SCIENCE CHINA Information Sciences, Volume 64 , Issue 7 : 172201(2021) https://doi.org/10.1007/s11432-020-2912-2

Optimal comfortability control of hybrid electric powertrains in acceleration mode

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  • ReceivedJan 22, 2020
  • AcceptedApr 1, 2020
  • PublishedMay 18, 2021



The work of the third author was supported by National Natural Science Foundation of China (Grant No. 61973053). The authors would like to thank Toyota Motor Corporation, Japan, for technical support.


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  • Figure 1

    (Color online) Structure of the powertrain system.

  • Figure 2

    (Color online) The visual examples of human feeling function. (a) The structure and application of the function block; (b) the acceleration curve with ${\rm~score}=~60.5141$; (c) the acceleration curve with ${\rm~score}=~11.7848$.

  • Figure 3

    (Color online) The comfortability problem in acceleration mode.

  • Figure 4

    (Color online) Block diagram of the proposed design approach.

  • Figure 5

    (Color online) The basic structure of the genetic algorithm.

  • Figure 6

    (Color online) The optimization process using GA for ${v_0}=~70$ km/h.

  • Figure 7

    (Color online) The simulation results of a hybrid powertrain. From top to bottom, the figures show the curves including (a) the velocity, (b) the acceleration, (c) the engine torque, (d) the Motor 1 torque, and (e) the Motor 2 torque, respectively.

  • Figure 8

    (Color online) The simulation results of a hybrid powertrain. From top to bottom, the figures show the curves including (a) the gear ratio, (b) the efficiency of gear box, (c) the power of MG1 and MG2, (d) the speed of MG1 and engine, and (e) the speed of MG2, respectively.

  • Table 1  

    Table 1List of GA parameters

    Parameter Value
    Dimension of input $14$
    Maximum generation number, $k_{\rm~max}$ $100$
    Population size $70$
    Initial crossover probability, ${p_{c0}}$ $0.7$
    Initial mutation probability, ${p_{m0}}$ $0.1$
    Constant, $\alpha_c$ $0.02$
    Constant, $\alpha_m$ $0.005$
  • Table 2  

    Table 2List of vehicle parameters

    Parameter Nomenclature Value Unit
    Vehicle mass $M$ 2850 kg
    Engine inertia $I_e$ 0.22 kg$\cdot$m$^2$
    MG1 inertia $I_{m1}$ 0.06 kg$\cdot$m$^2$
    Accumulated inertia $I_{\Sigma~d2}$ 0.92 kg$\cdot$m$^2$
    Accumulated inertia $I_{\Sigma~w}~$ 6.1 kg$\cdot$m$^2$
    Mechanical parameter $G_m$ 5.75
    Mechanical parameter $G_f$ 3.307
    Transmission efficiency $\eta_f$ 0.87
    Tire radius $R_{\rm~tire}$ 0.39 m
    Air density $\rho~$ 1.2 kg/m$^3$
    Frontal vehicle area $A$ 2.239 m$^2$
    Drag coefficient ${C_{d}}$ 0.32
    Rolling resistance ${\mu~_r}$ 0.022
    Gravity acceleration $g$ 9.8 N/kg
    Gear ratios $i_g$ 4.93; 3.26; 2.35; 1.95; 1.50;
    1.20; 1.00; 0.80; 0.66; 0.61
  • Table 3  

    Table 3Optimization process with ${v_0}~=~70$ km/h

    Index value Shifting time ${t_2}$ Gear number ${gn_2}$ Terminal time ${t_f}$ Iteration step $k$
    $75.4020$ $2.06$ $4$ $3.60$ $1$
    $75.6269$ $2.03$ $5$ $3.88$ $4$
    $76.2351$ $2.34$ $4$ $3.61$ $30$
    $76.6778$ $2.29$ $4$ $3.57$ $40$
    $76.8027$ $2.33$ $4$ $3.57$ $53$
    $76.8045$ $2.34$ $4$ $3.61$ $101$
  • Table 4  

    Table 4Results with different initial speeds

    Case Initial speed ${v_0}$ (km/h) Index value Shifting time ${t_2}$ (s) Gear ${gn_1}$ Gear ${gn_2}$ Terminal time ${t_f}$ (s)
    $2$ $80$ $70.8641$ $1.26$ $4$ $6$ $5.06$
    $3$ $90$ $70.4341$ $1.43$ $4$ $5$ $5.29$

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