# Parallel Hybrid Electric Vehicle Modelling and Model Predictive Control

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, H

_{∞}, or sliding mode. However, all conventional control methods cannot include the real-time dynamic constraints of the vehicle physical limits, the surrounding obstacles, and the environment (road and weather) conditions. Therefore, a MPC with horizon state and open loop control prediction subject to dynamic constraints are mainly used to control as real-time the HEV speeds and torques. Due to the limit size of this paper, we have reviewed some of the most recent research of MPC applications for HEVs. In this paper, vehicle dynamic formulas and calculations are referred to the reference [1].

## 2. Modelling of the Parallel HEV

_{S}is the clutch friction coefficient.

## 3. Model Predictive Control for the HEV

## 4. The MPC with Softened Constraints for the HEV

_{0}, does not lead to any violation of states and input (${x}_{min}=\left[\begin{array}{c}-1\\ -1\end{array}\right]$ and $-2\le u\le 2$). In this ${x}_{0}$, the solutions of the two control schemes are always available. We can see that the NMPC with a softened state approaches the asymptotic point faster than the hard constraints. It means that, if we somehow loosen some of the constraints, the optimizer can generate easier optimal inputs and the system will be more stable.

## 5. The MPC with Softened Constraints for the HEV

#### 5.1. The MPC for the HEV in Pure Electrical Drive

^{2}. The output torque on the shaft 2 is constrained as $\left|T\right|=\tau \pi \frac{{d}^{3}}{16}$, with the diameter $d=0.05\mathrm{m}$. Then, the torque softened constraint on shaft 2 is $\left|{T}_{2}\right|=455\mathrm{Nm}$.

#### 5.2. The MPC for the HEV in High Speed with ICE

## 6. Conclusions

## Author Contributions

## Funding

**CZ.02.1.01/0.0/0.0/16_025/0007293**.

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Vu, T.M.; Moezzi, R.; Cyrus, J.; Hlava, J.; Petru, M. Parallel Hybrid Electric Vehicle Modelling and Model Predictive Control. *Appl. Sci.* **2021**, *11*, 10668.
https://doi.org/10.3390/app112210668

**AMA Style**

Vu TM, Moezzi R, Cyrus J, Hlava J, Petru M. Parallel Hybrid Electric Vehicle Modelling and Model Predictive Control. *Applied Sciences*. 2021; 11(22):10668.
https://doi.org/10.3390/app112210668

**Chicago/Turabian Style**

Vu, Trieu Minh, Reza Moezzi, Jindrich Cyrus, Jaroslav Hlava, and Michal Petru. 2021. "Parallel Hybrid Electric Vehicle Modelling and Model Predictive Control" *Applied Sciences* 11, no. 22: 10668.
https://doi.org/10.3390/app112210668