2012 Intelligent Vehicles Symposium Alcala de Henares, Spain, June 3-7,2012

ACC of Electric Vehicles with Coordination Control of Fuel Economy and Tracking Safety

Dang Ruina, He Chaozhe, Zhang Qiang, Li Keqiang & Li Yusheng

advantages of both Intelligent Transportation Systems (ITS) Abstract-An adaptive cruise control system of and Clean Vehicle, and realizes the performances of traffic electric vehicles is proposed, considering both fuel safety, fuel efficiency and ride comfort simultaneously [2]. To economy and tracking safety with model predictive equip the Clean Vehicle with the adaptive cruise control control theory. Firstly, the mathematical relationship (ACC) system, and coordinate both economy and safety, is between fuel cost and longitudinal acceleration is just a typical application of i-EFV [3]. analyzed through a simulation model. Secondly the At present, the research of ACC faced to Clean Vehicle has 2-norm number is adopted to indicate the integrated begun to catch more attention [4]. Toyota and Volkswagen cost function, which integrates economy performance carried ACC on their to reach safe and tracking performance together. Finally the assistant [5]. Keulen in Eindhoven University of Technology proposed optimization problem is solved by model of Holland designed an optimal track of desired velocity for a predictive control theory, and a contrast controller is certain road, with the information of GPS, and achieved built with linear quadratic algorithm. Both simulation adaptive cruise control on hybrid electric vehicle [6]. All of and real vehicle test results show that the MPC these above did not consider synthesizing fuel economy and controller can reduce fuel cost by above 5% than LQ tracking safety simultaneously. LUG Yugong in Tsinghua controller in the range of safe tracking, and it University proposed a layered control system for ACC in successfully coordinates fuel economy and tracking hybrid electric vehicle, which synthesized two optimal curves safety. in the middle-level control to coordinate both economy and safety. For the optimal curves, one was the optimal engine fuel Index Terms-Adaptive Cruise Control; Model Predictive characteristic curve, another one was the optimal efficiency Control; Electric Vehicles; Energy Saving curve of motor and battery [7]. All in all, the research of ACC in Clean Vehicle is in its infancy, and most of the exit techniques just added the two functions together instead of I. INTRODUCTION considering the coordination of them.The design of ACC With the rapid increase of the vehicle population in the system design aims at multiple objectives coordination can be modern society, traffic accidents, energy consumption, cast in to Model predictive control (MPC) framework. We environmental pollution and such problems have been refer the reader to [8] for ACC system design with multiple prominent day by day [1]. The intelligent objectives of traditional vehicles applying MPC. Inspired by Environment-Friendly Vehicles (i-EFV) integrates the the success stories shown in traditional vehicle ACC design, we attempt to apply MPC on Clean Vehicle in this paper. Manuscript received January 6th, 2012. (Write the date on which you This paper proposes an adaptive cruise control system of submitted your paper for review.) This work was supported in part the electric vehicles considering both economy and safety. An National Science Foundation of (50975155). Dang Ruina is with State Key Laboratory of Automotive Safety and EV-economy analysis system is built, to research the Energy, Tsinghua University, , China, 100084, and China North numerical relation between the acceleration and the Vehicle Research Institute, Beijing, China, 100072 (Phone: EV-economy. Based on this, the performance index 86-10-62771667-81; E-mail: [email protected]). Chaozhe He is with School of Mathematics and System Science, Beihang integrating fuel economy and tracking safety is designed in the University, Beijing China 100191 (E-mail:[email protected]). form of 2-form number, and MPC theory is adopted to solve Zhang Qiang is with Changan Automobile (Group) Co., Ltd, the optimization problem. Finally simulations and real vehicle Chongqing, China, 400020 (E-mail: [email protected]). tests are carried out to verify the proposed controller, under Li Keqiang is with State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China, 100084 (Corresponding author the sine wave acceleration of the preceding vehicle's driving E-mail: [email protected]) condition. The experiment results indicate that the Li Yusheng is with Chongqing Changan Automobile (Group) Co.,Ltd, Chongqing, China, 400020(E-mail: [email protected]).

978-1-4673-2118-1/$31.00 ©2012 IEEE 240 controller can save fuel cost by above 5% under the premise resistance, the grade resistance and the acceleration oftracking safety. resistance. The inverse model is built based on the longitudinal dynamic model, and it is used to compensate for I. THE NUMERICAL ANALYSIS OF THE EV-ECONOMY BASED ON the nonlinear dynamic characteristics ofthe vehicle model. PI THE LONGITUDINAL ACCELERATION is motored by permanent magnet DC motor, the torque To design the proposed controller which can coordinate appears a piecewise linear relationship with the voltage fuel economy and tracking safety, the performance index of controlled variable, as shown in Equation 2. Figure 3 is the the controller should include fuel economy. Therefore, a power distribution. concise and exact quantification method for EV-economy is needed. There are many factors influencing the EV-economy, = mg cos a f such as the longitudinal acceleration, the vehicle mass, the (1) vehicle structure and so on. According to the research result in

1 2 [9, 10], the longitudinal acceleration makes an obvious +-CDApV mgsina mga j + + j difference to the EV-economy. Based on the conclusion 2 above, a simulation system for EV-economy analysis is Where I is the wheel inertia (kgm"), 11 is the transmission designed based on the longitudinal acceleration, and the efficiency, r; is the wheel radius (m); m is the vehicle mass EV-economy quantification method is expected through the (kg), g is the acceleration of gravity (m/s"), a is the road simulation results.The vehicle model in the simulation system grade, f is the rolling resistance coefficient, CD is the air comes from the Stanford PI steer-by-wire research vehicle, resistance coefficient, A is the preceding face area (m') and p shown in Figure 1 [11]. is the air density (N°s2om-4).

---( 232U(t)-441) (U (t) > 1.9) O.Ols+1 T (t) = (2) ---(47U(t) + 90) (U (t) < 1.9) O.Ols+1 Fig. I. Stanford PI Steer-by-Wire Research Testbed Where T(t) is the motor torque (N.m) and U(t) is the A. System Design voltage controlled variable. An EV-economy analysis system is designed to study the quantitative relationship between longitudinal acceleration and EV-economy. As shown in Figure 2, there are four components in the system structure, and they are PID controller, inverse model of the vehicle longitudinal dynamics, motor model and vehicle model. The system input is the desired velocity Vdes (m/s), consisting of the initial velocity and the integral of the desired acceleration. The initial velocity is just the desired average velocity. The outputs are the factual velocity vf(m/s), the factual acceleration Qf (m/s'') and the energy cost ofmotor Eenr(J). In the process of simulation, the PID controller adjusts the factual velocity to follow the desired velocity exactly and timely, then the fuel Fig.3. Power Distribution Figure 4 shows the simulation results of the designed costs under a series of longitudinal accelerations are got with system, under the condition that the desired average velocity various desired velocity. is 60km/h and the desired sine wave acceleration amplitude is 0.5 m/s". Both the factual acceleration and velocity can follow the desired value precisely and quickly, the energy consumption is also calculated in real time. So this system can Fig.2. EV-economy Analysis System Structure be used to analyze the relationship between the acceleration In Figure 2, Qdes is the desired acceleration (m/s2), Tdes is and the EV-economy. the desired torque (N.m) , Udes is the controlled variable of B. Quantitative Analysis the desired motor voltage, W is the wheel speed (rad/s) and w Through the designed system, the relationship between the i is the final-drive ratio. g longitudinal acceleration and the EV-economy in full range of Equation 1 describes the vehicle longitudinal dynamics, the velocity is analyzed here. The fuel cost is calculated by considering the wheel inertia, the road resistance, the air

241 simulation, when the desired acceleration changes as sine which can coordinate economy and safety at the same time. wave under a series of amplitude, and when the desired Model predictive control theory is adopted to design the average velocities also changes. The values of the desired controller because of its advantage of multi-object average velocity are [40,50,60,70,80]kmJh, the amplitudes of coordination [12]. The controller frame is shown in Figure 8. the desired acceleration are [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8, 55 ----+- 80 0.9,1.0]m/s2, and the frequency is O.IHz. Figure 5 shows ----4- 70 50 the desired acceleration and velocity when the desired average """') ------R-- 60 (,D o ----B- 50 velocity is 60kmJh. ~ 45 ~ ----e---- 40 o --Des o ~ tr~ ~ --Fac 40 /' a « -1 U 5 10 15 20 >. 35 o 9 ~ 165~ --Des w G' 60 --Fac 30 :g (jj 55 > 0 5 10 15 20 251:'..------"------"------'------"------l: o 0.2 0.4 0.6 0.8 ~0.2~ -- Energy 2) Amplitude of Acceleration (m/s >. 0.1 ~ Fig.? Energy-Acceleration Per 100km ~ 00 5 10 15 20 In the frame, car-following model is the foundation of the Timet s) FigA. Simulation Result whole system, and it exports the current system status x(k) according to the current velocity vik) and acceleration ajk). N IJl --0 E --0.1 The performance index L is the reference of the controller, f------="I-=--~=----~=______c~­ § 0 --0.2 and it is a 2-norm number considering both the economy and « --0.3 IJl Q) --0.4 safety performances. Predictive model and rolling o -1 I:.------'=""'------''______------'''''''------l: o 10 15 20 --0,5 optimization are the keys to solve the algorithm. The first --0.6 :2 70 --0.7 element of the solved input vector will be imported into the ~ --0.8 vehicle dynamic model. Here, k is the current sample time, i is .-g 60 ~==-.~~~=--=""'" --0.9 (jj --1 the predictive sample time. > ~ 50 Ol:.------'~----''------''------'' 10 15 20 lime( s) Fig.5. Desired Acceleration and Velocity Figure 6 shows the variation of the energy consumption with the change ofthe acceleration amplitude in 180s' driving time. Figure 7 shows the energy consumption with the acceleration amplitude for 100 kilometers' driving range. Both figures show that the energy consumption increases when the amplitude increases, and they appears an Fig.8. Frame ofEV-ACC with MPC theory approximately linear relationship. So the value of the A. Car-following Model longitudinal acceleration can stand for the EV -economy Car-following model is built with the driver desired quantitatively, and it also can be used to be the reference ofthe distance and the inter-vehicle dynamic characteristic. economy performance index for the ACC controller. Equation 3 describes the driver desired distance [13],

----+- 80 equation 4 shows the relationship of the inter-vehicle ----4- 70 dynamic. ------R-- 60 """') ----B- 50 d =T v -vd ~ 1.5 d es h J 0 (3) ~:7-----f:~0---4----e--~-v ----e---- 40 IJl a U 9 Where ddes is the desired distance (m), Th is the time ~ w headway(s), do is the safe distance when the two vehicle stop (m). I1d d - d = des 0.5 "------L_-----L...-_-----L.--_...I...------l: o 0.2 0.4 0.6 0.8 (4) I1v=v -v Amplitude of Acceleration (s2) p f Fig.6. Energy-Acceleration in 180s Where d is the factual distance (m), LJd is the distance error

(m), vp is the velocity ofthe preceding vehicle (mJs), LJvis the II. CONTROLLER DESIGN velocity error (mJs). According to the previous analysis result, we continue to A simulation system is built to analyze the vehicle dynamic design the algorithm of the adaptive cruise control system, relationship as Figure 9 shows. The frequency response

242 method is adopted to identify the system's input and output all the errors equally, 2-norm number pays more attention to characteristics, and finally the transfer function is got as larger errors and 00 -norm number just takes care of the Equation 5. maximum error. Since the driver tends to react to larger errors, the 2-norm number is chosen to stand for each performance index here. For the economy performance index, the longitudinal acceleration is used based on the previous analysis result. Considering that the factual acceleration relies on the desired Fig.9. Vehicle Dynamic System acceleration during the driving process, the economy performance index is designed as Equation 10 with the desired K a = ---a acceleration. f fdes Ts+1 (5) L = w a e "fdes (10) K = 1.06,T = 0.015 Where W u is the weight coefficient of the desired Where K is the gain and T is time delay(s). acceleration. Combining Equation 3, 4 and 5, car-following model is got For the safety performance index, distance error and as Equation 6, and Equation 7 is the discrete form of the velocity error are utilized as Equation 11 shows. car-following model. For the ACC system with measurable (11) disturbance variable, the system output is shown as Equation 8. Where WLld and WLlv are the weight coefficients of the distance error and velocity error. ;::::Ax+Bu+Gv By substituting Equation 10 and 11 into Equation 9, we can r x = !1v a] u::::a v:::: a [!1d j' jdes' p get Equation 12:

-1: L = L + L 1° h 1° C e t ,I (12) -1 ,B I A :::: 10 ° :::: I ° (6) Lo ° -1 IT LK IT To guarantee the control performance, the parameter 1° restrictions are shown as below: ,I G :::: 11 x < x < x

Lo 11 11 1 d min l 1 d max l IIII x min = I 11 V min I' x max = I 11 V max I' Where x is the system status variable, U is the system input, v is the disturbance of the input which is the preceding l a f min J l a f max J (13) vehicle's acceleration ap (m/s2) here, A ',B "G' are the u < u < u coefficient matrix ofthe input. u = a f min' U max = a f max' x(k+l) = Ax(k)+Bu(k)+Gv(k)

(7) Y min < y < Y max' A = TsA' + I,B = TsB',G = TsG'

Y min = CX , Y max = cX Where v(k) is the current disturbance, A,B, G are the input m in m a x coefficient matrix ofthe discrete equation. Where X max, Xmim LJdmax, LJdmim LJvmax, LJvmim Umax, Umim afmax, afmin, Ymax, Ymin are the maximum and minimum values y(k)::::Cx(k)+w(k) (8) ofeach parameter. Where C is the output coefficient matrix and w(k) is the C. Derivation ofthe Optimization Problem output disturbance. Model predictive control theory is adopted to solve the B. Performance Index Design proposed optimization problem. First, the status variable in the predictive sample time is got based the car-following As the control reference of the system, performance index model as Equation 14 shows. Then the predictive forms of is the summation of the economy performance index and performance index and parameter restrictions are built as safety performance index, as Equation 9 shows. Equation 15 and 16 shows. Finally a quadratic equation ofthe (9) predictive optimization problem is shown as Equation 17. Where L; L; L, are the composite, economy and tracking performance indexes. Economy performance index and tracking performance index are designed separately. Usually I-norm number treats

243 x(k+ilk) The acceleration of the preceding vehicle changes as sine wave. i-I A. Simulation Test

m=O (14) The driving condition of the preceding vehicle is defined as i-I Figure 10 shows. In the beginning, the initial velocity is

m=O 20m/s. Both the distance error and the speed error are zero. Starting from the 90s, the acceleration changes as sine wave = f(x(k),u,v) shape, the change lasts one period and then the acceleration Where m is the power number for A. returns to O. The frequency of the sine wave is O.628Hz, and p ~ ~d the amplitude is 1 m/s", Figure 11 shows the simulation L = L II d (k + i + 11 k ) II: results. i=1

p p +L II~v(k + i + Ilk)II:~v + L Ilu(k + i Ik)ll: u (15) i=1 i=1 ~l=~\;~-- p p 80 90 100 110 120 = L Ilx(k + i + Ilk)ll: +L Ilu(k + i Ik)ll: x u i=1 i=1 = f(x,u,v) Where P is the length of the predictive sample time. 90!\100 110 120 Time( s) Fig. I O. the Driving Condition of Preceding Vehicle for Simulation x. ~x(k+ilk)~x mm max In Figure II(a), the two controllers can keep the errors in a

U. ~u(k+ilk)~u m m max' i=O:P-I (16) small range, the MPC controller's velocity error is larger and its distance error is smaller. In Figure 11(b), from the 90s, the v.. < y(k+ilk)~ y mm m= power changes as sine wave, the MPC controller's power min L ( x, u, v ) changes more smoothly and the amplitude is also lower. The i=O:P-I two control results get steady in the 11Os. From the 90s to the Subj. to : (17) 110s, the MPC controller saves energy by 5.47%. (1) Car - following mod el (9), (10) 4 --MPC (2) I / 0 restriction( 15) 3 --LQ There are various methods of the MPC solutions. DWAS E 2 (Dantzig-Wolfe Active-Set method) not only calculates e numerical stably, but also has a quick constringency. Here we W (]) choose DWAS to realize the online optimization solution. o ~ 0 en (5 III. EXPERIMENTAL RESULTS -1

A contrast controller is designed to verify the proposed -2e..------"------"------"------controller. linear quadratic (LQ) is an optimal control method -2 -1 0 1 2 Velocity Errore rn/s) applied to linear object, and it can solve the problem of (a) multi-objects coordination to a certain extent, so we choose LQ as the contrast control algorithm. Equation 18 is the performance index form of the LQ controller. Finally the --MPC LEl Linear feedback control law of the LQ controller can be got through the Riccati function. ~_::~------"--- 90 95 100 105______l: 110 (18)

»r--: 0.2 Where wx is the weight coefficient of the system status variable. iO.1~ The simulation models of the two controllers are built by MATLAB/SIMULINK. The two controllers are also installed c 0 r W 90 95 100 105 110 on PI vehicle to carry out the real vehicle test. The driving Time (s) conditions of the preceding vehicle are realized by virtual (b) radar, which defines the value of the acceleration and velocity. Fig.II. Simulation Results

244 In the whole process, the MPC controller restricts the IV. CONCLUSION acceleration of the host vehicle changing too fast or too large, This paper proposes an algorithm to realize the then the lower change and smaller acceleration leads to a coordination of economy and safety for the adaptive cruise larger velocity error, and this also makes the power stay in the control system in the electric vehicles, using model predictive low cost area to save energy. At the same time, considering control theory and based on the numerical analysis of the that the drivers prefer reacting to distance error rather than to relationship of the longitudinal acceleration and the velocity error, the MPC controller sacrifices some velocity EV-economy. A contrast controller using linear quadratic characteristics to guarantee the distance characteristics to method is designed to verify the proposed MPC algorithm. keep safe tracking. Both simulation and real vehicle test are executed, and two From the analysis above, it is easy to see that the MPC meaningful conclusions are got as below: controller can realize energy saving by limit the change of (1) A numerical method using longitudinal acceleration acceleration in the range of safe tracking, so the controller is to scale and stand for the EV -economy is put forward. The able to coordinate fuel economy and tracking safety method is concise and accurate, and it supplies the design of simultaneity. the EV -economy performance index with a reasonable reference. B. Real Vehicle Test (2) Model predictive control theory is utilized to design Figure 12 shows the driving condition of the preceding an adaptive cruise control algorithm considering fuel vehicle. Limited by the maximum of PI's velocity and the economy and tracking safety simultaneity, both the simulation area of the test field, the initial velocity is 4m/s, the and real vehicle test results prove the success of the proposed acceleration changes as sine wave in the whole test. The algorithm. frequency is 0.628Hz and the amplitude is 0.4 m/s". Figure 13 shows the steady tracking results for 4 periods. REFERENCES

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