- Original Article
- Open Access

# City-Bus-Route Demand-based Efficient Coupling Driving Control for Parallel Plug-in Hybrid Electric Bus

- Qin-Pu Wang
^{1}, - Chao Yang
^{2}View ORCID ID profile, - Ya-Hui Liu
^{2}Email author and - Yuan-Bo Zhang
^{2}

**31**:58

https://doi.org/10.1186/s10033-018-0257-y

© The Author(s) 2018

**Received: **14 December 2016

**Accepted: **22 June 2018

**Published: **5 July 2018

## Abstract

Recently, plug-in hybrid electric bus has been one of the energy-efficient solutions for urban transportation. However, the current vehicle efficiency is far from optimum, because the unpredicted external driving conditions are difficult to be obtained in advance. How to further explore its fuel-saving potential under the complicated city bus driving cycles through an efficient control strategy is still a hot research issue in both academic and engineering area. To realize an efficient coupling driving operation of the hybrid powertrain, a novel coupling driving control strategy for plug-in hybrid electric bus is presented. Combined with the typical feature of a city-bus-route, the fuzzy logic inference is employed to quantify the driving intention, and then to determine the coupling driving mode and the gear-shifting strategy. Considering the response deviation problem in the execution layer, an adaptive robust controller for electric machine is designed to respond to the transient torque demand, and instantaneously compensate the response delay and the engine torque fluctuation. The simulations and hard-in-loop tests with the actual data of two typical driving conditions from the real-world city-bus-route are carried out, and the results demonstrate that the proposed method could guarantee the hybrid powertrain to track the actual torque demand with 10.4% fuel economy improvement. The optimal fuel economy can be obtained through the optimal combination of working modes. The fuel economy of plug-in hybrid electric bus can be significantly improved by the proposed control scheme without loss of drivability.

## Keywords

- Hybrid electric vehicle
- Single-shaft parallel electromechanical powertrain
- Coupling driving mode
- Adaptive robust control

## 1 Introduction

As representative of new energy vehicles, plug-in hybrid electric vehicle is always a hot topic in the field of recent vehicle technology [1]. Especially in areas of urban public transport, the excellent performance of low energy consumption and low emissions makes the plug-in hybrid electric bus (PHEB) become the primary solution [2, 3]. Recently, with the application of the idle-stop technology [4], the all-electric range of PHEB might be extended by utilizing more pure electric driving [5]. Considering the traffic congestion in the big city of China, the vehicle launch and accelerating condition might frequently appear in the driving cycles of the city bus [6]. However, in most cases the electric energy stored in the PHEB might not cover the whole city-bus-route, the optimal coordinated operation between the engine and the electric machine (EM) is very worthy of study [7]. Because of the configuration features, the coordinated control becomes very difficult especially for the single-shaft parallel hybrid powertrain with the automated mechanical transmission (AMT) [8–10]. To solve this problem, several solutions have been presented for real-time optimization of the steady-state energy flows utilizing dynamic programming presented by Li et al. [11] and Lin et al. [12], equivalent consumption minimization strategy presented by Yang et al. [13] and Geng et al. [14], or model predictive control (MPC) strategy presented by Yan et al. [15]. Nevertheless, the transient process, such as the complicated electromechanical coupling working mode and the multi-modes transition, was not considered in these control strategies.

During a vehicle launch and accelerating process, PHEB might fulfill an electromechanical coupling-driving mode after a pure electric driving mode to ensure the operation efficiency until the engine torque satisfies the demand torque on a high efficient zone [16–18]. Therefore, the coupling driving mode, which refers to the hybrid driving mode or the engine active charging mode, is crucial for the vehicle launch and accelerating process of PHEB [16].

Considering the difference between dynamic characteristics of the engine and the EM, it is necessary to further study the coordinated control method for an efficient solution of the hybrid powertrain. Therefore, a novel torque-demand control approach based on the MPC was proposed by He et al. [19], to implement the torque control of parallel hybrid powertrain. In addition, for a parallel hybrid powertrain, the coordinated control method using dynamic input allocation, MPC, and sliding mode control method presented by Cordiner et al. [20], Minh et al. [21], and Metin et al. [22], respectively. Using the fast response behavior of the EM, an electromechanical coupling driving control scheme was proposed by Yang et al. [23, 24] to achieve good torque tracking performance.

The coordinated control strategies can ensure the torque tracking performance during a coupling driving process. However, the instantaneous variation of the traffic flows, road conditions, and the passenger loads in a city-bus-route, might greatly affect the robustness of the control system. To adaptively deal with the stochastic driving intention, a city-bus-route demand-based coupling driving control approach is designed for the single-shaft parallel PHEB with AMT. Firstly, the time-varying driving intention is quantified with a fuzzy logic, and then the coupling driving mode and the AMT gear-shifting strategy are determined with a strategy determination module. Secondly, considering the dynamic characteristics of the EM, the adaptive robust controller is designed for the EM to respond to the transient torque demand. Meanwhile, the response deviation and the transient fluctuation of the engine torque are compensated with the fast response behavior of the EM.

The rest of the paper is organized as follows: Section 2 gives the models of the single-shaft parallel PHEB. The efficient coupling driving control approach is developed in Section 3. The results of simulation and hard-in-loop (HIL) test are given in Section 4. Finally, the conclusion and discussion are given in Section 5.

## 2 Model Descriptions

Parameters of HEB powertrain

Components | Description |
---|---|

Diesel engine | YC6J200-42, nominal power: 147 kW |

EM | Permanent magnet, max torque: 750 Nm, nominal power: 94 kW, peak power: 121 kW |

Battery | Lithium titanate battery, capacity: 60 Ah, nominal voltage: 346 V |

Gearbox | AMT, gear ratios: 7.05, 4.13, 2.52, 1.59, 1, 0.78. Efficiency of gearbox is assumed 95% |

Final drive ratio | 4.2 |

### 2.1 Energy Demand Analyses of City Bus Route

### 2.2 Diesel Engine Model

*ϕ*represents the accelerator pedal position.

*J*

_{e}is the moment of inertia of the crankshaft;

*ω*

_{e}is the rotational speed of the crankshaft;

*φ*(d

*ω*

_{e}/d

*t*) is the dynamic compensation factor;

*k*

_{e}and

*τ*

_{e}are the proportional coefficient and the time constant, respectively;

*T*

_{e}and

*T*

_{L}are the effective torque and the load torque of the engine, respectively;

*T*

_{es}is the static torque of the engine, which could be obtained from the engine map;

*ΔT*

_{e}represents a dynamic correction item of the engine torque, which could be described as follows:

### 2.3 EM Model

*i*

_{d}and

*i*

_{q}are the d and q axis stator currents, respectively;

*u*

_{d}and

*u*

_{q}are the d and q axis stator voltages, respectively;

*R*

_{s},

*L*,

*P*and

*Φ*represent the stator resistance, the stator inductance, the number of the pole pairs, and magnet’s flux linkage, respectively;

*J*

_{m}and

*B*

_{μ}are the moment of inertia of the EM output shaft and the damping coefficient, respectively;

*T*

_{e}is the engine torque when the PHEB runs in the active charging mode, and

*T*

_{m}is the EM torque, which can be described as the following equation:

## 3 City-Bus-Route Demand-based Efficient Coupling Driving Control Strategy

In this section, a novel city-bus-route demand-based coupling driving control strategy is presented. Firstly, the fuzzy logic controller quantifies the driver’s driving intention. Then the AMT gear-shifting strategy and the coupling driving mode are determined with the quantified driving intention in the strategy determination module. Secondly, the designed PI controller for engine and adaptive robust controllers for EM implement the torque tracking control in the coupling driving mode. Moreover, considering the properties of the single-shaft parallel hybrid powertrain, the response error of engine torque is compensated by the accurate EM torque control to guarantee the torque tracking performance of powertrain.

### 3.1 Fuzzy Logic Inference for Driving Intention

*v*

_{veh}, the relative accelerator pedal position

*ϕ*

_{rel}, and the absolute value of the change rate of accelerator pedal position d

*ϕ*/d

*t*, the output variable is driving intention

*I*

_{d}. The relative accelerator pedal position could be obtained by the equation as follows:

*ϕ*is actual accelerator pedal position,

*ϕ*

_{equ}is equilibrium accelerator pedal position reflecting the accelerator pedal position which maintains the vehicle driving on flat road with a uniform speed, and the value of

*ϕ*

_{equ}might be obtained through looking up the steady-state table with the inputs of the engine torque and the engine rotational speed, and the engine torque could be obtained by the vehicle longitudinal dynamics equation as follows:

*F*

_{f}and

*F*

_{w}are the rolling resistance and the aerodynamic drag, respectively.

*r*,

*η*

_{T},

*i*

_{g}, and

*i*

_{f}are wheel radius, transmission efficiency, AMT gear ratio, and differential ratio, respectively.

*v*

_{veh}are L, M, and H, which represent the low speed, the middle speed, and the high speed, respectively. The memberships of

*f*

_{rel}are Nb, Ns, Z, Ps, and Pb, which are the negative big, the negative small, the zero, the positive small, and the positive big of the equilibrium accelerator pedal open, respectively. The memberships of d

*f*/d

*t*are S, Mi, and Bi, which are the small, the middle, and the big of the change rate of accelerator pedal open, respectively. Moreover, the output variable

*I*

_{d}obtained by the defuzzification are quantified as St, D, K, A, and B, which represent the intention of stop, decelerating, keep, accelerating, urgent accelerating.

Fuzzy logic rule base

Relative pedal open | Change rate of accelerator pedal position d | Vehicle speed
| ||
---|---|---|---|---|

S | M | H | ||

Nb | S | St | D | D |

Mi | St | D | D | |

Bi | St | D | D | |

Ns | S | St | K | K |

Mi | St | D | D | |

Bi | St | D | D | |

Z | S | St | St | K |

Mi | St | K | K | |

Bi | St | K | K | |

Ps | S | A | K | K |

Mi | A | A | A | |

Bi | B | B | B | |

Pb | S | A | A | A |

Mi | A | A | A | |

Bi | B | B | B |

### 3.2 Balanced AMT Gear-shifting Strategy and Driving Mode Determination Module

The double-parameters balanced AMT gear-shifting strategy (BGS), which balances the dynamic gear-shifting (DGS) maneuver and the economic gear-shifting (EGS) maneuver, is employed. This strategy tends to dynamic or economic depending on the driving intention, which could be quantified by the designed fuzzy inference. Taking the effects of engine operating points for example, the full DGS ensures that engine might work on the external characteristic line, and the full EGS reflects that engine would work on the optimal operating line with the highest efficiency. According to the quantified driving intention, the AMT gear-shifting maneuver might be determined that the gear-shifting maneuver tends to DGS with urgent accelerating intention and conversely tends EGS with keep and normal accelerating intention. Therefore, the energy-efficient operation of PHEB without drivability loss might be fulfilled by the proposed gear-shifting strategy.

*I*

_{d}(

*t*

_{switch}) is the driving intention when the engine engages into the driveline at the time

*t*

_{switch}, and

*I*

_{th}represents the logic threshold of driving intention, and its value could be obtained by repeated tests.

### 3.3 PI torque Controller for Diesel Engine

*u*

_{eng}is the engine control input that represent the fuel injection quantity,

*T*

_{e}

^{r}is demand powertrain speed,

*k*

_{p},

*k*

_{i}are proportional and integral gains, respectively.

### 3.4 Adaptive Robust Controllers for the EM Torque Tracking Control

*ω*

_{m}

^{r},

*i*

_{d}

^{r},

*i*

_{q}

^{r}are the desired values of the EM speed, the d-axis, and the q-axis stator currents when the EM operates in the driving mode, respectively.

*ω*

_{m}

^{*},

*i*

_{d}

^{*},

*i*

_{q}

^{*}are the desired values of the EM speed, the d-axis, and the q-axis stator currents when the EM operates in the generating mode, respectively. Combining with the EM model described in Eqs. (3) and (4), the error equations that have considered the uncertainties can be defined when EM operates in the driving mode:

*θ*

_{1},

*θ*

_{2},

*τ*

_{1}, and

*τ*

_{2}are given as follows:

*i*= 1, 2) are the error between the uncertain parameters and the adaptive estimated value, which would be described in later part. Moreover,

*w*

_{1},

*w*

_{2}represent the load disturbances of EM control system. Then the performance vectors are defined as follows:

*ρ*

_{i}and \(\bar{\rho }_{i}\) (

*i*= 1, 2, 3) are the weighting factors.

*T*

_{E}is an error term. Moreover,

*u*

_{1},

*u*

_{2},

*u*

_{3},

*u*

_{4}are equivalent control inputs described as follows:

*L*

_{2}-gain, that is, when

*w*≠ 0, the system from the disturbance inputs

*w*

_{i}(

*i*= 1, 2) to the penalty outputs

*z*and \(\bar{z}\) has finite

*L*

_{2}-gain not larger than

*γ*

_{i}(

*i*= 1, 2).

*T*> 0 is any given scalar.

*γ*

_{i}(

*i*= 1, 2) are the evaluating factors. Thus, regarding the system described in Eqs. (10) and (11), an adaptive robust controller for EM is designed when EM operates in the driving mode:

*k*

_{i}(

*i*= 1, 2, 3) and \(\bar{k}_{i} (i = 1,2,3)\) are adjustable parameters of the controller, \(Z_{1} = x_{3} - \alpha_{1} (x_{1} ,\hat{\theta }_{1} )\) and \(Z_{2} = \bar{x}_{3} - \alpha_{2} (\bar{x}_{1} ,\hat{\tau }_{1} )\), \(\alpha_{1} (x_{1} ,\hat{\theta }_{1} )\) and \(\alpha_{2} (\bar{x}_{1} ,\hat{\tau }_{1} )\) are virtual controllers which could be chosen as follows:

*χ*

_{i}(

*i*= 1, 2) and

*β*

_{i}(

*i*= 1, 2) are adjustable parameters of adaptive laws.Taking the driving mode of EM for example, the adaptive robust controller described in Eqs. (17) and (18) might be designed by the close-loop system Lyapunov stability analysis. First, a positive definite Lyapunov function is defined as follows:

*w*

_{1}, the inequality transform might be used which can be written as follows:

*k*

_{i}(

*i*= 1, 2, 3) should satisfy the conditions as follows:

Therefore, combing with the LaSalle invariant set principle, it can be concluded that the designed controller can achieve the mentioned above control objectives. Because the adaptive controller described in Eqs. (19) and (20) for the generating mode of EM is deduced that is similar with that of the driving mode of EM, so the proof procedure will be omitted here.

## 4 Validation Results and Analysis

Control parameters

Parameter | Value | Parameter | Value |
---|---|---|---|

| 0.9 | \(\bar{k}_{3}\) | 7.5 |

| 9.1 |
| 0.759 |

| 0.62 |
| 0.317 |

| 11.6 |
| 0.561 |

| 23.5 |
| 0.232 |

\(\bar{k}_{1}\) | 0.06 |
| 0.92 |

\(\bar{k}_{2}\) | 1.21 |
| 0.11 |

To verify the effectiveness of the proposed control approach, a driving condition of city-bus-route 613 in Chongqing, China, is selected as the simulation condition.

### 4.1 Driving Intention Quantification

*I*

_{th}could be selected as 3.2. Because the focus in this paper is the process of PHEB driving mode, two vehicle launch process are extracted from the selected driving condition and the results are shown in Sections 4.2 and 4.3.

### 4.2 Results under Different Driving Intentions

As shown in Figure 11(a), the results of vehicle speed obtained from the simulation are close to the test data, and the deviation reflects the error between simulation model and actual vehicle. With the increasing vehicle speed, the AMT will execute the gear shifting operation in accordance with BGS strategy. The engine torque tracking performance can be ensured, which is shown in Figure 11(c). The designed adaptive robust controller can respond to the demand EM torque quickly and accurately, as shown in Figure 11(d).

*I*

_{d}(

*t*

_{switch}) <

*I*

_{th}. The simulation results are shown in Figure 12. As shown in Figure 12(a), the vehicle speed of simulation is in accordance with the test data, and with the intention of slow driving, Figure 12(c) shows that the engine demand torque is elevated by the generating torque of EM in the driving condition of the low torque demand. In addition, due to the engine response characteristics, the PI controller with the control input of fuel injection cannot eliminate the torque deviation. However, the proposed coupling driving control approach utilizes the EM torque to compensate the above torque deviation, and the good tracking performance is ensured by the designed adaptive robust controller for EM, the effect curves of which is shown in Figure 12(d). Therefore, it can be concluded that the efficient operation of PHEB is ensured. It should be noted that Figure 11 and Figure 12 show two different driving conditions with relevant driving intentions. Under urgent driving condition, the test vehicle uses less time than that under slow driving condition, when it reaches the same speed. Thus, the timeline in Figure 11 shows less than that in Figure 12.

### 4.3 HIL Test Results

Comparison results of two control strategy

Strategy | FC (L) | Improvement (%) | Average BSFC(g/kWh) |
---|---|---|---|

Rule-based | 1.25 | ‒ | 228.23 |

Proposed | 1.12 | 10.4 | 204.51 |

## 5 Conclusions

- (1)
The driving intention is recognized by the designed fuzzy logic inference.

- (2)
According to the quantified intention, the mode selection method in the coupling driving mode and AMT gear-shifting strategy given in the strategy determination module by the pre-set threshold.

- (3)
The adaptive robust controller is designed for EM to ensure the tracking effect with the uncertainties and disturbances.

- (4)
The proposed control approach could guarantee the torque tracking performance, and the fuel economy can be improved 10.4% through adjusting the engine working points under different driving intentions.

- (5)
The real time capability of the control approach has been validated by HIL tests. The proposed control method has the potential to apply in the actual vehicle.

## Declarations

### Authors’ Contributions

Q-PW and CY were in charge of the whole trial; CY wrote the manuscript; Y-HL and Y-BZ assisted with sampling and laboratory analyses. All authors have read and approved the final manuscript.

### Authors’ Information

Qin-Pu Wang, born in 1964, is the General Manager Assistant at *Zhongtong Bus Hold Co., Ltd., China*. He received his bachelor degree from *Xi’an Highway Institute, China*, in 1984. His research interests include design and manufacture of hybrid electric vehicle. E-mail: QinPu_Wang@163.com.

Chao Yang, born in 1986, is currently a postdoctoral fellow at *State Key Laboratory of Automotive Safety and Energy, Tsinghua University, China*. He received his PhD degree on Control Science and Engineering from *Yanshan University, China*, in 2016. His research interests include energy-efficient control strategy design for hybrid electric vehicles. E-mail: chaoyang1986@tsinghua.edu.cn.

Ya-Hui Liu, born in 1980, is currently an associate professor at *State Key Laboratory of Automotive Safety and Energy, Tsinghua University, China*. He received his bachelor degree from *Jilin University, China*, in 2003 and PhD degree from *Beihang University, China*, in 2009, respectively. His research interests include vehicle system dynamics, steering system and driver-vehicle system. E-mail: liuyahui@tsinghua.edu.cn.

Yuan-Bo Zhang, born in 1990, is currently working at *State Key Laboratory of Automotive Safety and Energy, Tsinghua University, China*. His research interests include regenerative braking control strategy for electrified vehicles. E-mail: yuanbzhang@163.com.

### Competing Interests

The authors declare no competing financial interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51605243), National Key Science and Technology Projects of China (Grant No. 2014ZX04002041), and 1-class General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2016M590094).

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## Authors’ Affiliations

## References

- Yong Sun, Zi-Lin Ma, Gong-You Tang, et al. Estimation method of state-of-charge for lithium-ion battery used in hybrid electric vehicles based on variable structure extended kalman filter.
*Chinese Journal of Mechanical Engineering*, 2016, 29(4): 717–726.View ArticleGoogle Scholar - Chao Yang, Liang Li, Si-Xiong You, et al. Cloud computing-based energy optimization control framework for plug-in hybrid electric bus.
*Energy*, 2017, 125: 11–26.View ArticleGoogle Scholar - Liang Li, Si-Xiong You, Chao Yang, et al. Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses.
*Applied Energy*, 2016, 162: 868–879.View ArticleGoogle Scholar - Marcello Canova, Yann Guezennec, Steve Yurkovich. On the control of engine start/stop dynamics in a hybrid electric vehicle. ASME Transactions, Journal of Dynamic System, Measurement, and Control, 2009, 131(12), 061005: 1–12.Google Scholar
- Zheng Chen, Bing Xia, Chenwen You, et al. A novel energy management method for series plug-in hybrid electric vehicles.
*Applied Energy,*2015, 145: 172–179.View ArticleGoogle Scholar - Chao Yang, Jian Song, Liang Li, et al. Economical launching and accelerating control strategy for a single-shaft parallel hybrid electric bus.
*Mechanical Systems and Signal Processing*, 2016, 76-77: 649–664.View ArticleGoogle Scholar - Tian-Heng Feng, Lin Yang, Qing Gu, et al. A supervisory control strategy for plug-in hybrid electric vehicles based on energy demand prediction and route preview.
*IEEE Transactions on Vehicular Technology,*2015, 64(5): 1691–1770.View ArticleGoogle Scholar - Hong-Cai Li, Qing-Dong Yan, Chang-Le Xiang, et al. Analysis method and principle of dual-mode electro-mechanical variable transmission program.
*Chinese Journal of Mechanical Engineering*, 2012, 25(3): 524–529.View ArticleGoogle Scholar - Wei-Da Wang, Li-Jin Han, Chang-Le Xiang, et al. Synthetical efficiency-based optimization for the power distribution of power-split hybrid electric vehicles.
*Chinese Journal of Mechanical Engineering*, 2014, 27(1): 58–68.View ArticleGoogle Scholar - Dongsuk Kum, Huei Peng, Norman Bucknor. Control of engine-starts for optimal drivability of parallel hybrid electric vehicles. ASME Transactions, Journal of Dynamic System, Measurement, and Control, 2014, 135(3), 021020: 1–10.Google Scholar
- Liang Li, Chao Yang, Ya-Hui Zhang, et al. Correctional DP-based energy management strategy of plug-in hybrid bus for city-bus-route.
*IEEE Transactions on Vehicular Technology*, 2015, 64(7): 2792–2803.View ArticleGoogle Scholar - Chan-Chiao Lin, Huei Peng, Jessy-W. Grizzle et al. Power management strategy for a parallel hybrid electric truck.
*IEEE Transactions on Control Systems Technology*, 2003, 11(6): 839–849.View ArticleGoogle Scholar - Chao Yang, Siyu Du, Liang Li, et al. Adaptive real-time optimal energy management strategy based on equivalent factors optimization for plug-in hybrid electric vehicle.
*Applied Energy*, 2017, 203: 883–896.View ArticleGoogle Scholar - Bo Geng, James-K. Mills, Dong Sun. Energy management control of microturbine-powered plug-in hybrid electric vehicles using the telemetry equivalent consumption minimization strategy.
*IEEE Transactions on Vehicular Technology*, 2011, 60(9): 4238–4248.View ArticleGoogle Scholar - Feng-Jun Yan, Jun-Min Wang, Kai-Sheng Huang. Hybrid electric vehicle model predictive control torque-split strategy incorporating engine transient characteristics.
*IEEE Transactions on Vehicular Technology*, 2012, 61(6): 2458–2467.View ArticleGoogle Scholar - Li Chen, Gang Xi, Jing Sun. Torque coordination control during mode transition for a series-parallel hybrid electric vehicle.
*IEEE Transactions on Vehicular Technology*, 2012, 61(7): 2936–2949.View ArticleGoogle Scholar - K Koprubasi, E R Westervelt, G Rizzoni. Toward the systematic design of controllers for smooth hybrid electric vehicle mode changes. Proceedings of the 2007 American Control Conference, 2007: 2985–2990.Google Scholar
- Hyunsup Kim, Jihun Kim, Hyeongcheol Lee. Mode transition control using disturbance compensation for a parallel hybrid electric vehicle.
*Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering*, 2012, 225: 125–150.Google Scholar - Lin He, Tie-Long Shen, Liang-Yao Yu, et al. A model-predictive-control-based torque demand control approach for parallel hybrid powertrains.
*IEEE Transactions on Vehicular Technology*, 2013, 62(3): 1041–1052.View ArticleGoogle Scholar - Stefano Cordiner, Sergio Galeani, Francesco Mecocci, et al. Torque setpoint tracking for parallel hybrid electric vehicles using dynamic input allocation.
*IEEE Transactions on Control Systems Technology*, 2014, 22(5): 2007–2015.View ArticleGoogle Scholar - V T Minh, A A Rashid. Modeling and model predictive control for hybrid electric vehicles.
*International Journal of Automotive Technology*, 2012, 13(3): 477–485.View ArticleGoogle Scholar - Metin Gokasan, Seta Bogosyan, D J Goering. Sliding mode based powertrain control for efficiency improvement in series hybrid-electric vehicles.
*IEEE Transactions on Power Electronics*, 2006, 21(3): 779–790.View ArticleGoogle Scholar - Chao Yang, Xiao-Hong Jiao, Liang Li, et al. Electromechanical coupling driving control for single-shaft parallel hybrid powertrain.
*SCIENCE CHINA Technological Sciences*, 2014, 57(3): 541–549.View ArticleGoogle Scholar - Chao Yang, Xiao-Hong Jiao, Liang Li, et al. Robust coordinated control for hybrid electric bus with single-shaft parallel hybrid powertrain.
*IET Control Theory and Application*, 2015, 9(2): 270–282.View ArticleGoogle Scholar