哈尔滨工业大学学报  2019, Vol. 51 Issue (1): 150-156, 161  DOI: 10.11918/j.issn.0367-6234.201803073 0

### 引用本文

SONG Dafeng, YUN Qianrui, YANG Nannan, ZENG Xiaohua, WANG Xingqi. Model predictive dynamic coordinated control of planetary hybrid electric bus[J]. Journal of Harbin Institute of Technology, 2019, 51(1): 150-156, 161. DOI: 10.11918/j.issn.0367-6234.201803073.

### 文章历史

Model predictive dynamic coordinated control of planetary hybrid electric bus
SONG Dafeng, YUN Qianrui, YANG Nannan, ZENG Xiaohua, WANG Xingqi
State Key Laboratory of Automotive Simulation and Control (Jilin University), Changchun 130025, China
Abstract: Planetary hybrid electric buses usually have a great jerk while the drive mode switched. PID-based controller could not effectively ensure vehicle ride comfort during the mode switching process. Model predictive control(MPC), which can obtain optimal control sequences by online rolling optimization, is used to solve this issue, and a dynamic coordination control method based on MPC is proposed to start the engine. Based on the vehicle dynamic equations and vehicle historical data, the data-driven engine model and the closed-loop simulation model are set up in the Matlab/Simulink. Taking the start-up process of the engine as a constrained multi-objective optimization problem, the model predictive controller is designed according to the system state space equation and optimization problem. In the process of switching from the pure electric mode to the hybrid mode, the model predictive controller is compared with the traditional PID-based control method and without control. The simulation results demonstrate that under the premise of ensuring the dynamic performance of the vehicle, compared with the PID control and without control, during the mode switching process, the dynamic coordinated control method based on MPC can not only achieve the normal start of the engine, but also greatly reduce the peak jerk and also make the vehicle follow the target speed well.
Keywords: hybrid electric bus     model predictive control     dynamic coordinated control     data-driven     jerk     ride comfort

1 系统构型

 图 1 系统结构简图 Figure 1 Configuration of system
2 系统分析 2.1 动力学模型

 $\left\{ \begin{array}{l} {T_{{\rm{s1}}}} = {T_{{\rm{c1}}}}/\left( {1 + {k_1}} \right),\\ \left( {1 + {k_1}} \right){\omega _{{\rm{c1}}}} = {k_1}{\omega _{{\rm{rl}}}} + {\omega _{{\rm{sl}}}}. \end{array} \right.$ (1)
 $\left\{ \begin{array}{l} {T_{{\rm{s2}}}} = {T_{{\rm{c2}}}}/\left( {1 + {k_2}} \right),\\ \left( {1 + {k_2}} \right){\omega _{{\rm{c2}}}} = {\omega _{{\rm{s2}}}}. \end{array} \right.$ (2)

 ${I_{{\rm{r1}}}}{{\dot \omega }_{{\rm{r1}}}} = {F_1} \cdot {R_1} - {T_{{\rm{r1}}}},$ (3)
 ${I_{{\rm{c1}}}}{{\dot \omega }_{{\rm{c1}}}} = {T_{{\rm{c1}}}} - {F_1} \cdot {S_1} - {F_1} \cdot {R_1},$ (4)
 ${I_{{\rm{s1}}}}{{\dot \omega }_{{\rm{s1}}}} = {F_1} \cdot {S_1} - {T_{{\rm{s1}}}}.$ (5)
 图 2 前行星排自由体图 Figure 2 Free-body diagram of front planetary gear set

 $\left( {{I_{\rm{e}}} + {I_{{\rm{c1}}}}} \right){{\dot \omega }_{\rm{e}}} = {T_{\rm{e}}} - {F_1} \cdot {R_1} - {F_1} \cdot {S_1},$ (6)
 $\left( {{I_{\rm{g}}} + {I_{{\rm{s1}}}}} \right){{\dot \omega }_{\rm{g}}} = {F_1} \cdot {S_1} - {T_{\rm{g}}}.$ (7)

 图 3 后行星排自由体图 Figure 3 Free-body diagram of rear planetary gear set

 ${T_{{\rm{c2}}}} = {T_{\rm{m}}}\left( {1 + {k_2}} \right) - \left[ {\left( {{I_{\rm{m}}} + {I_{{\rm{s2}}}}} \right){{\left( {1 + {k_2}} \right)}^2} - {I_{{\rm{c2}}}}} \right]{{\dot \omega }_{{\rm{c2}}}}.$ (8)

 图 4 输出部分自由体图 Figure 4 Free body diagram of system output

 $\begin{array}{l} {{\dot \omega }_{{\rm{r1}}}}\left[ {\frac{{{R_{\rm{t}}}^2m}}{{{i_{\rm{o}}}}} + {I_{{\rm{r1}}}}{i_{\rm{o}}} + \left( {{I_{\rm{m}}} + {I_{{\rm{s2}}}}} \right)\left( {1 + {k_2}} \right)2{i_{\rm{o}}} - {I_{{\rm{c2}}}}{i_{\rm{o}}}} \right] = \\ \;\;\;\left[ {{T_{\rm{m}}}\left( {1 + {k_2}} \right) + {F_1}{R_1}} \right]{i_{\rm{o}}} - {T_{\rm{f}}}. \end{array}$ (9)

 ${T_{\rm{f}}} = {T_{{\rm{fb}}}} + mg{f_{\rm{r}}}{R_{\rm{t}}} + 0.5\rho A{C_{\rm{D}}}{\left( {{\omega _{{\rm{r1}}}}/{i_{\rm{o}}}} \right)^2}{R_{\rm{t}}}^3.$

2.2 车辆运行过程动态方程推导

 ${{I'}_{\rm{g}}}{k_1}{{\dot \omega }_{{\rm{r1}}}} - \left[ {\frac{{{{I'}_{\rm{e}}}}}{{1 + {k_1}}} + {{I'}_{\rm{g}}}\left( {1 + {k_1}} \right)} \right]{{\dot \omega }_{\rm{e}}} = {T_{\rm{g}}} - \frac{{{T_{\rm{e}}}}}{{1 + {k_1}}},$ (10)

 图 5 发动机工作点 Figure 5 Engine operation point

 $\left\{ \begin{array}{l} \alpha = {\alpha _1},\beta = {\beta _1},{\omega _{\rm{e}}} < 440\;{\rm{r/min}};\\ \alpha = {\alpha _2},\beta = {\beta _2},440\;{\rm{r/min}} \le {\omega _{\rm{e}}} < 460\;{\rm{r/min;}}\\ \alpha = {\alpha _3},\beta = {\beta _3},460\;{\rm{r/min}} \le {\omega _{\rm{e}}} < 567\;{\rm{r/min;}}\\ \alpha = {\alpha _4},\beta = {\beta _4},567\;{\rm{r/min}} \le {\omega _{\rm{e}}} < 640\;{\rm{r/min;}}\\ \alpha = {\alpha _5},\beta = {\beta _5},{\omega _{\rm{e}}} \ge 640\;{\rm{r/min}}. \end{array} \right.$

 $\begin{array}{*{20}{c}} {\left[ {\frac{{R_{\rm{t}}^2m}}{{{i_0}}} + {I_{\rm{m}}}{{\left( {1 + {k_2}} \right)}^2}{i_0}} \right]{{\dot \omega }_{r1}} + {I_{\rm{e}}}\frac{{{k_1}}}{{1 + {k_1}}}{i_0}{{\dot \omega }_{\rm{e}}} = }\\ {{T_{\rm{m}}}\left( {1 + {k_2}} \right){i_0} + \frac{{\alpha {\omega _e}{k_1}}}{{1 + {k_1}}}{i_0} + \frac{{\beta {k_1}}}{{1 + {k_1}}}{i_0} - {T_{\rm{f}}}.} \end{array}$ (11)

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{\dot x}} = {\mathit{\boldsymbol{A}}_{\rm{c}}}\mathit{\boldsymbol{x}} + {\mathit{\boldsymbol{B}}_{{\rm{cu}}}}\mathit{\boldsymbol{u}} + {\mathit{\boldsymbol{B}}_{{\rm{cd}}}}\mathit{\boldsymbol{d}},\\ y = \mathit{\boldsymbol{Cx}}. \end{array} \right.$

 $\mathit{\boldsymbol{d}} = {\left[ {\begin{array}{*{20}{c}} { - \frac{\beta }{{1 + {k_1}}}}&{\frac{{\beta {k_1}}}{{1 + {k_1}}}{i_{\rm{o}}} - {T_{\rm{f}}}} \end{array}} \right]^{\rm{T}}},y = {\omega _{\rm{e}}},$
 ${\mathit{\boldsymbol{A}}_{\rm{o}}} = \left[ {\begin{array}{*{20}{c}} { - \frac{{{{I'}_{\rm{e}}}}}{{1 + {k_1}}} - {{I'}_{\rm{g}}}\left( {1 + {k_1}} \right)}&{{{I'}_{\rm{g}}}{k_1}}\\ {{I_{\rm{e}}}\frac{{{k_1}}}{{1 + {k_1}}}{i_{\rm{o}}}}&{\frac{{R_{\rm{t}}^2m}}{{{i_{\rm{o}}}}} + {I_{\rm{m}}}{{\left( {1 + {k_2}} \right)}^2}{i_{\rm{o}}}} \end{array}} \right],$
 ${\mathit{\boldsymbol{A}}_{\rm{c}}} = {\mathit{\boldsymbol{A}}_{\rm{o}}}^{ - 1}\left[ {\begin{array}{*{20}{c}} { - \frac{\alpha }{{1 + {k_1}}}}&0\\ {\frac{{\alpha {k_1}}}{{1 + {k_1}}}{i_o}}&0 \end{array}} \right],{\mathit{\boldsymbol{B}}_{{\rm{cu}}}} = {\mathit{\boldsymbol{A}}_{\rm{o}}}^{ - 1}\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&{\left( {1 + {k_2}} \right){i_{\rm{o}}}} \end{array}} \right],$
 ${\mathit{\boldsymbol{B}}_{{\rm{cd}}}} = {\mathit{\boldsymbol{A}}_{\rm{o}}}^{ - 1},\mathit{\boldsymbol{C}} = \left[ {\begin{array}{*{20}{c}} 1&0 \end{array}} \right].$
3 模型预测控制器设计

3.1 模型预测

 $\left\{ \begin{array}{l} \Delta \mathit{\boldsymbol{x}}\left( {k + 1} \right) = \mathit{\boldsymbol{A}}\Delta \mathit{\boldsymbol{x}}\left( k \right) + {\mathit{\boldsymbol{B}}_{\rm{u}}}\Delta \mathit{\boldsymbol{u}}\left( k \right) + {\mathit{\boldsymbol{B}}_{\rm{d}}}\Delta \mathit{\boldsymbol{d}}\left( k \right),\\ {y_{\rm{c}}}\left( k \right) = {\mathit{\boldsymbol{C}}_{\rm{c}}}\Delta \mathit{\boldsymbol{x}}\left( k \right) + {y_{\rm{c}}}\left( {k - 1} \right). \end{array} \right.$ (12)

 ${\mathit{\boldsymbol{B}}_{\rm{d}}} = \int_0^{{T_{\rm{s}}}} {{e^{{A_{\rm{c}}}\tau }}{\rm{d}}s} \cdot {\mathit{\boldsymbol{B}}_{{\rm{cd}}}},\Delta \mathit{\boldsymbol{x}}\left( k \right) = \mathit{\boldsymbol{x}}\left( k \right) - \mathit{\boldsymbol{x}}\left( {k - 1} \right),$
 $\Delta \mathit{\boldsymbol{u}}\left( k \right) = \mathit{\boldsymbol{u}}\left( k \right) - \mathit{\boldsymbol{u}}\left( {k - 1} \right),\Delta \mathit{\boldsymbol{d}}\left( k \right) = \mathit{\boldsymbol{d}}\left( k \right) - \mathit{\boldsymbol{d}}\left( {k - 1} \right).$
3.2 预测输出方程

1) 控制时域之外，控制量不变，即

 $\Delta u\left( {k + i} \right) = 0,\;\;\;i = {N_{\rm{u}}},{N_{\rm{u}}} + 1, \cdots ,{N_{\rm{p}}} - 1.$

2) 可测干扰在k时刻之后不变，即

 $\Delta d\left( {k + i} \right) = 0,\;\;\;i = 1,2, \cdots ,{N_{\rm{p}}} - 1.$

k时刻，定义系统的预测输出为

 ${\mathit{\boldsymbol{Y}}_{\rm{c}}}\left( {k + 1\left| k \right.} \right) = \left[ {\begin{array}{*{20}{c}} {{y_{\rm{c}}}\left( {k + 1\left| k \right.} \right)}\\ {{y_{\rm{c}}}\left( {k + 2\left| k \right.} \right)}\\ \vdots \\ {{y_{\rm{c}}}\left( {k + {N_{\rm{p}}}\left| k \right.} \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{e}}}\left( {k + 1\left| k \right.} \right)}\\ {{\omega _{\rm{e}}}\left( {k + 2\left| k \right.} \right)}\\ \vdots \\ {{\omega _{\rm{e}}}\left( {k + {N_{\rm{p}}}\left| k \right.} \right)} \end{array}} \right],$

 $\Delta \mathit{\boldsymbol{U}}\left( k \right) = \left[ {\begin{array}{*{20}{c}} {\Delta \mathit{\boldsymbol{u}}\left( {k\left| k \right.} \right)}\\ {\Delta \mathit{\boldsymbol{u}}\left( {k + 1\left| k \right.} \right)}\\ \vdots \\ {\Delta \mathit{\boldsymbol{u}}\left( {k + {N_{\rm{u}}} - 1\left| k \right.} \right)} \end{array}} \right],$

 $\begin{array}{l} \Delta \mathit{\boldsymbol{u}}\left( {k + i\left| k \right.} \right) = \left[ {\begin{array}{*{20}{c}} {\Delta {\mathit{\boldsymbol{T}}_{\rm{g}}}\left( {k + i\left| k \right.} \right)}\\ {\Delta {\mathit{\boldsymbol{T}}_{\rm{m}}}\left( {k + i\left| k \right.} \right)} \end{array}} \right],\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;i = 0,1, \cdots ,{N_u} - 1. \end{array}$

 $\begin{array}{l} {\mathit{\boldsymbol{Y}}_{\rm{c}}}\left( {k + 1\left| k \right.} \right) = {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{x}}}}\Delta \mathit{\boldsymbol{x}}\left( k \right) + {\mathit{\boldsymbol{I}}_{\rm{c}}}y\left( k \right) + \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{u}}}}\Delta \mathit{\boldsymbol{U}}\left( k \right) + {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{d}}}}\Delta \mathit{\boldsymbol{d}}\left( k \right). \end{array}$ (13)

3.3 优化问题及反馈控制律

 ${\mathit{\boldsymbol{R}}_{\rm{e}}}\left( {1 + k} \right) = \left[ {\begin{array}{*{20}{c}} {r\left( {k + 1} \right)}\\ {r\left( {k + 2} \right)}\\ \vdots \\ {r\left( {k + {N_{\rm{p}}}} \right)} \end{array}} \right].$

 $\left\{ \begin{array}{l} \mathop {\min }\limits_{\Delta \mathit{\boldsymbol{U}}\left( k \right)} \mathit{\boldsymbol{J}}\left( {y\left( k \right),\Delta \mathit{\boldsymbol{U}}\left( k \right),{N_{\rm{u}}},{N_{\rm{p}}}} \right),\\ \mathit{\boldsymbol{J}} = {\mathit{\boldsymbol{J}}_1} + {\mathit{\boldsymbol{J}}_2},\\ {\mathit{\boldsymbol{J}}_1} = {\left\| {{\mathit{\boldsymbol{Q}}_1}\left( {{\mathit{\boldsymbol{Y}}_c}\left( {k + 1\left| k \right.} \right) - {\mathit{\boldsymbol{R}}_{\rm{e}}}\left( {k + 1} \right)} \right)} \right\|^2},\\ {\mathit{\boldsymbol{J}}_2} = {\left\| {{\mathit{\boldsymbol{Q}}_2}\Delta \mathit{\boldsymbol{U}}\left( k \right)} \right\|^2}.\\ {\rm{s}}.\;{\rm{t}}.\;{\omega _{{\rm{e}}\min }}\left( k \right) \le {\omega _{\rm{e}}}\left( k \right) \le {\omega _{{\rm{e}}\max }}\left( k \right),\\ \;\;\;\;\;{\omega _{{\rm{r1}}\min }}\left( k \right) \le {\omega _{{\rm{r1}}}} \le {\omega _{{\rm{r1}}\max }}\left( k \right),\\ \;\;\;\;\;\Delta {T_{{\rm{g}}\min }}\left( k \right) \le \Delta {T_g}\left( k \right) \le \Delta {T_{{\rm{g}}\max }}\left( k \right),\\ \;\;\;\;\;\Delta {T_{{\rm{m}}\min }}\left( k \right) \le \Delta {T_{\rm{m}}}\left( k \right) \le \Delta {T_{{\rm{m}}\max }}\left( k \right),\\ \;\;\;\;\;{T_{{\rm{g}}\min }}\left( k \right) \le {T_g}\left( k \right) \le {T_{{\rm{g}}\max }}\left( k \right),\\ \;\;\;\;\;{T_{{\rm{m}}\min }}\left( k \right) \le {T_{\rm{m}}}\left( k \right) \le {T_{{\rm{m}}\max }}\left( k \right). \end{array} \right.$

 $\left\{ \begin{array}{l} \mathop {\min }\limits_{\Delta \mathit{\boldsymbol{U}}\left( k \right)} \frac{1}{2} {\varDelta} \mathit{{U}}{\left( {^k} \right)^{\rm{T}}}\mathit{\boldsymbol{H}} {\varDelta} \mathit{\boldsymbol{U}}\left( k \right) + \mathit{\boldsymbol{G}}{\left( {^k + 1\left| k \right.} \right)^{\rm{T}}} {\varDelta} \mathit{\boldsymbol{U}}\left( k \right),\\ {\rm{s}}.\;{\rm{t}}.\;{\mathit{\boldsymbol{C}}_{\rm{u}}} {\varDelta} \mathit{\boldsymbol{U}}\left( k \right) \ge b\left( {k + 1\left| k \right.} \right). \end{array} \right.$

 $\mathit{\boldsymbol{G}}\left( {k + 1\left| k \right.} \right) = - 2\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{u}}}^{\rm{T}}\mathit{\boldsymbol{Q}}_1^{\rm{T}}{\mathit{\boldsymbol{Q}}_1}{\mathit{\boldsymbol{E}}_{\rm{p}}}\left( {k + 1\left| k \right.} \right),$
 ${\mathit{\boldsymbol{E}}_{\rm{p}}}\left( {k + 1\left| k \right.} \right) = {\mathit{\boldsymbol{R}}_{\rm{e}}}\left( {k + 1} \right) - {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{x}}}} {\varDelta} \mathit{\boldsymbol{x}}\left( k \right) - {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{d}}}} {\varDelta} \mathit{\boldsymbol{d}}\left( k \right) - {I_{\rm{c}}}\mathit{\boldsymbol{y}}\left( k \right),$
 ${\mathit{\boldsymbol{C}}_{\rm{u}}} = {\left[ {\begin{array}{*{20}{c}} { - \mathit{\boldsymbol{I}}}&\mathit{\boldsymbol{I}}&{ - {\mathit{\boldsymbol{L}}^{\rm{T}}}}&{{\mathit{\boldsymbol{L}}^{\rm{T}}}}&{ - \mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{u}}}^{\rm{T}}}&{\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{u}}}^{\rm{T}}} \end{array}} \right]^{\rm{T}}},$
 ${\mathit{\boldsymbol{Y}}_{\min }}\left( {k + 1} \right) = \left[ {\begin{array}{*{20}{c}} {{y_{\min }}\left( {k + 1} \right)}\\ {{y_{\min }}\left( {k + 2} \right)}\\ \vdots \\ {{y_{\min }}\left( {k + {N_p}} \right)} \end{array}} \right],$
 ${\mathit{\boldsymbol{Y}}_{\max }}\left( {k + 1} \right) = \left[ {\begin{array}{*{20}{c}} {{y_{\max }}\left( {k + 1} \right)}\\ {{y_{\max }}\left( {k + 2} \right)}\\ \vdots \\ {{y_{\max }}\left( {k + {N_p}} \right)} \end{array}} \right],$
 $\begin{array}{l} \mathit{\boldsymbol{b}}\left( {k + 1\left| k \right.} \right) = \\ \left[ {\begin{array}{*{20}{c}} { - \Delta {\mathit{\boldsymbol{u}}_{\max }}\left( k \right)}\\ \vdots \\ { - \Delta {\mathit{\boldsymbol{u}}_{\max }}\left( {k + {N_u} - 1} \right)}\\ {\Delta {\mathit{\boldsymbol{u}}_{\min }}\left( k \right)}\\ \vdots \\ {\Delta {\mathit{\boldsymbol{u}}_{\min }}\left( {k + {N_u} - 1} \right)}\\ {\mathit{\boldsymbol{u}}\left( {k - 1} \right) - {\mathit{\boldsymbol{u}}_{\max }}\left( k \right)}\\ \vdots \\ {\mathit{\boldsymbol{u}}\left( {k - 1} \right) - {\mathit{\boldsymbol{u}}_{\max }}\left( {k + {N_u} - 1} \right)}\\ {{\mathit{\boldsymbol{u}}_{\min }}\left( k \right) - \mathit{\boldsymbol{u}}\left( {k - 1} \right)}\\ \vdots \\ {{\mathit{\boldsymbol{u}}_{\min }}\left( {k + {N_u} - 1} \right) - \mathit{\boldsymbol{u}}\left( {k - 1} \right)}\\ {\mathit{\boldsymbol{IY}}\left( k \right) + {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{x}}}}\Delta \mathit{\boldsymbol{x}}\left( k \right) + {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{d}}}}\Delta \mathit{\boldsymbol{d}}\left( k \right) - {\mathit{\boldsymbol{Y}}_{\max }}\left( {k + 1} \right)}\\ {{\mathit{\boldsymbol{Y}}_{\min }}\left( {k + 1} \right) - {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{x}}}}\Delta \mathit{\boldsymbol{x}}\left( k \right) - {\mathit{\boldsymbol{S}}_{{\rm{c}},{\rm{d}}}}\Delta \mathit{\boldsymbol{d}}\left( k \right) - \mathit{\boldsymbol{IY}}\left( k \right)} \end{array}} \right], \end{array}$

I为单位矩阵，L为各元素都为单位矩阵的下三角矩阵.

 图 6 MPC控制器结构 Figure 6 MPC controller structure
4 系统建模与仿真分析

 图 7 离线仿真模型 Figure 7 Offline simulation model
 图 8 中国典型循环工况 Figure 8 Typical urban driving cycle in China

 图 9 电机转矩对比 Figure 9 Comparison of MG1 and MG2 torque
 图 10 发动机转速和转矩对比 Figure 10 Comparison of engine speed and torque

 图 11 冲击度比较 Figure 11 Jerk comparison
 图 12 车速对比 Figure 12 Vehicle speed comparison in simulation
5 结论

1) 本文提出一种基于模型预测控制的模式切换过程中转矩动态补偿控制方法，并设计一种基于数据驱动的模型预测控制器.仿真结果表明，在保证动力性的前提下，相比于PID控制和被动切换，提出的模型预测控制器有效地减小了整车模式切换时的峰值冲击度，并且符合德国汽车行业中冲击度的推荐值——| j |≤10 m·s-3[15]，同时实现了发动机的正常启动，保证了汽车模式切换时的平顺性，提高了模式切换品质.

2) 本文以行星式混合动力客车为研究对象建立系统仿真模型，提出的模型预测控制方法以及优化问题对其他构型的混合动力车辆的起步协调控制、控制目标及参数的调整同样具有一定的借鉴意义和参考作用.

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