# Fractional Order PI-Based Control Applied to the Traction System of an Electric Vehicle (EV)
## 1 Introduction  
Among the many problems that have been considered important worldwide the two that stand out are pollution and overpopulation. Overpopulation has created high demands for transport, both short and long-distance, which increases the problem of pollution [1]. Electric motors consume half of the electric power generation, so increasing their efficiency impacts the saving of electric energy. Different control techniques that use digital systems (as well as new power electronics devices) have evolved in the works looking for improving the performance of electric motors [2]. These electric machines have also made progress in their design. Three-phase induction motors (IM) are normally used in the industrial sector, due to their simple design, high reliability and low cost. Frequency converters are traditionally used to control the speed and stop of induction motors with precision [3]. The control of the speed of the motors allows the saving of electrical energy. Therefore, the use of variable speed drives has been increased to control not only the speed, but also the torque, flow and position. The majority of the vehicles that circulate around the world nowadays consume fossil fuels. These vehicles use internal combustion engines (ICE), with a performance of the transformation of energy from the fuel tank into mechanical energy of less than 30%, which represents a great loss. They also produce \(CO_{2}\) and \(NO_{x}\) emissions into the atmosphere, which leads to a large localized pollution in large cities. In recent years, electric vehicles (EV) and hybrid electric vehicles (HEV) have proven to be an alternative as they are a clean, effective and ecologically friendly transportation system [4]. In an electric vehicle, its movement is provided by an electric motor that has batteries as its primary source of energy. Excluding the generation of electricity, EVs do not generate \(CO_{2}\) andemissions, allowing buffering and presenting a part of the solution to the problem of global warming. In addition, they stand out for their high performance in the transformation of the electrical energy of the battery into the mechanical energy with which the vehicle will move (60-85%) [5]. However, EVs present two main problems that must be addressed and resolved, they have low autonomy and long recharge times. These problems are closely related to the vehicle's battery bank. The batteries must have enough energy for the vehicle to make a certain journey and can accelerate and decelerate if necessary [6]. Mathematical models are important in estimating the energy consumption of electric vehicles [7; 8], since they allow us to numerically simulate the behavior under different conditions and scenarios. The design or implementation of each component (e.g., transmission system, electric motor, power electronics and battery) is a delicate task since the power levels of one component can affect that of others, making the vehicle unnecessarily expensive or inefficient. The present work covers the process of modeling, control and simulation of an EV. The motor used for the traction system is an induction motor (IM) of 1.1 kW. Then, the dimensions and characteristics of each element of the EV (batteries, voltage converters, traction and control systems) were selected according to the characteristics of the IM, together with the following minimum specifications: maximum speed without slope of 30 km/h (maximum speed allowed within the campus university, CU-BUAP) and with a total mass (including the driver) of 200 kg. Special attention was paid on the development of IM speed control, which allows implementing a speed cruise control for the EV. This control is done through the well-known direct torque control (DTC) and a proportional and integral (PI) control of fractional order. DTC is an approach employed to regulate electric motors. This technique selects an appropriate voltage vector to regulate torque and flow in electric motors. That vector is chosen from a switching table, which is predefined.