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Coordinated control strategy for mode transition of DM-PHEV based on MLD

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Abstract

In this paper, a hybrid variable cost function model predictive control strategy (HC-MPC) is developed for the mode transition process of a novel motor compound power-split plug-in hybrid electric vehicle (DM-PHEV). Based on the layout of DM-PHEV, the mode transition process from electric driving mode to hybrid driving mode is divided into 5 stages. Considering the hybrid characteristics of mode transition process, the dynamic models under different stages are transmitted into an equivalent mixed-logical dynamical hybrid model. MPC based on hybrid model (H-MPC) is applied as the coordinated controller. Moreover, considering that fixed cost functions for the finite time horizon are not reasonable if stage transition happened during the prediction horizon, so variable cost functions changing with predictable stages is useful for improving the control effect of MPC. H-MPC considering variable cost functions (HC-MPC) is proposed as the coordinate controller in this paper. Simulation and hardware-in-the-loop test show that HC-MPC can efficiently improve the PHEV drivability.

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Abbreviations

\(T_\mathrm{en\_cmd}\) :

Engine torque command

\(\tau _\mathrm{en}\) :

Time constant of engine

\(T_\mathrm{en\_fric}\) :

Resistance torque of engine

\(n_\mathrm{m1}, n_\mathrm{m2}\) :

Speed of motor 1, 2

\(T_\mathrm{m1\_cmd}, T_\mathrm{m2\_cmd}\) :

Torque command of motor 1, 2

\(x_{\mathrm{p}0}\) :

Initial displacement compressed on return spring

\(x_\mathrm{p}\) :

Displacement of clutch piston away the initial position

\(F_\mathrm{cl}\) :

Reaction force of clutch friction plate on piston

\(Q_\mathrm{c}\) :

Average flow of clutch

\(V_0\) :

Volume of clutch oil chamber

\(\rho \) :

Hydraulic oil density

\(P_s\) :

Oil pressure provided by the tank

\(A_h\) :

Area of valve supporting port

\({{{\tilde{Q}}}}_\mathrm{in}\) :

Average flow of supplying port

\(P_0\) :

Oil pressure of gearbox

\(J_\mathrm{m1}\) :

Equivalent inertia moment of motor 1 and planetary gears

\(J_{r}\) :

Inertia moment of clutch driving shaft speed

\(\omega _{l}\) :

Clutch driven shaft speed

\(J_\mathrm{p}\) :

Inertia moment of planetary mechanism

TDS:

Equivalent elastic shaft of the tire and half shaft

\(k_\mathrm{TDS}\) :

Equivalent torsional stiffness of TDS

\(C_\mathrm{TDS}\) :

Equivalent damping coefficient of TDS

\(i_{0}\) :

Final drive ratio

\(C_\mathrm{d}\) :

Air drag coefficient

\(\theta \) :

Angular displacement

\(m_\mathrm{veh}\) :

Vehicle mass

\(\eta _\mathrm{t}\) :

Efficiency of transmission system

\(\alpha \) :

Road slope

\(n_\mathrm{thresh}\) :

Speed limit of engine drag torque change

\(z_{i}\) :

Continuous auxiliary variables

\(A_\mathrm{fric}\) :

Engine resistance torque coefficient

W :

Clutch slipping energy

Q, R :

Weight matrix

\(T_\mathrm{en}\) :

Output torque of engine

\(n_\mathrm{en}\) :

Engine speed

\(T_\mathrm{m1}, T_\mathrm{m2}\) :

Output torque of motor 1, 2

\(\tau _\mathrm{m1}, \tau _\mathrm{m2}\) :

Time constant of motor 1, 2

\(k_p\) :

Stiffness of the clutch return spring

\(s_\mathrm{max}\) :

Maximum displacement away the initial position

\(F_\mathrm{p}\) :

Static pressure on clutch piston

\(A_\mathrm{C2}\) :

Clutch piston area

\(x_{\max }\) :

Maximum clutch piston displacement

\(\beta \) :

Effective volume elastic modulus of hydraulic fluid

\({P}_\mathrm{c}\) :

Control pressure of clutch

\(C_h\) :

Valve flow coefficient

\(\tau \) :

Duty cycle of PWM

\({{{\tilde{Q}}}}_\mathrm{out}\) :

Average flow of recycle port

\(J_\mathrm{en}\) :

Inertia moment of engine

\(J_\mathrm{m2}\) :

Equivalent inertia moment of motor 2 and clutch disc

\(J_\mathrm{veh}\) :

Vehicle equivalent inertia

\(\omega _{r}\) :

Clutch driving shaft speed

TH:

Torsional damper spring

\(k_\mathrm{TH}\) :

Equivalent torsional stiffness of TH

\(C_\mathrm{TH}\) :

Equivalent damping coefficient of TH

\(i_{2}\) :

Gear ratio of motor 2

\(T_{f}\) :

Equivalent running resistance torque of vehicle

A :

Effective frontal area

v :

Vehicle speed

f :

Roll resistance coefficient

R :

Radius of tire

\(\delta _i\) :

Introducing binary auxiliary variable

\(T_\mathrm{ega},n_\mathrm{ega}\) :

Predefined positive scalar

j :

Vehicle jerk

\(J_i\) :

Cost function

\(\varepsilon \) :

Auxiliary variables in cost functions

\(x_e\) :

State variable reference value

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Acknowledgements

This work is financially supported by the National Key Research and Development Project [No. 2017YFB0103200], the National Natural Science Foundation of China [No. 51705204], Six Talent Peaks Project in Jiangsu Province (CN) [No. JXQC-036], the China Scholarship Council [No. 201908320221].

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Authors and Affiliations

  1. Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Cong Liang, Xing Xu & Feng Wang

  2. School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, People’s Republic of China

    Cong Liang, Xing Xu & Feng Wang

  3. New Energy Development Department Powertrain Technology Center, Chery Automobile Company, Wuhu, People’s Republic of China

    Zhiguang Zhou

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  1. Cong Liang
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Correspondence to Xing Xu.

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Liang, C., Xu, X., Wang, F. et al. Coordinated control strategy for mode transition of DM-PHEV based on MLD. Nonlinear Dyn 103, 809–832 (2021). https://doi.org/10.1007/s11071-020-06126-z

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  • DOI: https://doi.org/10.1007/s11071-020-06126-z

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