## Numerical optimization methods for improving energy efficiency in Battery Electric Vehicles using wheel torques and steering angles

##### Typ

Examensarbete för masterexamen

##### Program

Automotive engineering (MPAUT), MSc

##### Publicerad

2021

##### Författare

Suvarna, Manish

Prabhu, Anand

##### Modellbyggare

##### Tidskriftstitel

##### ISSN

##### Volymtitel

##### Utgivare

##### Sammanfattning

The planar motion of a ground vehicle is affected by controls given to it in the form of the front axle steering
angle and the individual wheel torques. A battery electric vehicle with four in-wheel motors is an over-actuated
system where the control space has multiple control solutions for allocating the wheel torques and front axle
steering angle for achieving the desired planar motion of the vehicle. Of these available solutions, a particular
energy efficient control solution can be found to achieve this desired planar motion of the vehicle and ultimately
improve the drive range of the BEV. This is achieved by formulating and solving a Control Allocation (CA)
problem. The authors of this thesis report have proposed an energy efficient optimization based CA problem
which is inspired from Mixed-Optimization CA problem. The control solution obtained by solving this proposed
optimization based CA problem is intended to minimize the energy consumption by reducing the energy losses,
specifically the electric loss in wheel motors and tire losses such as lateral and longitudinal slip losses and rolling
resistance loss, while maintaining the path tracking performance of BEV with minimum lateral deviation. The
path tracking algorithm was developed only to dictate the desired behaviour to the BEV in order to track
a path, therefore replacing the need for the driver model. The proposed CA method is implemented in two
different ways, one is by solving the CA problem to achieve the required behaviour of the BEV at every time
step, and the other where the CA problem is solved by considering the required behaviour of BEV for certain
upcoming time frame. The former approach is known as Instantaneous optimization based CA and the latter
approach known as Predictive CA is implemented using Nonlinear Model Predictive Control (NMPC). The
cost function and the constraints involved in optimization based CA problem are nonlinear in nature and is
solved as an NLP problem. Two different Newton type optimization algorithms namely Sequential Quadratic
Programming (SQP) and Interior Point are explored in order to solve the NLP problem. It was found that
the formulated NLP problem is better solved by a large-scale algorithm such as IP rather than solving using
SQP which is a small-scale algorithm. Of the two approaches, the predictive method i.e. the NMPC based CA
problem's solution was found to have less energy consumption than the solution given by the instantaneous
method of solving the CA problem by 3.89 %. The combined electric energy losses in motor and energy losses
due to tire dynamics was less by 3.41 % .The allocated torques had least amount of torque vectoring in NMPC
based CA compared to instantaneous CA method. The lateral deviation for path tracking was also less in
NMPC relative to instantaneous. The front axle steering angle allocated for both the methods had transient
behaviour, more prominent in solutions given by instantaneous CA problem. A comparison between energy
consumption for torques allocated by NMPC based CA and equal torque distribution (ETD) using IPG driver
model controlling the lateral dynamics was done. It was found that the ETD driving scenario had lesser energy
consumption by 2.03 % and overall losses less by 2.4 % compared to NMPC based CA. Out of which 65 % of
this excess loss in NMPC based CA compared to ETD was due to excess in lateral slip loss due to transient
steering angle control allocated by NMPC based CA. Therefore the energy savings given by NMPC based CA
can be further improved by regularizing the transient behaviour of the allocated steering angles.

##### Beskrivning

##### Ämne/nyckelord

Battery Electric Vehicle , Vehicle Dynamics , Control allocation , Numerical optimization methods , Model predictive control , Nonlinear programming