A New Method to Design Optimal Power Compensator in Hybrid Electric Vehicles

A New Method to Design Optimal Power Compensator in Hybrid Electric Vehicles Hoang Mai Nguyen 1 , Tien Dung Le 1 , Le Hoa Nguyen 1 , and Quang Vinh Doan 2 1 University of Science and Technology-The University of Danang, Danang, Vietnam 2 The University of Danang, Danang, Vietnam Emails: {nhmai, ltdung, nglehoa}@dut.udn.vn, dqvinh@ac.udn.vn Abstract—The most important task for hybrid electric vehicles (HEV) is to optimal control of the distribution of the electric and mechanical powers in the system. Despite many studies have been focused on this issue, there are still many methods to fully exploit the capacity as well as re-charge power in other operating modes of HEV. This paper presents a new algorithm to determine optimal operation mode of HEV to estimate the distribution of electric- mechanical power. The simulation results and experience indicate the validity of the proposed algorithm. The obtained results can be applied in practice to improve qualities of HEVs in Vietnam.  Index Terms—hybrid car, HEV, optimum control, robust control, split power, combustion, engine, fuel consumption I. FUNDAMENTAL OF HYBRID CAR The car is a motion hanging system that its weight load and fuel can be changed in practice. Therefore, the inertial of the car also can be changed. Because, the road is not smooth, therefore, the car can be controlled in three directions of motion, corresponding to three variables x, y, z in the inertial coordinate. Because the links are not steady in the car, so the car can be considered to consist of three parts: body car, wheels, and weight load. Each part is described by one dynamic equation. Suppose there are four wheels that are assembled in ¼ hanging system, then 6 1 i k K K    and 6 1 i k P P    (1) where, Ki is a kinetic energy, and Pi is a potential energy of the part i th . The system can be described by Lagrange II equation as follows: ( ) ( )d L q L q T dt q q          (2) However, the model as depicted in Fig. 1 is too simple because only the traction F movement is considered, therefore, this model cannot be able to describe the components of change in motion forces. To solve this problem, this paper offers models describing multi- component force motions: Manuscript received October 30, 2014; revised May 11, 2015. 0 n k k T T    (3) where Tk including: the body force T1, weight load T2, torques of four-wheels T3 ... T6, friction force T7, environmental noise such as wind power, pressure difference T8, and elastic force T9 caused by the tires. Here, fluctuating component of the fuel in the tank is ignored. At the time of vehicle parameters are determined through three motion coordinates x, y, z, and angles respectively. For models depicted in Fig. 2 and [1], we can obtain the dynamic equations as follows: 6 1 1 1,2...6, 2 3 , , , , , , , , , ,i i I f m q q q r                 (4) 6 2 2 1,2...6, 2 3 , , , , , , , , , ,i i I f m q q q r                 (5) 6 6 6 1,2...6, 2 3 , , , , , , , , , ,i i I f m q q q r                 (6) where, q = [q1, ... q6] are the coordinate variables describing the motion of the car body, and the load of each wheel. α = [1,..,6] is the angle of rotation of each substance when projected onto a vertical plane, and β=[1,... 6] is the angle of rotation of each substance when affined onto plane versus horizontal axis ox. The composition of air resistance T8 is defined as: Figure 1. Analyzing model of car's motion 140 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering doi: 10.12720/joace.4.2.140-146 Figure 2. The model determines the spatial dynamics 3D motion 8 T d cT C S q q (7) where, Cd is air drag coefficient, with a value of about 0.1 to 0.3, Sc is the frontal area of the vehicle that depends on vehicle types, the last term in (7) is the square of vehicle velocity. Friction force depends on vehicle weight Pc, the road surface f, and tire area St is following: 2 2 7 x y c t c t z F F T P S f P S N    (8) where Fx, Fy, and Nz, respectively, are the vertical force, horizontal force and the normal force to the tires. Because vehicle travels on the different types of road, so these friction forces always change. Generally, the friction force cannot be determined exactly as a constant, therefore, it is necessary to estimate the magnitude of these forces. Eq. (8) does not show the direction of the friction force. In fact, the direction of friction force is not always move in the opposite direction of the car movement because the oscillations due to the diffusion of vehicle operation that results in the instantaneous friction might look chaotic in practice. When the vehicle is braked by brake force Tb on four wheels, we assume the braking force are the same in four wheels. Part braking capacity is the negative capacity, it works obstruct movement should be seen as opposite to the remaining capacity. In the mechanical movement, instantaneous power p(t) of a force is applied to cause movement is described: ( ) ( ). ( )p t T t q t (9) So total required power of the car is described as: 1 1 ( ) ( ) ( ). ( ) n n k k k k k p t p t T t q t      (10) II. SHARE POWER IN THE HEV We define share coefficient power as follows: 1 mP P s P m r r PP P r P P P P (11) This coefficient estimates ability operation of electrical power to mechanic power. The range of rs is 0≤rs≤1. When rs = 1, the car use only mechanical power such as conventional cars, while rs = 0 then the car is in EV or HEV mode. Clearly, we can see that the power is always designed to ensure:  . axS PP P P q m T    (12) where, PP is a pulling power and PS is a store power section. Moreover, we do not consider the case of self-run vehicle inertia when there is no initial velocity, so P 0. The power PP in (12) equals to the total power P in (10). The power component in (10) and (12) as the basis for design models divided power operators in (11). An important part of the HEV system reserves, consists of two parts: the rapid charge (transition response) and slow charging section (meet established process). Sewing quick charger is described: f g f g f eg m f c u L i R i k q i Cu       (13) where, uf is the voltage of the generator and uc is the voltage on quick charger, only symbols g generator parameters, R, L, , respectively, is the resistior, inductor and magnetic flux. Slow charging section is described as the stage of inertial degree 1: b C C m b l u Tu u p u i p     (14) where, the subscritpt m denotes electric motor. To facilitate the determination of the instantaneous power split point, we use the concept of phase function, which is defined as follows:  The function describing phase power mode combustion engine Ge.  Phase function describes the institutional capacity of electric motors Gm.  Describe the phase function generator mode Gf corresponds brake status.  Mixed function mode description Gb storage capacity. The operation of system is based on the combination of four-phase functions. Specifically Ge direct link with Gm and Gf direct link with Gb. Figure 3. Characteristics relations capacity, speed and fuel consumption rate. 141 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering Figure 4. The principle model of SPH car. The relationship between capacity Ge pace with the rate of fuel consumption of a specific engine is shown in Fig. 3. [2]: From Fig. 3, we can determine the optimal curve, which corresponds to the motor speed approximately in the range 2600 rpm - 3200 rpm. The power supply to motor is decided by the relation of voltage sign as follows: sgn( )F F S bP k P u u  (15) The system will draw power from UPS if PF>0 (corresponding to engine mode) and vice versa respectively generator mode. HEV model SPH type power divider shown in Fig. 4. [2]. To determine the relationship between the torque capacity of the vehicle, we rely on the properties of the relations car makers offer. They alsmot have the same shape but different specific value. A characteristic feature is shown in Fig. 5. As shown in Fig. 5, we can see the ideal characteristics is different from the real ones, with the use of common parameters, we have: bas; ; . T ic eng dm basic P c q q q T T q q p T q      (15) From model described in (4), we build a block diagram as shown in Fig. 6. a) Actual b) Ideal Figure 5. Characters of power, torque, and speed. Figure 6. Modeling HEV vehicle type HEV. In which, R1 is the engine power controller, R2 is the braking power controller, R3 is charging controller and power generators, Td is the gas pedal power, the brake pressure TBR, Thev is traction the sum of vehicle, TFR is the total friction. The model has been presented from (2) to (14). III. DESIGN FOLLOW OPTIMAL CONTROLLER The controller is designed on the principle of the robustness. The robust - optimal controller is designed by using a sliding algorithm combined with optimal quadratic partial capacity. To design the controller, we made some assumptions:  Elasticity of four wheels are the same.  Lateral impact force, power means used to get the car moving horizontally to the center of the road is random and does not describe, just as the noise power.  The car structure is symmetry, while the car is seen as central axis coincides with the center car. Then the vehicle dynamics is rewritten as: ( )( ) ( )( )( ) ( ) ( ) ( ) ( ) ( ) frS brP p tp t p tp tp t q t q t q t q t q t            (16) The fuel consumption is defined in Fig. 3:    2 2 1 1 ( ) ( ), ( ) ( ) ( ), ( ) ( , , ) t t t t f t g p t q t F f t dt g p t q t dt F p q T      (17) where T = t2 - t1 is the required time to travel for given distance. Because the carrying capacity of the engine is dependent on factors as shown above, the engine should follow the optimum power characteristics, needs electrical power control to compensate for the excess capacity either positive or negative. As the model in Fig. 5 cannot be determined the optimal capacity for motor control only stable conventional balance drag. For controllers feature in Fig. 4, this study offers model-driven optimal grip characteristics as shown in Fig. 6 and Fig. 7. In which, controls the position R2 moved into phasic brake pedal evenly distributed on four wheels. The controller R2 is described as a stage of inertia degree 1: 2 1 br br K R T s   (18) 142 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering Figure 7. Control model features optimal grip. Design controller R1: The controller R1 is designed to open the throttle signal corresponding to the gas pedal in position 0% to 100%. This relationship empirically is considered to be linear [4]. Thus R1 is selected as the PID controller with the transfer function: 1 i P d K R K K s s    (19) Design controller R3: According to the (13) and (14), the models of load power source and the electric motor are as follows: 1 f g f g f eg m b f f m b l u L i R i k q T u i i dt C C p u i p           (20) The model of DC motor is: ops . . b m m m em m T m m S m u u L i R i k q k i J q T p u i          (21) In the state space, the model is expressed as follows: ; m m m S x A x B u y C x y p     (22) where,    1 2 ops / / , , ; / 0 1/ 0 0 ; ; , 0 1/ 0 0 T T m m eg m m m T Tm m m m m R L k L x x x i q A k J L u B C u u T J                            here, Lm, Rm are the rotor inductor and resistance, respectively, m is the motor flux that is assumed to be constant, Jm is the moment of inertia of the system on the motor shaft, the torque Tops prevent motor axis conversion the spindle,  = pS / pm is the motor performance. Energy exchange model is shown Fig. 8. According to Fig. 3, by using graph identification software, we determined the relationship between engine power and engine speed Popt as follows: Figure 8. Model of 2-dimensional energy conversion. 8 4 7 3 4 2 0,144.10 .q 118,936.10 .q 355,477.10 .q 72,784.q 45041 opt eng eng eng eng p          (23) Based on (15), (20) and the model of motor DC converter as shown in Fig. 8, the equation that describes the status generator - engine is as follows:  ( ). . .sgn( )e m m m bu k q q L i R i u u     (24) where (ub - u) > 0 will correspond to the electric motor mode and (ub - u) <0 corresponding generator mode for battery charging. The model in Fig. 6 is moved to R3 controller so that input power deviation R3 is minimum. Because the voltage on the charger and the motor terminals (transmitters) are different, simultaneous voltage value depends on the amount of current flowing through change as shown in (20)-(22). Should work power control switch to control the current through changes in both the magnitude and direction to cling characteristics make optimal capacity. It is assumed that the storage capacity is unlimited, we have the following theorem: Theorem 1: If the system (16), (20), (21) satisfies the following conditions:  p(t) = 0 \ dq/dt = 0 and p(t) ≠ 0 \ dq/dt ≠ 0 means that is not the case at the car but the engine stand.   M> 0, pb (t)> 0 \ sup| pb(t) |> M, t> 0 means that the size of the capacitors and batteries are all capable of charging energy from the engine.  The engine and electric motor are operating in continuous mode when the car is running, meaning that we do not consider the case of engine running style on/off.  The frictional force, power brakes, traction is limited quantities, in which the braking force is always smaller TBR maximum traction. This condition is given to ensure that there is no case to run backwards when the car brakes. Then the control law in R3 controller is given as:           (4) ops (3) ops ops ops (4) ops 1 sgn( ( )) (1 ) S P S opt t T T m f f p p p R S e Jq T i Ck e Q Jq T Q Jq T Jq T Jq T                                     (25) R3 is the sliding control to change the system always ensures grip PS on Pcom = PP - popt. The electrical power 143 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering compensation of system is stable and always balances with diesel power to load harmony. Proof: From (20), (21) we have:   ops 1 1 1 S f f f g f eg m g f f f T m p Q Jq Q T i u L i k q R T Q i i dt k C C                 (26) From (26) we have:       ops ops ops ops f f S f Q Jq T Q Jq T p Q Jq T Jq T              (27) where, the notation of current i is as follows:  In engine mode: i = im  In the generator mode: i = if. Thus, (24) can be written: / .sgn( )m f bi i u u  (28) From this we obtain the following:       ops ops ops ops 1 S f f f p Q Jq T Q Jq T Jq T Q Jq T             (29) QF obtained in (29) is the true test of differential equations in (26), assuming that all initial conditions are zero, i.e., the transition from the current phase I will go through the stop point. It is totally reasonable for reversing the current wants, needs to take the current value of the zero line, then avoid dead zones to flow reducing balance, beginning phase reversal, to avoid overloading of the electric DC motor. Let choose sliding surface: 0 ( ) 0 P opt S com S S e e e e p p p p p         (30) where, pcom is a component of compensation power. In order to the error signal follows sliding surface, then the following condition must be satisfied. ( ). ( ) 0S e S e  (31) The condition (28) is equivalent to: ( ). ( ) ;S e S e o    (32) From (30) we have:     ( ) P opt S P opt S P S P S opt S e p p p p p p p p p p R              (33) We can see that the component pcom depends on characteristics and speed of the car and the engine. Because ( ) 0S e e e   , therefore, S(e) = |S(e)|sgn(S(e)) and condition (29) can be rewritten:  ( ). ( ) sgn ( ) ;S e S e S e o    (34) Base on (27), (32), and (33) we have:    ( ) .sgn ( ) .sgn ( ) ; ( ) S e S e S e o S e        (35) Hence condition (30) be agreed code, i.e., reversible motor control systems for sustainable stability. Combining (29) with (26), with the convention (28), we find the current control law as shown in (25). This completes the proof. IV. SIMULATION RESULTS AND CONCLUSIONS By applying the proposed algorithm, we build simulation model of HEV as shown Fig. 3. After changing the input signal (pedal force), we obtain results as shown in Fig. 9 to Fig. 13. We suppose the way is not smooth to always changes pedal. In Fig. 9, the engine power changes follow friction on the road. With the simulation time of 10s, we can see that engine power reaches stable state and slide into optimal orbit. Both the time with Fig. 3, the engine power has optimal consumption area. In Fig. 11, system makes optimal power by (23). That is a power which supply to system. It has changed too because system operates without filter. We can see that compensation power has strongly changes. If we do not use capacitor then batteries will be not have ability to store decay energy. In this time, there is not important change speed of DC motor, so problem is ability store of electric system. Figure 9. Simulation of engine power. Figure 10. Simulation of total power. As shown in Fig. 12 and Fig. 13, when we change speed of engine by pedal force, the torque will change speed of engine as in Fig. 3. We can see compensation power of motor in Fig. 12 has value equivalent optimal index. It explains compensation of store energy for the system. 144 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering Figure 11. Simulation of optimal power. Figure 12. Simulation of optimal follow power. Figure 13. Simulation of engine speed. Fig. 14 describes optimal power when HEV using following mode for engine. With the error power in Fig. 15, we see engine power is not enough power, so it has to use power from motor as shown Fig. 15. Figure 14. Optimal power in following mode Figure 15. Error power as same power of motor V. CONCLUSIONS The paper proposes a new method to compensate power for HEV as SPH mode. The new feature is using electrical equipment without mechanic of pedal. By doing that, the safety of the HEV can be increased and the life time of HEV can be extended also. The proposed algorithm can be applied in practice in factories of HEV. REFERENCES [1] N. V. Doai and H. Ng. Mai, “The application of adaptive sliding mode to control share power in the HEV,” M.S. thesis, Control Engineering and Automation, Danang 2014. [2] M. Ehsani and Y. Gao, Modern Electric, Hybrid Electric and Fuel Cell Vehicles, CRC Press LLC, 2005. [3] T. V. Keulen, Fuel Optimal Control of Hybrid Vehicles, TechnischeUniversiteit Eindhoven, 2011. [4] J. B. Heywood, Internal Engine Combustion Fundamentals, McGraw-Hill Inc., 1988. [5] R. Campbell, “Battery characterization and optimization for use in plug-in hybrid electric vehicle: Hardware in the loop duty cycle testing,” M.S. thesis, Dept. of Mechanical & Materials Engineering, Queen’s University Kingston, Canada, 2011. [6] S. J. Moura, H. K. Fathy, D. S. Callaway, and J. L. Stein, “A stochastic optimal control approach for power management in plug-in hybrid electric vehicles,” IEEE Trans. Control Syst. Technol., vol. 19, no. 3, pp. 545-555, May 2011. [7] S. Mahapatra, T. Egel, R. Hassan, R. Shenoy, and M. Carone, Model-Based Design for Hybrid Electric Vehicle Systems, The Math Works, Inc., 2008. [8] J. Lygeros, C. Tomlin, and S. Sastry, Hybrid Systems: Modeling, Analysis and Control, University of California, Berkeley Electronics Support Group, EECS, December 28, 2008. [9] G. Rousseau, D. Sinoquet, A. Sciarretta, and Y. Milhau, “Design optimisation and optimal control for hybrid vehicles,” in Proc. International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 2008, pp. 1-10. [10] C. Guardiola, B. Pla, S. Onori, and G. Rizzoni, “Insight into the HEV/PHEV optimal control solution based on a new tuning method,” Control Engineering Practice, vol. 29, pp. 247–256, 2014. [11] P. M. Gomadam and J. W. Weidner, “Mathematical modeling of lithium-ion and nickel battery systems,” Journal of Power Sources, vol. 110, pp. 267–284, 2002. Hoang Mai Nguyen was bon in 1969. He received his B.S. degree in Electrical Engineering from Danang University of Science and Technology in 1992, and his M.S. and Ph.D. degrees in Automation and Control from Hanoi University of Science and Technology in 1998 and 2008, respectively. Dr. Nguyen is currently a senior lecturer in Department of Electrical Engineering, Danang University of Science and Technology. His research interests include sliding mode control, adaptive control, nonlinear control, and control of energy systems. Tien Dung Le received the B.S. degree from Automation Division, Faculty of Electrical Engineering, Hanoi University of Technology, Vietnam in 2004. He received the M.S. degree from Department of Electrical Engineering, The University of Danang, Vietnam in 2009. In 2013 he received his Ph.D degree in Electrical Engineering from University of Ulsan, Korea. He is currently a lecturer in Department of Electrical Engineering, Danang University of Science and Technology, Vietnam. His interests are Mechanism analysis and control, intelligent control, Closed-chain robotic manipulators, Control of electrical drives, and Fault diagnosis in control systems 145 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering Le Hoa Nguyen was born in 1979. He received his B.S and M.S degrees in Electrical Engineering from Hanoi University of Science and Technology in 2003 and 2005, respectively, and his Ph.D. degree in Mechanical Engineering from Pusan National University, Korea, in 2012. He is currently lecturer in Department of Electrical Engineering, Danang University of Science and Technology. His research interests include adaptive control, nonlinear control, vehicle control, chaotic control, brain computer interface, and brain signal processing. Quang Vinh Doan–The University of Danang. He earned his Engineer title in 1986 at the Institute of Mechanical and Electrical Engineering in Pilsner, Czechoslovakia. He received the Ph.D degree in 1996 at the University of West Bohemia, Czech Republic. Till now he is the lecturer of the University of Science and Technology, the University of Danang. 146 Journal of Automation and Control Engineering Vol. 4, No. 2, April 2016 ©2016 Journal of Automation and Control Engineering