Adaptive Cruise Control for Electric Bus based on Model Predictive Control with Road Grade Prediction Jindong Bian, Bin Qiu, Yahui Liu and Haotian Su State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Haidian District, Beijing, China Keywords: Adaptive Cruise Control, Model Predictive Control, Road Grade Prediction, Electric Bus. Abstract: Adaptive Cruise Control (ACC) makes the driving experience safer and more pleasurable. To comprehensively deal with tracking capability and energy consumption issue of ACC-activated vehicle on rugged roads, this paper presents a MPC based vehicular following control algorithm with road grade prediction. A simulation model of ACC for electric bus based on MPC is built for analysing the performance of the algorithm. The simulation results show that road grade prediction can improve improves both energy consumption and tracking capability. 1 INTRODUCTION consumption to the full extent under the premise of ensuring safety. The design of an ACC system with Cruise Control (CC) executes the task of multiple objectives can be naturally cast into a maintaining the vehicle speed at a desired value. model predictive control (MPC) framework. MPC However, it cannot reasonably alter the speed of the has already proved its merit in ACC design in vehicle according to different situations. When the literature, (Li et al., 2011). Nonetheless, ACC preceding vehicle equipped with CC is traveling system based on MPC designed for conventional slower than the latter, the driver has to step on the fuel vehicles is not suitable for electric buses which brake pedal in order to deactivate the Cruise Control are equipped with regenerative braking system. and step on the accelerator when the preceding When taken into account, the road grade effect vehicle speeds up, (Howard, 2013). This drawback can play an important role in advanced navigation is overcome by the more advanced Adaptive Cruise and navigation algorithms, where the system can Control (ACC), which is able to adjust the vehicle help drivers avoid steep roads to achieve better fuel speed by analysing various influential factors, economy and reduce carbon dioxide emissions, without manual intervention from the driver, (Boriboonsomsin et al., 2009). A research has found (Howard, 2013; Shakouri et al., 2012, 2014). that fuel saving capability of ACC system can be Adaptive Cruise Control system (ACC) has been strenthened by the prediction of road grade, widely investigated due to its merits of reducing (Lattemann et al., 2009). Knowledge about the driver workload and ensuring safety, (Mba et al., upcoming road grade can be used in ACC to avoid 2016). Due to concerns about global warming and unnecessary braking and shifting. Due to the energy conservation, vehicle energy consumption relatively large mass of a city bus, such system can has become a consideration of great importance for save a great deal of energy. In addition, road grade the automotive industry. Close attention has been level has an effect on crash risk, (Wu et al., 2017). given to another important issue in ACC, Therefore, if in the future road grade can be specifically energy consumption problem, (Li et al., accurately predicted, the valuable data can reduce 2017). Tsugawa and Ioannou suggested the use of not only the energy consumption of buses, but also ITS technologies, including adaptive cruise control, the risk of traffic accidents, (Zeng et al., 2015; Luo to reduce fuel consumption of vehicles, (Tsugawa, et al., 2015). 2001; Ioannou et al., 2005; Bose et al., 2003). ACC There are many methods to measure or estimate system is designed to follow the vehicle in front the current road slope during driving, (Kim et al., automatically, simultaneously to reduce energy 2013). These methods generally rely on different types of sensors, mainly Global Position System 217 Bian, J., Qiu, B., Liu, Y. and Su, H. Adaptive Cruise Control for Electric Bus based on Model Predictive Control with Road Grade Prediction. DOI: 10.5220/0006641702170224 In Proceedings of the 4th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2018), pages 217-224 ISBN: 978-989-758-293-6 Copyright c 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved VEHITS 2018 - 4th International Conference on Vehicle Technology and Intelligent Transport Systems (GPS), inertial sensors, pressure sensors, (Boroujeni 3 ACC ALGORITHIM BASED ON et al., 2013), wheel speed sensors, (Wragge-Morley et al., 2013), acceleration sensors, LIDAR, (Tsai et MPC al., 2013), etc. GPS can provide the altitude and velocity information of the vehicle, but the signal 3.1 Discrete State Space Model accuracy is greatly influenced by the environment. GPS cannot provide reliable data in conglomerations With respect to inter-vehicular dynamics, we define of high-rise buildings and inside tunnels and so on, two variables reflecting the tracking errors: (Bae et al., 2001). IMU (Inertial Measurement Unit) clearance error ∆d and speed error ∆v. The discrete can provide acceleration and angular velocity state space model can be described as: information and is not affected by environment x( k 1) Ax ( k ) Bu ( k ) G ( k ) factors. However, its measurement accuracy can be easily influenced by suspension movements, and its y()() k Cx k signal oscillation can be very serious, (Lee et al., d d ddes, v v p v f 2012). Based on prior analysis, researchers have x[],, d v u a a proposed some methods and algorithms to improve f des p (1) 22 the accuracy of road slope estimation, such as 1 Tc 0. 5TTcc 0. 5 Kalman filter, extended Kalman filter, (Srinivasaiah ABG,, 01 TT et al., 2014), etc. cc This paper is organized as follows. The second y[] dmm v part introduces the longitudinal vehicle dynamics. The third part introduces the MPC algorithm in this where C is identity matrix, Tc is the sample paper, including the state space description of the time, d is distance between two vehicles, d is problem and the construction of cost function. The des fourth part introduces the road grade prediction. A desired distance, vp is the preceding vehicle speed, simulation model and results are shown in the fifth is the following vehicle speed, is the part, indicating the improvement of ACC based on v f ap MPC with road grade consideration. preceding vehicle acceleration, a fdes is the needed acceleration of following vehicle. For a typical ACC system, radar and accelerometer are equipped, which 2 LONGITUDINAL VEHICLE means the states are measurable. DYNAMICS 3.2 Construction of Optimization Figure 1 shows the schematic diagram of an electric Problem bus’s longitudinal model, where aaccl represents Tracking capability, fuel economy, driver behaviour, the acceleration pedal position, abrk is brake pedal driving safety, ride comfort and environmental position, F is aerodynamic drag, F is rolling issues, as well as limitations on the model and traffic a f flow, all of the above factors constrain the behaviour resistance and Fi is climbing resistance. The motor of the ACC system. In this paper, emphasis is given torque is mainly affected by the accelerator pedal to energy consumption and tracking capability while signal and the motor speed. Compared with allowing driver permissible tracking error. traditional vehicles, most electric vehicles are According to MPC framework, the cost function equipped with a regenerative braking system, which to be optimized can perform a trade-off between the can recover energy while braking. former two issues since they are reversely interactive with each other. Driver permissible tracking error Vehicle Speed v issue mainly results from driver behaviour in actual a traffic flow. If inter vehicular distance is larger, the accl Driver F Motor Motor Torque Vehicle Body a Train cut-in of front vehicle from adjacent lane occurs Ff Regenerative Brake Torque Fi frequently, thus leading to frequent decelerating of Drive Torque ego car and the deterioration of fuel economy. On abrk Brake System Friction Brake Torque the other hand, if the distance is smaller, driver is prone to intervene ACC control to avoid potential Figure 1: Longitudinal dynamics of electric bus. 218 Adaptive Cruise Control for Electric Bus based on Model Predictive Control with Road Grade Prediction rear-end collision. Both strategies are sure to disturb of traditional fuel vehicles. Because of the existence ACC’s regular working order. So, the upper and of regenerative braking system, the energy lower bounds of tracking errors usually exist, called consumption cannot be simply regarded as the linear the driver permissible tracking error. function of the squared value of the acceleration. An Fine tracking capability does not mean that the energy consumption model of electric bus is energy consumption is optimal. ACC system established as follow: designed for the electric bus is different from the one Gfcos G si n CA m P(,)() v a v D v3 v a (2) wh f f des3600 3600 f 76140 f 3600 f f des Pwh ,0Pwh 0,P 0 wh PPr eqTd Md , r eq (3) PPwh Tb Mb(1 ) el c , wh 0 0,Pwh 0 where α is the road gradient and while the vehicle is is the windward area, and are the downhill, the value of α is negative, f is the rolling Td Tb powertrain efficiency, Md and Mb are the motor resistance coefficient, m is the vehicle mass, CD efficiency, β is the ratio of front-rear braking force is the coefficient of air resistance that is characterized by the shape of the vehicle’s body, allocation, elc