21/(N•m/rad) 14,130
m s/kg 3350 23/(N•m/rad) 71,200
/kg•m 2 2510 1/(N•m•s/rad) 4,000
/kg•m 2 2810 1/(N•m•s/rad) 3,800
/kg•m 2 18800 /m 0.23
1/(N/rad) -2900 /kg•m 2 0.04
2/(N/rad) -2900 0.62

Table 2. The initial value and range of each variable
Design variable Initial value Lower Upper
2
(m ) 1.2∗10 −4 0.5∗10 −4 2∗10 −4
(m) 0.008 0.003 0.01
(N/m) 80 30 150
/kg•m 2 5∗10 −3 10 −3 10 −2
(m) 0.05 0.01 0.1
(m) 10 −3 10 −4 2∗10 −3

3. INTEGRATION OPTIMIZATION
As mentioned above, the optimization of EHPS system involves three evaluation indexes, steering road feel,
steeringsensitivity,andsteeringenergyloss. Therefore,Amulti-objectivecollaborativeoptimizationmodelhas
been built, which simplifies the system decoupling, and the multi-objective optimization algorithm is applied
to the model for a Pareto optimal solution set. Besides, the basic parameters of the EHPS system are shown in
Table 1.

3.1. Optimization model
Based on collaborative optimization theory, the main system is divided into three independent subsystems,
which is convenient for parallel computation and reduces the optimization time. In the main system, three
optimizationobjectives,steeringroadfeel,steeringsensibilityandenergyloss,areoptimizedbymulti-objective
optimization algorithm. Besides, the consistency constraint of design parameters is taken as the optimization
goal of each subsystem, and the sequential quadratic programming (NLPQL) algorithm is used to optimize
each system.

In this paper, the effective area of piston , the moment of inertia of motor , the stiffness coefficient , the
stator thickness , the gap width of rotary valve and the radius of the rack and pinion are selected as the
optimization variables. The initial value and design scope of each variable are given in Table 2.

The main system of optimization model is given by













: (13)


 3 ≤ ≤ 5




 ≤ , , , , , ≤


 1,2,3 ≤ 0.01

where is effective power torque, which is computed by
(14)
=