Journal of Advanced Transportation

Volume 2017 (2017), Article ID 4125384, 19 pages

https://doi.org/10.1155/2017/4125384

## Electric Vehicle Longitudinal Stability Control Based on a New Multimachine Nonlinear Model Predictive Direct Torque Control

Electrotechnical Engineering Laboratory, Tahar Moulay University, Saida, Algeria

Correspondence should be addressed to Abdelkader Merah

Received 3 March 2017; Accepted 28 August 2017; Published 12 November 2017

Academic Editor: Xing Wu

Copyright © 2017 M’hamed Sekour et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to improve the driving performance and the stability of electric vehicles (EVs), a new multimachine robust control, which realizes the acceleration slip regulation (ASR) and antilock braking system (ABS) functions, based on nonlinear model predictive (NMP) direct torque control (DTC), is proposed for four permanent magnet synchronous in-wheel motors. The in-wheel motor provides more possibilities of wheel control. One of its advantages is that it has low response time and almost instantaneous torque generation. Moreover, it can be independently controlled, enhancing the limits of vehicular control. For an EV equipped with four in-wheel electric motors, an advanced control may be envisaged. Taking advantage of the fast and accurate torque of in-wheel electric motors which is directly transmitted to the wheels, a new approach for longitudinal control realized by ASR and ABS is presented in this paper. In order to achieve a high-performance torque control for EVs, the NMP-DTC strategy is proposed. It uses the fuzzy logic control technique that determines online the accurate values of the weighting factors and generates the optimal switching states that optimize the EV drives’ decision. The simulation results built in Matlab/Simulink indicate that the EV can achieve high-performance vehicle longitudinal stability control.

#### 1. Introduction

One of the most fundamental differences between electric vehicles (EVs) and the conventional internal combustion engine vehicles (ICEVs) is that EVs are fully or partially driven by electric motors, which can bring about a lot of unique advantages for dynamic traction control [1]. With the superior control performance of electric motors compared to ICEVs, EVs could be not only clean, but also able to achieve higher levels of safety and handling [1, 2].

The distinct advantages of well-controlled electric motors may include fast torque response [1, 3], simple dynamics [1, 4], easy-to-obtain torque feedback (the torque generated from electric motors is proportional to the motor current for industrial applications [5, 6]), capability of generating both traction and braking forces (regenerative braking during deceleration can be realized using electric motors [7, 8]), and easy-to-implement distributed in-wheel motor systems (electric motors usually have compact sizes but powerful and flexible outputs, which can improve dynamic control stability [4, 9, 10], energy efficiency [11], and fun to drive [12]).

Antilock braking system (ABS) and traction control (TC) system represent both classic effective approaches to longitudinal vehicle dynamics control. The primary functions of these systems can be formulated as follows in accordance with reference literature [13]: ABS is a system that prevents the locking of wheels during braking in order to achieve high brake performance while simultaneously maintaining vehicle stability. TC is a system that prevents the skidding of wheels during take-off and acceleration. As for TC, an alternative term is also known from the technical literature: acceleration slip regulation (ASR).

In the last years, several techniques based on nonlinear control have been applied in wheel slip control research. In [14], a model control structure named the behavior model control (BMC), well adapted to the nonlinear systems, which realizes the wheel slip control, is used to solve the nonlinear problem of adhesion. As a result, the skid phenomenon disappeared and the stability of the vehicle was ensured. A fuzzy logic slip control system for EVs with in-wheel motors was introduced in [15]. Reference [16] proposed a nonlinear wheel slip control algorithm which ensures the stability in a closed loop. Reference [17] proposed a fuzzy logic antiskid control structure which is used to overcome the main problem of powertrain systems in the wheel road adhesion characteristic. This structure can prevent vehicle slipping and show good vehicle stability on a curved path. In [18], a wheel slip controller based on sliding mode framework is proposed. A nonlinear model predictive controller for wheel slip control of EV equipped with four in-wheel motors is studied in [19]. The research object in [20] is to study the acceleration slip regulation (ASR) control for two-wheel independent driving EV based on dynamic torque distribution.

The loss of adherence of one of the four wheels is likely to destabilize the vehicle, which needs to be solved either in traction or in braking mode. In order to improve the safety and dynamic performance of electric vehicles and prevent the wheel from locking or slipping when braking or accelerating, it is necessary to control the slip ratio of each wheel in the stable region. Combining the two functions ASR and ABS, this paper presented a new longitudinal control for the electric vehicle equipped with four PMS in-wheel motors. A main significant advantage of this proposed longitudinal control is that it can act as an antilock braking system (ABS) by preventing the wheels from getting locked during braking and as acceleration slip regulation (ASR) by preventing the wheels from slipping during acceleration. Moreover, using the wheel angular acceleration and the slip ratio, a fuzzy ASR/ABS controller is designed; based on the experimental road, the vehicle will achieve a good acceleration performance when the slip ratio is maintained within the optimal range, and this is done by adjusting the correspondent PMS in-wheel motor torque dynamically. Compared with previous studies, the proposed longitudinal control, which has been verified under accelerating maneuvers and braking maneuvers, proves its robustness and the longitudinal slip ratio of each wheel can reach quickly the optimal longitudinal slip ratio.

Permanent magnet synchronous motors (PMSMs) have been considered the potential candidate for electric vehicle (EV) applications due to their high power density, low maintenance cost, effectiveness, high torque ratio, wide speed range, dynamic qualities, and robust operations [21, 22]. Focusing on the EV-traction application, a fast and robust torque response of the PMSM is required in a wide speed range to meet the instantaneous torque demand commanded by the driver.

Examining the control structure for EV traction, direct torque control (DTC) for traction means the torque control of a traction motor (e.g., a permanent magnet synchronous motor (PMSM) drive). Thus, the DTC strategy for PMSM drive is the right candidate for the high-performance control to meet the EV-traction requirements. However, high torque and flux ripples and variable switching can be observed because of an included switching table, and these are some of its drawbacks [23].

To overcome these drawbacks, improved DTC schemes have been reported in the literature [21, 22, 24, 25]. In order to obtain fast and robust torque response and to solve the problems caused by the torque ripple affecting the mechanical transmission of the electric traction chain, the basic DTC strategy can be integrated with a space vector modulation (SVM) [26–28]. In this case, the torque and stator flux are regulated more accurately with a fixed switching frequency. Other methods based on fuzzy logic control have been adopted to ensure good performance [21]. A fuzzy direct torque control (FDTC) based on space vector modulation, which uses the stator flux and the torque errors through two fuzzy logic controllers to generate a voltage space vector (reference voltage), is to provide the inverter switching states.

Model predictive control (MPC) is now regarded as one of the most robust control strategies. Several variants of MPC have been proposed in the technical literature. They are based on the optimization of a cost function consisting of the difference between the actual output and the trajectory to be tracked [29]. Several applications have employed the discrete-time linear model (DTLM) for predictive control. It allows a fast analytical solution of the optimization problem. The predictive control of the PMSM based on the DTLM has been described in [30], where the load torque is considered as a known disturbance.

Recently, model predictive control (MPC) strategy, which can take into account the plant constraints and nonlinearities with multiple inputs/outputs and handle them in a proper way, has been reported [31]. It generally has an optimal, naturally robust, and simple structure. Thus, it can be combined with the basic DTC scheme to synthesize a high-performance controller for the PMSM drives. Unlike the basic DTC or FOC with SVM, the MP-DTC strategy is based on the optimal control approach. Having the cost function designed to minimize the torque and flux control errors [32], optimized switching states can be generated.

In this paper, we propose a direct torque control (DTC) strategy based on nonlinear model predictive (NMP) control for the EV traction, using PMS in-wheel drive. Given the EV system dynamics and an objective cost function, the proposed NMP-DTC strategy uses the fuzzy logic control technique to determine online the accurate values of the weighting factors (i.e., penalty factors) and generate the optimal switching states that optimize the EV drives’ decision.

Some applications in the field of electrical drives require using several electric machines and many static converters that have an important place among electromechanical systems. These systems are called multimachine multiconverter systems (MMSs) [33]. When several machines are associated to carry out cooperative functions (the contribution of the four-machine efforts for the advancement of an electric vehicle, in our case), the embedded mass can still be reduced by sharing power electronics. Until recently, together with the development of semiconductor technology and the introduction of powerful microprocessor and power electronic devices, among others, systems which began to be more interesting and which include multisynchronous machines (especially PMSMs) are driven by a single inverter. Our work is developed in this context. The power reduced structures based on power electronics are able to feed two or more electric machines in parallel and provide control laws to improve energy efficiency. This system is called a multimachine single-converter system [17]. Thus, in high-power applications such as traction systems, two or more machines are fed by one converter. The control of multimachine single-converter systems is the subject of this study. Several methods have been proposed to control bimachine monoinverter systems. In this case, a master-slave based on nonlinear model predictive direct torque control (NMP-DTC) strategy is developed.

The motivation of the present work is to verify the enhancement of performances and stability of the electric vehicle, using a new multimachine robust control. This work realizes the acceleration slip regulation (ASR) and antilock braking system (ABS) functions, based on nonlinear model predictive (NMP) direct torque control (DTC) for four permanent magnet synchronous (PMS) in-wheel motors. The coordinated ASR and ABS control offers the wheel slip control through PMS in-wheel electric motors actuation both in traction and in braking mode.

This paper is organized as follows. In Section 2, the structure of the electric vehicle studied is presented. It is composed of two sets of bi-PMS in-wheel motors connected in parallel and supplied by a three-phase two-level inverter, one on the left and one on the right. In Section 3, a general description about the nonlinear model predictive direct torque control (NMP-DTC) for PMS in-wheel motor will be presented. A fuzzy logic control for the cost function optimization is studied and explained in detail. Section 4 discusses the principle of the new multimachine robust control, based on NMP-DTC for two permanent magnet synchronous (PMS) in-wheel motors operating in parallel and supplied by a single three-phase two-level inverter. The master-slave based on NMP-DTC is verified via simulation. High performance with respect to speed tracking and torque control of both motors has been demonstrated. In Section 5, the vehicle longitudinal dynamics and the fuzzy logic control strategy of ASR and ABS based on the wheel angular acceleration and the slip ratio are presented. Finally, the conclusion will be pointed out at the end of the paper.

#### 2. Structure of the Electric Vehicle Studied

In this paper, the EV studied is equipped with four in-wheel motors (i.e., PMSMs) mounted in each wheel. The configuration of the vehicle system is shown in Figure 1. Two structures of the four-wheel independent driving electric vehicle are presented. As shown in Figure 1(a), each PMS in-wheel motor is fed by its own individual inverter. However, in Figure 1(b), we can see two sets of bi-PMS in-wheel motors which will be connected in parallel and supplied by a single inverter, one on the left and one on the right. Consequently, in the latter figure, the number of power electronic components is clearly reduced, and the volume and size of the system also decrease. Some studies have been carried out concerning control problems of these systems in [34, 35]. Our work will be on the second structure for the motivation of this structure; not only does it allow the achievement of an electric differential system [23, 36], but also it opens opportunities for new ABS and ASR architectures. Furthermore, the individually controlled electric motors allow (i) reduction or even elimination of the involvement of conventional friction brakes into the control on the wheel slip and recuperation of the braking energy (in the case of ABS) and (ii) improvement of driving comfort. Within this context, the possible advantages of this structure are the faster response time and possibility of dual direct control, either by speed or by torque.