for a Multimode Hybrid Electric Vehicle

Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle SAE Paper #21-1-816 816 Dominik Karbowski, Jason Kwon, Namdoo Kim, Aymeric Rousseau Argonne National Laboratory, USA SAE World Congress 21

Introduction Toyota Prius, and some other hybrids, use a Power Split system: 1 planetary gearset, 2 electric motors Engine speed can be controlled independently from the vehicle speed Limited cost (simplicity), well suited forlow low speed driving Combining several planetary gearsets or multiple ways of connecting the components leads to a Multimode system. Oii Originally developed dby General lmotors, also used by Mercedes, BMW. Dozen of patents on multimode transmissions. Increased level of complexity and degrees of freedom. This study: an optimized and implementable way of controlling the vehicle UsingArgonne Powertrain System Analysis Toolkit (PSAT): forward looking powertrain simulation environment dynamic plant models Matlab/Simulink/Stateflow Based Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 2

A Multi-Mode Hybrid System Combines Power Split and Fixed Gear Modes Components: 2 electric motors + battery 2 or more planetary gears, several clutches and brakes Combines: Electric continuously Variable Transmission (EVT) modes Fixed Gear (FG) modes, comparable to a conventional car with a multi speed gearbox Engine can be ON/OFF, battery SOC needs to be balanced GM Tahoe hybrid: 4 clutches, 3 planetary gearsets 2 EVT + 4 FG = 6 modes 2.7 ton / 25 kw engine / 2x 6 kw motors / 6.5 Ah NiMH battery TahoeHybrid wasvalidated in PSAT (actual vehicle tested on Argonne s 4WD chassis dynamometer) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 3

Equations Defining a Multi-Mode Transmission One Electrical l Equation Multiple Mechanical Equations (Torques and Speeds) Fixed Gear EVT Generic form for each EVT mode j : Torque multiplication for gear i for each component 2 Degrees of Freedom (Torque Split) 2 Degrees of Freedom: 1 in Speed 1 in Torque Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 4 4

Summary of States, Constraints and Degrees of Freedom Objective of controller: To find the power split between mechanical components (ICE, EM1, EM2) that meets the driver request for the current speedofthe vehicle, while maintaining acceptable battery state of charge and minimal fuel consumption Target Driver torque demand at gearbox output Constraints t Component limitations, it ti drivability, SOCbalance Engine ON/OFF Transmission Mode Degrees of Freedom (Fixed Gear) (EVT) Motor 1 torque Engine Speed Motor 2 torque Engine Torque Controller Output Torques, mode, eng ON/OFF States SOC, Output speed, mode, eng ON/OFF, speeds Controller has to decide on Engine ON/OFF, mode and 2 other degrees of freedom Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 5 5

Possible Approaches to Control Rule Based All 4 degrees of freedom = heuristic rules eg e.g. engine is ON above a certain threshold Partial instantaneous optimization high level hybrid operations (Engine On/Off, battery power) = rules 2 remaining degrees of freedom = optimization Cost function = fuel power Full Instantaneous Optimization All 4 degrees of freedom = optimization Cost function: combination of fuel and battery power Control Implemented Dynamic Programming find the combination of commands that minimizes fuel consumption Requires the prior knowledge of the trip speed trace Easily Implementable, Heuristically tuned Computationally Challenging, Optimal Control Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 6 6

Partial Instantaneous Optimization Combines Rules and Optimization high level hybridization decisions (engine ON/OFF, battery use) Rule Based Remaining 2 degrees of freedom Optimized 1 1 Rule Based 2 3 In1 In2 In1 ENGINE ON/OFF SOC CONTROL Out1 Out1 INSTANTANEOUS OPTIMIZATION MODULE 2 Optimized Cost function = fuel power (battery ypower is set before optimization) For each mode, the optimal (lowest fuel consumption) operation point (torques, speeds) is found, and is used to compute the cost associated to that mode. Selected mode is the one with the lowest cost Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 7 7

Mode Change Is Based on Fuel Power Comparison For Each Mode 12 Threshold depends on: current and prospective mode vehicle speed time since last mode change 1 8 Mode 5 results in lower fuel 6 power (or rate) than any other mode 4 Mode change occurs when difference is higher than a threshold V veh (mph) Mode (x1) Fuel Power: (mode 1) (kw) (mode 2) (kw) (mode 3) (kw) (mode 4) (kw) (mode 5) (kw) (mode 6) (kw) 2 Current mode is Optimal! 667.6 667.7 667.8 667.9 668 668.1 668.2 668.3 668.4 668.5 668.6 Current mode = Mode 1 Time (s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 8

General Organization of the Supervisory Control A. Di Driver command wh_trq_dmd 1 wh_trq_dmd ess_pwr_max_pro 6 ess_pwr_max_pro ess_pwr_max_reg reg 7 ess_pwr_max_reg mc_trq_max_pro 2 mc trq max pro mc_trq_max_reg 3 mc trq max reg mc2_trq_max_pro 4 mc2 trq max pro mc2_trq_max_reg 5 mc2 trq max regen 8 eng_trq_max eng_trq_max 1 mc_spd mc _spd 16 mc_trq mc_ trq mc2 _spd 9 mc2_ spd 13 mc2_trq mc2_trq 15 eng_spd eng_spd 17 eng_on eng_ on SENS_BUS 12 veh_spd veh spd ess.init.soc_init 11 ess_soc abs soc 14 accelec_pwr accelec pwr gb_mode 18 gb_mode 19 gb_sft_in_progress gb_sip wh_trq_dmd B. Constraints H. Braking Torque I. Final Torque Split & Speed Control LOC_DRV_BUS DRV_BUS <veh_spd> veh_spd info_gb_pwr_out_dmd A_Driver _dmd gb_pwr_ou IN_COMPO_CSTR_BUS CSTR_BUS LOC_CSTR_BUS IN_SENS_BUS B_Constraint ess_soc <ess_soc> LOC_SOC_CTRL_BUS SOC_BUS veh_spd <veh_spd> INFO_SOC_CTRL_BUS C_SOC_Control C. SOC Regulation [INFO_SOC DRV_BUS CSTR_BUS DRV_BUS SENS_BUS CSTR_BUS D. Eng ON/OFF D_Engine_ON_Control DRV_BUS eng_on_dmd eng_on_dmd SOC_BUS INFO_ENG_ON_BUS SENS_BUS SENS_BUS ESS_BUS SPD_TRQ_TARGET_BUS E_optim_module E.Optimization Module THRESH_OPTIM_BUS FO_ENG_O eng_on_dmd gb_mode_dmd DRV_BUS CSTR_BUS SENS_BUS eng_on_dmd Mode_dmd mc_trq_dmd_brake mc2_trq_dmd_brake wh_trq_brake_dmd H_Torque_Calc_Brake DRV_BUS DRV_BUS CSTR_BUS CSTR_BUS eng_trq_dmd SENS_BUS SENS_BUS SPD_TRQ_TARGET_BUS mc_trq_dmd OPT_BUS eng_on_dmd eng_on_dmd mc2_trq_dmd gb_mode_dmd Mode_dmd G_Torque_Calc_Prop DRV_BUS DRV_BUS eng_on_dmd eng_on_dmd F_mode_control SENS_BUS DRV_BUS SENS_BUS SENS_BUS gb_mode_dmd THRESH_BUS gb_mode_dmd 1 eng on/off dmd 5 mode F. Mode Selection Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 mc_trq_dmd_brake mc2_trq_dmd_brake wh_trq_brake eng_trq_prop_dmd mc_trq_prop_dmd mc2_trq_prop_dmd DRV_BUS SENS_BUS eng_on_dmd eng_trq_dmd mc_trq_dmd mc2_trq_dmd wh_trq_brake_dmd J_Torque_Split_Logic 2 eng trq dmd 4 mc trq dmd 3 mc2 trq dmd 6 brake trq dmd prop_state_info 12 SOC_BUS ptc_brake_regen_state_info SOC_CTRL_BUS G. Propelling Torque, Speed Control 9

Inside the Optimization Module (Online Mode Comparison) Optimal operating conditions are computed for each mode based on demands and state Target component speeds and torques Operating conditions; the ones corresponding to current gear are selected and used as targets Comparison between current mode fuel power and candidate fuel power =1 if current mode is possible and better Optimal Operating Point Computation Comparison with Current Mode Mode change OK? Optimal Operating Point Computation Comparison with Current Mode Current Mode Mode change OK? Optimal Operating Point Computation The fuel power corresponding to current gear is selected and used for comparison Comparison with Current Mode for current gear Mode change OK? Fuel Power for the current gear Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 1

In the Optimization Module The Optimal Operating Point Is Computed For Each Mode Fixed Gear EVT Givens: Engine, Motors speed (proportional to vehicle speed) Target battery power One motor torque is known => other motor torque known too (electric power equation) To avoid partial load: one motor = all battery power demand other one = no torque out T (Nm m) gb Givens: battery power transmission output speed An offline optimization code finds the optimal engine speed and torque Off line optimization takes into account engine losses and motor losses Resulting look up tables are used in each EVT mode 2 15 1 5 T eng (Nm) 45 4 35 3 25 2 15 out T gb (Nm m) 2 15 1 eng (rpm) 1 5 Example of Targets 5 for Battery power = 1 2 out gb (rpm) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 1 2 out gb (rpm) 4 35 3 25 2 15 11

Mode and Engine Operations 6 V veh [ICE OFF] (mph x1) V veh [ICE ON] (mph x1) w eng (rpm (p x.1) 6 (Nm) T eng Mode (x1) 5 4 3 UDDS 5 4 3 HWFET 2 2 1 1 5 1 15 5 1 15 Time (s) Time (s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 12

Vehicle Operations on Standard Cycles 8 6 V veh [ICE Off] (mph x1) Mode (x1) V veh [ICE On] (mph x1) Delta-SOC (% x1) 4 2-2 -4 UDDS -6 2 4 6 8 1 12 14 6 4 Time (s) Urban = mostly mode 1 (EV), mode 4 when engine is ON 2 HWFET -2 Highway = mode 5 & 6 In both cases, SOC is well balanced -4 1 2 3 4 5 6 7 8 Time (s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 13

nt ) nergy Spe Propelling al Wheel E (ICE ON + hare of Tota ach Mode ( %Sh in Ea Comparative Analysis 6 5 4 3 2 1 UDDS LA92 NEDC HWFET US6 mode 1 mode 2 mode 3 mode 4 mode 5 mode 6 Mode 1 : lower speeds in urban driving (UDDS, LA92, NEDC, US6) Mode 2 : aggressive driving (LA92, US6) Mode 4 : intermediate speeds in urban driving (UDDS, LA92) Mode 5 : high speeds (NEDC, HWFET, US6) Mode 6 : very high speeds (NEDC, HWFET, US6) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 14

Conclusion: Optimized Controller Takes Full Advantage of the Multimode Hybrid System Instantaneously optimized controller for a multimode hybrid powertrain: Implementable in an actual vehicle Easily adaptable to any multimode hybrid system Partial instantaneous optimization finds the optimal mode and operating points: Optimal operation within each mode Optimalmode mode selection with minimal tuning Partial instantaneous optimization uses rule based controls for hybrid controls: Battery SOC balance and drivability through strict control over engine ON/OFF Easy and intuitive to tune (very high level energy management) Also very suitable and flexible for design optimization studies: No tuning for most changes in powertrain (different component/ratios/mass) Controller can be quickly adapted to different mode pattern Future work will focus on: Implementing full instantaneous optimization Quantifying the benefits of optimized controllers over rule based controllers Will be done in Autonomie, Argonne s next generation model based ddesign tool Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 15

Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle SAE Paper #21 1 816 Acknowledgements Activity sponsored by Lee Slezak from the U.S. Department of Energy Contact / Website Dominik Karbowski, dkarbowski@anl.gov Aymeric Rousseau, arousseau@anl.gov www.transportation.anl.gov/modeling_simulation/psat/ Argonne National Laboratory, 97 South Cass, Argonne IL 6439

Additionnal Slides Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 17

Fuel Consumption Cycle mpg km/l L/1 km UDDS 29.1 12.3 8.1 HWFET 27.8 11.8 8.5 NEDC 28.1 11.9 8.4 LA92 23.3 9.9 1.1 US6 19.5 83 8.3 12.11 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 18

Resolution of the Optimization Takes Two Stages Mode 1 Find Optimal Operating Point Compute Associated Cost Compare cost for each mode Mode 6 Find Optimal Compute Associated Operating Point Cost 1. Solve the problem for each mode 2. Select the mode Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 19

Once the Mode Is Chosen, Two Degrees of Freedom Givens: vehicle speed, gearbox output torque (proportional to driver torque demand) In the case of a fixed gear: 2 degrees of freedom Speed: given by the vehicle speed Torque: 2 degrees of freedom, e.g. both electric machines Equivalent to battery power P ess and x EM1 : x EM1 : the fraction of total electric machines electrical input due to EM1 The function is invertible (idem for EM2), giving both electric machines torques, and therefore engine torque EVT: 2 degrees of freedom Speed: 2 linear equations, 3 unknowns = 1 degree of freedom (e.g. ICE speed) Torque: 2 linear equations, 3 unknowns = 1 degree of freedom (e.g. ICE torque) Known engine speed and torque is enough to define the system Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 2

Full Instantaneous Optimization Relies on Finding a Fuel Equivalence to Battery Power All degrees of freedom are resolved by an optimization algorithm At each time t, we are looking forthe command that will minimize the cost function. The cost function cannot be fuel power only, because it would lead to the use of free battery energy An equivalence factor can be used to compare fuel and battery energy: Challenges: the equivalence factor is likely to be cycle dependant, so it would have to be a function of SOC and probably other variables; the engine ON/OFF can be hard to manage Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 21

Fixed Gear : Finding the Optimum Operating Point For a given gear and battery power, the only degree of freedom left is the electric machine split x EM1. Simplifying assumptions: using one motor instead of both ones at the same time is more efficient, hence x EM1 can only be zero or one the motor with the highest speed is more efficient (EM1 in mode 6, EM2 in mode 4 and 5) The cost for that given gear is the fuel power: Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 22

EVT : Finding the Optimum Operating Point For a given mode, if the battery power is given, there is only one degree of freedom left, for example engine speed Since components speeds are not fixed, there is no simple relationship between battery power and the control variables (engine speed and torque) Of all the engine speeds and torques that verifies all equations and constraints, the one that results in the lowest fuel consumption will be the one used to compute the cost The resulting engine speed will also be used as a target later on. Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 23

D. Engine ON/OFF (Logic) Engine turns ON if: (Engine has been OFF for a minimum time)and (Power demand above threshold) AND (Power demand is increasing) OR (Electric System can not meet driver s demand) OR ( Performance Mode, i.e. pedal position close to 1) OR (Battery SOC is low) Engine shuts down if: (Engine has been ON for a minimum time) AND (Power Demand is blow threshold) h AND (Electric System can meet driver s demand on its own) AND (Transmission mode is 1, 2 or 3) AND (Battery SOC is not low) AND (Power demand is decreasing) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 24

E. Optimization Module (outline) Objective: compute the optimal operating point tfor each mode, compare each mode with the current mode and define targets for the current mode The fuel power for the current mode is fed back for comparison 1 <gb_mode> gb_mode 1<x<6 Main Block: online and offline computation 2_ Current _ Mode_ selector 2 gb_spd_out gb_spd_out THRESH _BUS_MODE1 THRESH _BUS_MODE2 Thresh_bus_mode1 Thresh_bus_mode2 3 gb_trq_out gb_trq_out THRESH _BUS_MODE3 THRESH _BUS_MODE4 THRESH _BUS_MODE5 THRESH _BUS_MODE6 Thresh_bus_mode3 Thresh_ bus_ mode4 Thresh_bus_mode5 Thresh_bus_mode6 2 THRESH_OPTIM_BUS 4 ess_pwr_dmd ess _pwr_dmd SPD_TRQ_TRGT_BUS_MODE1 SPD_TRQ_TRGT_BUS_MODE2 SPD_TRQ_TRGT_BUS_MODE3 SPD_TRQ_TRGT_BUS_MODE4 SPD_TRQ_TARGET_MODE1_BUS SPD_TRQ_TARGET_MODE2_BUS SPD_TRQ_TARGET_MODE3_BUS SPD_TRQ_TARGET_MODE4_BUS 1 SPD_TRQ_TARGET_BUS Threshold bus: fuel power and change allowed for EACH mode SPD_TRQ_TRGT_BUS_MODE5 THRESH _CURR _BUS SPD_TRQ_TRGT_BUS_MODE6 1_ENG_PWR_IN_TARGET_EACH_MODE SPD_TRQ_TARGET_MODE5_BUS SPD_TRQ_TARGET_MODE6_BUS Target bus: target speeds and torques for EACH mode Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 25

Fixed Gear Operating Points Speed calculation and constraints check Torque max for each component Fuel power 1 gb_spd_out compo_spd _OK gb_spd _out mc_spd mc2_spd gear # eng_spd 1_Spd_Calc mc_spd_target mc2_spd_target eng_spd_target mc_spd mc2_spd eng _spd EM_selection eng_trq_max EM _trq _max_prop EM_trq_max_chg eng_spd eng_pwr_in eng_trq 6_Fuel_Power 4 eng_pwr_in 6 compo_spd_possible 3_Trq_max mc_spd mc2_spd 3 pwr_elec_dmd 4 gear# gear EM_selection 2_ElecMachineSelection elec _mach_trq _dmd pwr_elec_dmd eng_trq_max EM_trq max prop EM_selection eng_trq eng_trq_target eng_spd_target eng_trq_target EM_trq_max_regen _ 4_Ess_pwr_dmd EM_trq_dmd EM_trq mc_spd_target EM_selection mc2_spd_target 2 gb_trq _out_dmd mc_trq_target gb_trq_out_dmd percent _trq_max gear # 1 MODE3_TRQ_TRGT_BUS Selects the working EM (makes the whole block generic) Torque necessary to provide battery power Torque calculation 5_Trq_calc Checks if battery btt power demand will be met EM_trq mc_trq _dmd EM_selection mc2_trq_dmd mc_spd ess_pwr_dmd_ok mc2_spd mc2_trq_target Elec pwr dmdess_pwr_error 3 ess_pwr_error 7_MC_MC2_Trq_and_Pwr_dmd_Conformity 2 percent_trq_maxtrq AND 5 possible_cmd Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 26

EVT Operating Point Optimization possible_idx= if there is no solution Fuel Power used for later comparison 1 gb_spd_out eng_pwr_in eng_pwr_in_target gb _spd_out 2 gb _trq_out _dmd gb_trq_out_dmd possible_idx eng_spd possible_cmd eng_spd_target 3 eng _pwr_in 4 possible _cmd 3 ess_pwr _dmd ess_pwr_dmd 1_Engine _Optimal _Point eng_trq eng_trq_target eng_spd mc_spd mc_spd_target Using 3 D look up tables, optimal ICE speed and torque is found; gb_spd_out mc2_spd 2_MC_MC2_SPD_CALC eng_trq mc_trq mc2_spd_target mc_trq_target 1 MODE 1_SPD_TRQ _TRGT _BUS gb_trq mc2_trq mc2_trq_target 3_MC_MC2_trq Mc_spd 2 ess_pwr_error Mc2_ spd Mc_trq ess_pwr_error ess_pwr_error Mc2_trq ess_pwr 6_ESS_PWR_CHECK Compute the difference between the target battery power and the actual one Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 27

Optimal Operating Points (EVT1 Input / P ess =) 2 45 T eng (Nm) 4 15 35 3 (Nm) out T gb ( 1 5 5 1 15 2 25 3 out gb (rad/s) 25 2 15 1 5 out T gb (N Nm) 2 15 1 EVT efficiency.95.9.85.8 out T (Nm) gb 2 15 1 (rad/s) eng 45 4 35 3 25 5.75.7 5 1 15 2 25 3 out gb (rad/s) 5 2 15 Includes electric path losses 5 1 15 2 25 3 Does not include gearbox mechanical losses 5 1 15 2 25 3 out gb (rad/s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 28

Optimal Operating Points (EVT2 Compound / 45 P ess = ) 1 45 T eng (Nm) 4 8 35 out T gb (Nm m) 6 4 2 1 2 3 4 5 out gb (rad/s) 1 3 25 2 15 1 5 45 t (Nm) out T gb 1 8 6 4 2 EVT efficiency.95.9.85.8.75 8 eng (rad/s) 4 7.7 1 2 3 4 5 35 out gb (rad/s) out T (Nm) gb 6 4 3 25 2 1 2 3 4 5 out gb (rad/s) 2 15 Includes electric path losses Does not include gearbox mechanical losses Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 29

UDDS UDDS - FE = 29.1 mpg ; SOC (init/final) = 56.5/56.38; Num Eng On = 37 UDDS - Wheel Energy spent in each mode (HEV and propelling) 1 8 8 6 4 2 V veh (m/s) P dmd drv (kw) Eng ON Mode Delta SOCx1 % 6 4 2 1 2 3 4 5 6 mode -2 5 4 UDDS - Operating points (HEV and propelling) -4 2 4 6 8 1 12 14 ng (rad/s) en 3 2 EVT1 EVT2 FG1 FG2 1 FG3 FG4 1 2 3 4 V veh (m/s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 3

UDDS Engine Speed and Torque UDDS - Part 1 - Engine speed and torque 6 6 UDDS - Part 2 - Engine speed and torque 4 4 2 2 5 1 15 15 2 25 3 35 6 UDDS - Part 3 - Engine speed and torque 6 UDDS - Part 4 - Engine speed and torque 4 4 2 2 3 35 4 45 5 55 6 65 6 65 7 75 8 85 9 95 1 6 UDDS - Part 5 - Engine speed and torque V veh x1 (m/s) 6 UDDS - Part 6 - Engine speed and torque 4 2 95 1 15 11 115 12 Eng ON 4 Mode x1 eng (rad/s) T eng (Nm) 2 115 12 125 13 135 14 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 31

HWY HWFET - FE = 27.5 mpg ; SOC (init/final) = 56.5/58.95; Num Eng On = 4 HWFET - Wheel Energy spent in each mode (HEV and propelling) 1 8 6 % 6 4 4 2 2-2 5 1 2 3 4 5 6 mode HWFET - Operating points (HEV and propelling) -4 V veh (m/s) -6 dmd P drv (kw) Eng ON 1 2 3 Mode 4 5 6 7 8 Delta SOCx1 eng (rad/s) 4 3 2 EVT1 EVT2 FG2 1 FG3 FG4 1 2 3 4 V veh (m/s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 32

HWY Engine Speed and Torque HWFET - Part 1 - Engine speed and torque 6 6 HWFET - Part 2 - Engine speed and torque 5 4 3 2 1 5 4 3 2 1 5 1 15 14 16 18 2 22 24 26 28 3 V veh x1 (m/s) HWFET - Part 3 - Engine speed and torque Eng ON 6 Mode x1 6 HWFET - Part 4 - Engine speed and torque 5 eng (rad/s) 5 T eng (Nm) 4 4 3 2 1 25 3 35 4 45 5 55 3 2 1 5 55 6 65 7 75 8 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 33

NEDC NEDC - Wheel Energy spent in each mode (HEV and propelling) 1 8 6 NEDC - FE = 27.1 mpg ; SOC (init/final) = 56.5/61.76; Num Eng On = 13 % 8 6 4 2 4 2 1 2 3 4 5 6 mode 5 NEDC - Operating points (HEV and propelling) -2-4 V veh (m/s) 3 dmd P drv (kw) EVT1 Eng ON 2 EVT2-6 Mode FG2 2 4 6 8 1 12 Delta SOCx1 1 FG3 FG4 1 2 3 4 V veh (m/s) eng (rad/s) 4 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 34

NEDC Engine Speed and Torque NEDC - Part 1 - Engine speed and torque 6 6 NEDC - Part 2 - Engine speed and torque 4 4 2 2 5 1 15 2 15 2 25 3 35 4 6 4 NEDC - Part 3 - Engine speed and torque V veh x1 (m/s) Eng ON Mode x1 eng (rad/s) 6 4 NEDC - Part 4 - Engine speed and torque 2 T eng (Nm) 2 35 4 45 5 55 6 55 6 65 7 75 8 6 NEDC - Part 5 - Engine speed and torque 6 NEDC - Part 6 - Engine speed and torque 4 4 2 2 75 8 85 9 95 1 1 15 11 115 12 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 35

LA92 LA92 - Wheel Energy spent in each mode (HEV and propelling) 1 8 LA92 - FE = 23 mpg ; SOC (init/final) = 56.5/6.9; Num Eng On = 33 6 1 % 4 5 2 1 2 3 4 5 6 mode -5 V veh (m/s) 5 4 LA92 - Operating points (HEV and propelling) -1 2 4 6 8 1 12 14 dmd P drv (kw) 3 Eng ON Mode 2 Delta SOCx1 eng (rad d/s) EVT1 EVT2 FG1 FG2 1 FG3 FG4 1 2 3 4 V veh (m/s) Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 36

LA92 Engine Speed and Torque LA92 - Part 1 - Engine speed and torque 6 6 LA92 - Part 2 - Engine speed and torque 4 4 2 2 5 1 15 2 25 2 25 3 35 4 45 5 55 6 6 LA92 - Part 3 - Engine speed and torque 6 LA92 - Part 4 - Engine speed and torque 4 4 2 2 6 55 6 65 7 75 4 2 LA92 - Part 5 - Engine speed and torque V veh x1 (m/s) Eng ON Mode x1 (rad/s) eng 4 T eng (Nm) 2 75 8 85 9 95 1 15 6 LA92 - Part 6 - Engine speed and torque 1 15 11 115 12 125 12 125 13 135 14 145 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 37

US6 Engine Speed and Torque US6 - Wheel Energy spent in each mode (HEV and propelling) 1 8 2 15 1 US6 - FE = 18.9 mpg ; SOC (init/final) = 56.5/65.89; Num Eng On = 9 V veh (m/s) P dmd drv (kw) Eng ON Mode Delta SOCx1 % 6 4 2 1 2 3 4 5 6 mode 5 5 US6 - Operating points (HEV and propelling) -5 4-1 1 2 3 4 5 6 eng (rad/s) 3 2 1 1 2 3 4 V veh (m/s) EVT1 EVT2 FG1 FG2 FG3 FG4 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 38

US6 6 US6 - Part 1 - Engine speed and torque 6 US6 - Part 2 - Engine speed and torque 5 5 4 4 3 3 2 2 1 1 5 1 15 14 16 18 2 22 24 26 28 3 V veh x1 (m/s) 6 US6 - Part 3 - Engine speed and torque Eng ON Mode x1 5 eng (rad/s) 4 3 2 1 T eng (Nm) 6 5 4 3 2 1 US6 - Part 4 - Engine speed and torque 25 3 35 4 45 5 55 54 55 56 57 58 59 6 Argonne National Laboratory Instantaneously Optimized Controller for a Multimode Hybrid Electric Vehicle 21 1 816 39