Online Optimizing Plug-In Hybrid Energy Management Strategy for Autonomous Guidance and Drive-aware Scenarios

9th IFAC Symposium on Intelligent Autonomous Vehicles 9th Intelligent Autonomous June 29 -Symposium July 1, 2016.on Messe Leipzig, Germany Vehicles 9th IFAC IFAC Symposium on Intelligent Autonomous Vehicles 9th IFAC on Intelligent Autonomous Vehicles June 29 --Symposium July 1, 2016. Messe Leipzig, Germanyonline Available at www.sciencedirect.com June 29 July 1, 2016. Messe Leipzig, June 29 - July 1, 2016. Messe Leipzig, Germany Germany

ScienceDirect IFAC-PapersOnLine 49-15 (2016) 157–162

Online Optimizing Plug-In Hybrid Energy Online Optimizing Plug-In Hybrid Energy Online Optimizing Plug-In Hybrid Energy Management Strategy for Autonomous Management Strategy for Autonomous Management Strategy for Autonomous Guidance and Drive-aware Scenarios Guidance and Drive-aware Guidance and Drive-aware Scenarios Scenarios

Raja Sangili Vadamalu  , Christian Beidl  , Christian Beidl Raja Sangili Vadamalu Raja Raja Sangili Sangili Vadamalu Vadamalu  ,, Christian Christian Beidl Beidl Institute for Internal Combustion Engines and Powertrain Systems, Institute Internal and Institute for for Internal Combustion Combustion Engines and Powertrain Powertrain Systems, Darmstadt University ofEngines Technology, Germany Systems, Institute for Internal Combustion Engines and Powertrain Systems, Darmstadt University of Technology, Germany Darmstadt University of Technology, Germany Darmstadt University of Technology, Germany Abstract: Recent advances in autonomous driving and vehicle connectivity help to ensure Abstract: Recent advances autonomous driving and vehicle connectivity help to ensure Abstract: Recent in autonomous driving and connectivity help to ensure safety and comfort in variousin driving conditions. These trends have widenened the system Abstract: Recent advances advances in driving autonomous drivingThese and vehicle vehicle connectivity helpthe to system ensure safety and comfort in various conditions. trends have widenened safety and comfort in various driving conditions. These trends have widenened the system boundary conditions for hybrid powertrain operation with driving trajectory planning hence safety and comfort in various driving conditions. These trends have widenened the system boundary conditions for powertrain operation with planning hence boundary conditions for hybrid hybrid powertrain operationefficiency. with driving driving trajectory planning hence offering potential to improve powertrain operational This trajectory paper presents an energy boundary conditions for hybrid powertrain operation with driving trajectory planning hence offering potential improve powertrain efficiency. This paper presents an energy offering potential to improve powertrain operational efficiency. This paper an management (EM)to controller for a plug-in operational hybrid vehicle exploiting predicted velocity trajectory offering potential tocontroller improve for powertrain operational efficiency. This paper presents presents an energy energy management (EM) a plug-in hybrid vehicle exploiting predicted velocity trajectory management (EM) controller for a plug-in hybrid vehicle exploiting predicted velocity trajectory together with its integration in both autonomous longitudinal guidance and driver-aware management (EM) controller for a plug-in hybrid vehicle exploiting predicted velocity trajectory together its integration in both longitudinal guidance and driver-aware together with its in autonomous longitudinal guidance and scenarios.with The driver-aware scenario usesautonomous Markov chain based stochastic modelling of driving together with its integration integration in both both autonomous longitudinal guidance and driver-aware driver-aware scenarios. The driver-aware scenario uses Markov chain based stochastic modelling driving scenarios. The driver-aware driver-aware scenario uses Markov Markov chain based stochastic modelling ofthe driving characteristics. The proposed EM controller solves online, a stochastic discretizedmodelling version ofof fuel scenarios. The scenario uses chain based of driving characteristics. The proposed EM controller solves online, a discretized version of the fuel characteristics. The proposed EM controller solves online, a discretized version of the fuel consumption minimization problem using directsolves methods transcribing the problem into a finite characteristics. The proposed EM controller online, a discretized version of the fuel consumption minimization using direct methods transcribing the problem into apart finite consumption minimization problem using direct methods transcribing the into finite dimensional mixed booleanproblem quadratic problem with polytopic constraints. The convex of consumption minimization problem using directwith methods transcribing the problem problem into aapart finite dimensional mixed boolean quadratic problem polytopic constraints. The convex of dimensional mixed boolean quadratic problem with polytopic constraints. The convex part of the resulting problem is solved using an active set method. Simulation results from different dimensional mixed boolean quadratic problem with polytopicSimulation constraints. The convex part of the resulting problem ison solved usingdriving an active active set method. results from different the resulting problem solved using an method. Simulation results different driving situations basedis standard cycleset and real world driving scenarios demonstrate the resulting problem ison solved usingdriving an active set method. Simulation results from from different driving situations based standard cycle and real world driving scenarios demonstrate driving situations on cycle real driving scenarios demonstrate the functionality ofbased the controller anddriving its flexbility to handle varying control objectives. driving situationsof based on standard standard driving cycle and and real world world driving scenarios demonstrate the functionality the controller and its flexbility to handle varying control objectives. the functionality of the controller and its flexbility to handle varying control objectives. the functionality of the controller and its flexbility to handle varying control objectives. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Energy Management, Plug-in Hybrid Electric Vehicle, Model Predictive Control, Keywords: Energy Plug-in Hybrid Keywords: Programming, Energy Management, Management, Plug-in Hybrid Electric Electric Vehicle, Vehicle, Model Model Predictive Predictive Control, Control, Quadratic Active Set Method Keywords: Energy Management, Plug-in Hybrid Electric Vehicle, Model Predictive Control, Quadratic Programming, Active Set Method Quadratic Programming, Active Set Method Quadratic Programming, Active Set Method 1. INTRODUCTION Vehicle connnectivity collectively defines the interaction 1. Vehicle connnectivity collectively defines the interaction 1. INTRODUCTION INTRODUCTION Vehicle connnectivity collectively defines interaction between the vehicle and its environment encompassing 1. INTRODUCTION Vehicle connnectivity collectively defines the the interaction between the vehicle and its environment encompassing between the vehicle and its environment encompassing communication between Vehicle to Vehicle (V2V) and the vehicle and its environment encompassing Rigourous regulatory requirements, customer demand for between communication between Vehicle to Vehicle (V2V) and Rigourous regulatory requirements, customer demand for communication between Vehicle to Vehicle (V2V) Vehicle to Infrastructure (V2I). Prognosed reduction in Rigourous regulatory requirements, customer demand for between Vehicle to Vehicle reduction (V2V) and and improved efficiency and increased competitiveness among Rigourous regulatory requirements, customer demand for communication Vehicle to Infrastructure (V2I). Prognosed in improved efficiency and increased competitiveness among Vehicle to Infrastructure (V2I). Prognosed reduction accidents, optimization of traffic flow and newreduction potential in improved efficiency and increased competitiveness among Vehicle to Infrastructure (V2I). Prognosed in vehicle manufacturers, have increased emphasis on reducimproved efficiency andhave increased competitiveness among accidents, optimization of traffic flow and new potential in vehicle manufacturers, increased emphasis on reducaccidents, optimization of traffic flow and new potential in individual mobility have been the motivating factors for vehicle manufacturers, have increased emphasis on reducaccidents, optimization of traffic flow and new potential in emissions tion of energy consumption and equivalent CO 2 vehicle manufacturers, have and increased emphasis on reduc- individual mobility have been the motivating factors for emissions tion of consumption CO individual mobility have been the motivating factors for increased attention the field autonomous emissions tionupcoming of energy energy powertrain consumption and equivalent equivalent CO22CO individual mobility in have beenof the motivatingdriving. factorsThe for in concepts. The fleet 2 emisemissions tion of energy consumption and equivalent CO 2 increased attention in the field of autonomous driving. The in upcoming powertrain concepts. The fleet CO emisincreased attention in the field of autonomous driving. The reported fuel savings of 22% (ECOMOVE, 2009) by avoid2 in upcoming powertrain concepts. The fleet CO emisincreased attention in the field of autonomous driving. The sionupcoming target forpowertrain new passenger cars The and light-commercial 2 emisin concepts. fleet CO 2 reported fuel savings 22% (ECOMOVE, 2009) by avoidsion target new fuel of 22% (ECOMOVE, 2009) by ing inefficient drivingof achieved using autonomous sion target for new passenger cars and light-commercial reported fuel savings savings ofcan 22%be (ECOMOVE, 2009) by avoidavoidvehicles by for 2020 in passenger the EU iscars set and as 95light-commercial gram per km. reported sion target for new passenger cars and light-commercial ing inefficient driving can be achieved using autonomous vehicles by 2020 in the EU is set as 95 gram per km. ing inefficient driving can be achieved using autonomous eco-guidance. The fuel saving potential can be further vehicles by 2020 in the EU is set as 95 gram per km. ing inefficient driving can be achieved using autonomous Automobile manufacturers face challenges to devise effecvehicles by 2020 in the EU is challenges set as 95 to gram pereffeckm. eco-guidance. The fuel saving be further Automobile manufacturers face devise eco-guidance. The potential can be further increased by combining it withpotential efficient can power in Automobile manufacturers face challenges to devise effececo-guidance. The fuel fuel saving saving potential can be split further measures due to demanding pollutant tive CO2 reduction Automobile manufacturers face challenges to devise effecincreased by combining it with efficient power split reduction measures measures due torequisite demanding pollutant increased tive CO CO22 regulations increased by combining combining itpaper withpresents efficienta power power split in in PHEV powertrains. This it EM controller reduction due to demanding pollutant tive by with efficient split in emission retaining the fun-to-drive. reduction measures due torequisite demanding pollutant PHEV tive CO2 regulations powertrains. This paper presents aa EM controller emission retaining the fun-to-drive. PHEV powertrains. This paper presents EM controller that uses the predictive information available from vehiemission regulations retaining the requisite fun-to-drive. PHEV powertrains. This paper presents a EM controller Further the measures shall not only be developed for emission regulations retainingnot theonly requisite fun-to-drive. that uses the predictive information available from vehiFurther the measures be for that uses information available from vehicle connectivity during autonomous manage Further the measures shall only be developed for that uses the the predictive predictive information guidance available to from vehilegal driving cycles butshall also not be effective indeveloped real driving Further the measures shall not only be developed for cle connectivity during autonomous guidance to manage legal driving cycles but also be effective in real driving cle connectivity during autonomous guidance to manage powerflow between the energy converters of PHEV. One legal driving cycles but also be effective in real driving connectivity during autonomous guidance to manage operation. Three technology trends that in strongly influ- cle legal driving cycles but also be effective real driving powerflow the converters operation. Three technology trends that strongly influpowerflow between between the energy energy converters isof oftoPHEV. PHEV. One exemplary use-case based on connectivity informOne the operation. Three technology trends that strongly influpowerflow between the energy converters of PHEV. One ence future mobility are powertrain hybridization, vehicle operation. Three technology trendshybridization, that stronglyvehicle influ- exemplary use-case based on connectivity to inform the ence future mobility are powertrain exemplary use-case based on connectivity is to inform the EM controller to maintain a certain batteryis charge reserve ence future mobility are powertrain hybridization, vehicle exemplary use-case based on connectivity is to inform the connectivity and autonomous driving. Hybridization of a ence future mobility are powertrain hybridization, vehicle EM controller to maintain aa certain battery charge reserve connectivity and autonomous driving. Hybridization of a EM controller to maintain certain battery charge reserve (enabling electric drive) before entering a zero-emission connectivity and autonomous driving. Hybridization of a EM controller to maintain a certain battery charge reserve conventional powertrain refers to its augmentation with connectivity and autonomous Hybridization with of a (enabling electric drive) before entering conventional powertrain refersdriving. to its its augmentation (enabling electric drive) before zero-emission zone. Extensions driver-aware scenario aaaarezero-emission realised usconventional refers to augmentation with electricto drive) before entering entering zero-emission an additional powertrain energy convertor energy storage device. conventional powertrain refers and to its augmentation with (enabling zone. Extensions to driver-aware realised usan additional energy convertor and energy storage device. zone. Extensions to driver-aware driver-aware scenario are realised using Markov chain based modelling scenario of future are power demand. an additional energy convertor and energy storage device. zone. Extensions to scenario are realised usOne possible solution which is currently favored is Plug-in an additional energy convertor and energy storage device. ing Markov chain based modelling of future power demand. One possible solution which is currently favored is Plug-in ing Markov chain based modelling of future power demand. One possible solution which is currently favored is Plug-in ing Markov chain based modelling of future power demand. Hybrid Electric Vehicle (PHEV), which is a combination One possible solution which is currently favored is Plug-in The paper is organized as follows: Section 2 describes the Hybrid Electric Vehicle (PHEV), a combination Hybrid Electric Vehicle (PHEV), which is a combination paper is organized as follows: Section the of the Internal Combustion Enginewhich (ICE)is and the Electric The The paper is as Section describes the Hybrid Electric Vehicle (PHEV), which is a combination system model and theoretical results used222indescribes subsequent The paper is organized organized as follows: follows: Section describes the of the Internal Internal Combustion Engine (ICE) andcapacity the Electric Electric of the Combustion Engine and the model and theoretical results used in subsequent Traction Machine (ETM) with high(ICE) energy bat- system system model and theoretical results used in subsequent of the Internal Combustion Engine (ICE) and the Electric sections. Formulation and solution methods of the Model system model and theoretical results used in subsequent Traction Machine (ETM) with high energy capacity batTraction (ETM) high capacity batFormulation and solution methods of the Model tery whichMachine can be externally charged. Presence of multiple sections. Formulation and solution methods of Model Traction Machine (ETM) with with high energy energy capacity bat- sections. Predictive Control (MPC) PHEV EM are presented sections. Formulation and based solution methods of the the Model tery which can be externally charged. Presence of multiple tery which can be externally charged. Presence of multiple Predictive Control (MPC) based PHEV EM are presented power sources increases the Degree-of-Freedom (DoF) of Predictive Control (MPC) based PHEV EM are presented tery which can be externally charged. Presence of multiple in Section 3. These are followed by results of the implePredictive Control (MPC) based PHEV EM are presented power sources increases the Degree-of-Freedom (DoF) of power sources increases the The Degree-of-Freedom (DoF) of in in Section 3.controller These are arethat followed by results results of the the impleimplethe hybrid propulsion unit. supervisory control layer Section 3. These followed by of power sources increases the Degree-of-Freedom (DoF) of mented EM are discussed in Section 4. in Section 3. These are followed by results of the implethe hybrid propulsion unit. Thetosupervisory supervisory control layer the propulsion unit. The EM controller that are discussed in Section 4. thathybrid uses this additional DoF manage thecontrol power layer flow mented mented EM controller that are discussed in Section 4. the hybrid propulsion unit. The supervisory control layer mented EM controller that are discussed in Section 4. that uses this additional DoF to manage the power flow that uses this additional DoF to manage the power flow between ICE and ETM meeting the driver power request that uses this additional DoF to manage the power flow 2. THEORY AND SYSTEM MODELING between ICE and ETM meeting the driver power request between and ETM the request is termedICE as the Management (EM)power controller. 2. THEORY THEORY AND SYSTEM SYSTEM MODELING between ICE andEnergy ETM meeting meeting the driver driver power request 2. is 2. THEORY AND AND SYSTEM MODELING MODELING is termed termed as as the the Energy Energy Management Management (EM) (EM) controller. controller. is termed as the Energy Management (EM) controller. MPC is employed to solve the predictive EM problem due MPC is employed to solve the predictive  Corresponding Author,(e-mail: vadamalu@ vkm.tu-darmstadt.de) MPC is to solve EM problem due its ability to track trajectoriesEM in problem presencedue of MPC is employed employed to set-point solve the the predictive predictive EM problem due  its ability to track set-point trajectories in presence of Corresponding Author,(e-mail: vadamalu@ vkm.tu-darmstadt.de)  its ability to track set-point trajectories in presence Author,(e-mail: vadamalu@ vkm.tu-darmstadt.de)  Corresponding its ability to track set-point trajectories in presence of of Corresponding Author,(e-mail: vadamalu@ vkm.tu-darmstadt.de) Copyright 2016 IFAC 157 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 157 Copyright © 2016 IFAC 157 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 157Control. 10.1016/j.ifacol.2016.07.725

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Fig. 1. Schematic of combustion engine assist powertrain hard constraints on states and inputs. The investigations in this paper employ the Combustion Engine Assist (CEA) powertrain depicted in Fig. 1 as a use-case. CEA is a PHEV in parallel P2 topology with a downsized 2cylinder ICE and an ETM (Beidl et al., 2012). The structure of the CEA powertrain is depicted in Fig. 1. The powerflow during propulsion is indicated by the torques (T ) and speeds (ω) at the component interfaces. The controlled quantities namely, torque from ICE, ETM and ICE state are denoted by dotted lines. From the functional perspective, it is a full hybrid offering pure electric drive functionality by decoupling the combustion engine using the clutch C1. 2.1 Model Predictive Control MPC realizes constrained finite horizon optimal control using control action resulting from repeated solution of an Optimal Control Problem (OCP) parameterized by the initial state. It uses a model which forecasts system behaviour over a time interval known as prediction horizon to determine control action for a certain control horizon. The generic nonlinear economic MPC for a prediction horizon of length N is of the form (Rawlings et al., 2012). min VN (x, u) u

s. t. x+ = f (x, u) x(0) = x (x(k), u(k))  Z

(1)

x(N )  XN k  Z0:N −1

VN denotes the value function or cost function, f (x, u) is the nonlinear system dynamics. XN and Z denote the terminal set and feasbile set respectively. There exist three broad class of methods for solving OCP (Diehl et al., 2005). Dynamic Programming (DP) based on the principle of optimality solves the OCP by HamiltonJacobi-Bellman equation (HJB), a sufficient condition for optimality. Among others, the curse of dimensionality discourages its direct application. Variants of DP have been investigated specifically for EM-OCP (Wahl et al., 2014). Indirect methods uses the Pontryagins Minimum Principle to reduce the OCP to a two-point boundary value problem. Inequality constraints thereby lead to ODE with state dependent switches and hence are difficult to handle. Direct methods discretize the infinite dimensional OCP into finite dimensional NLP problem and solve it using well developed sparse structure exploiting solvers. Direct methods can handle inequality constraints better and shall be employed for solving the EM-OCP. 158

Fig. 2. MPC structure for PHEV EM The structure of MPC employed for solving the EM-OCP is shown in Fig. 2. The slash symbol on the signals indicate that they are vector valued. The vector notation x(.|k) stands for the predicted value for a horizon of length N based on the current value. [x(k|k)x(k+1|k)...x(k+N |k)]T . The model predictive EM controller computes set point torque values of ETM and ICE as well as state of ICE from the predicted values of torque and speed at the gearbox input over the prediction horizon. The current value of state of charge(SoC), current state of ICE, torque values of ETM and ICE are fedback to the EM controller. The dynamic controller component of EM controller realises the command set point values (Vadamalu and Beidl, 2016). The torque and speed predictions TGB (.|k) and ωGB (.|k) (GB stands for Gearbox) are computed from the driver model and an inverse model. The driver model is realised as two DoF controller with a feedforward part and a Proportional-Integral (PI) feedback controller. The feedforward part computes the torque and speed values based on set velocity, to the contrary the PI controller acts on the resulting small deviations. The inverse model is a non-causal representation of the vehicle longitundinal dynamics, computing torque and speed predictions from predicted vehicle velocity v(.|k) and road grade vectors α(.|k) over the prediction horizon N. Information regarding future vehicle velocities and road grade with the current driver demand to generate speed and torque vectors at the gearbox input side with the length of the prediction horizon. The MPC controller is consituted by the model used to represent the process, optimization algorithm, objective function and constraints. Model, cost function and constraints depend on problem formulation which is handled in Section 3. As discussed direct optimal control methods and hence Nonlinear programming (NLP), specifically quadratic programming (QP) solvers shall be used. Direct methods use a finite dimensional control trajectory parameterization but have different realizations to deal with state trajectories. This work uses a sequential approach, which solves the differential or discretized difference equation during optimization. Only the first element of the computed control vector is fed to the Dynamic Controller block, which realizes the set values using component-level controllers. The procedure is repeated the next sampling

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instant with an updated system state x(k) resulting in a receding horizon control strategy. 2.2 Modeling System modeling deals with two aspects: nonlinear simulation model and prediction model. The nonlinear model serves as a validation environment for simulative performance analysis of the implemented EM algorithm. This model constitutes a driver and driving cycle apart from the nonlinear longitudinal vehicle dynamics. Whereas, the prediction model is a parameteric model used to predict future state trajectories within the MPC framework. Nonlinear simulation model This model represents the longitudinal dynamics of the vehicle with a powertrain configuration as shown in Fig. 1. The model is based on quasistatic approach (Sciarretta and Guzzella, 2007). The energy convertors ICE and ETM are modelled as torque sources together with a PT1 element to represent lag in torque buildup. Quasi stationary energy conversion efficiency is modelled using two dimensional maps with torque and speed as the respective coordinates. TICE = F (ωICE , α)

m ˙ f = G(TICE , ωICE )

(2)

PET M,e = H(TET M , ωET M )

(3)

m ˙ f stands for fuel mass flow rate and PET M,e denotes power on the electrial side of ETM including inverter losses during motoring and generating operation. The battery is modeled as a voltage source (with open circuit voltage Voc and terminal voltage Vt ) in series with an internal resistance Ri . SoC is defined as ratio of the current charge (Q) to the maximum charge of the battery (Qmax ). The dynamics of SoC is the most relevant dynamics from the energy-flow perspective and is given by Eqn. (4). ˙ = −Ib / Qmax SoC (4)

sC2  {0, 1} (5) sC1 = sICE  {0, 1} Tw = ηGB iGB iD TGB ωGB = iGB iD ωw (6) The clutches C1 and C2 are modeled without switching between stick and slip states using the Karnopp approach. The states of the clutches are denoted by sC1 and sC2 respectively. On/Off state of ICE, sICE corresponds to the state of clutch C1, sC1 . The longitundinal dynamics are modeled as first order non-linear differential Eqn. (7). The variable rw denotes the radius of wheel, cr coefficient of rolling resistance , A front area of vehicle, γ factor for rotational interia of vehicle, ηGB efficiency of gearbox, cw coefficient of wind resistance, ρair density of air and Tw wheel torque. Tw (t) = rw · (0.5ρair cw Av 2 (t) + cr mg cos(α(t)) + mg sin(α(t)) + γmv(t)) ˙

(7)

The powertrain torsional dynamics which are slower when compared to SoC dynamics are neglected. The solver Runge-Kutta(fourth order) and sample time of 1 ms are chosen based on eigenvalues of the linearized system and the solver stability region. Prediction model The prediction model computes the future system states based on the current state and future control action. As the goal of EM is to meet the driver 159

159

power demand keeping the battery SoC within predefined limits, the prediction model shall represent the ICE and ETM energy conversion dynamics. The torque dynamics of both the energy convertors are neglected as it is faster than EM sampling frequency (Sciarretta and Guzzella, 2007; Wahl et al., 2014). In order to reduce the computational complexity, the nonlinear behaviour shall be approximated by linear or quadratic approximations hence convexifying the problem. Willians line serves as an approximation for the energy conversion in ICE. It can be approximatied using linear (nm = 1) or quadratic (nm = 2) Eqn. as in (8), where the coefficients are functions of ICE speed. m ˙ f ≈ a0 (ωICE )sICE + Ib ≈

nm 

j aj (ωICE )TICE (ωICE ) (8)

j=0 n m 

j bj (ωET M )TET M (ωET M ) (9)

j=0

Similarly, the electrical energy consumption/generation during motoring/generator operation of the ETM is modelled using speed dependent linear or quadratic approximations. As observerd in (Vadamalu et al., 2015) the quadractic relationship provides better approximation of the fuel consumption. As the battery SoC limits form the constrains a linear approximation is selected resulting in polytopic constraints. The dynamics in (9) is discretized using explicit euler method. Ib = b1 (ωET M )TET M + b0 (ωET M ) (10) ˙ = −(b1 (ωET M )TET M + b0 (ωET M )) / Qmax (11) SoC Scenarios considered There are different realizations of driver assistance systems and autonomous driving. A comprehensive survey has been presented in (Maurer et al., 2015). The proposed EM algorithm in the autonomous case, assumes availability of autonomous longitudinal guidance and hence prior knowledge of future vehicle velocity and road grade over the prediction horizon N. The optimal velocity trajectory (Wahl et al., 2014) modulated by situation specific velocity limits, shall be an input to the EM controller. As the paper focusses on solving EM-OCP, vehicle environmental modelling shall not be investigated. In case of driver-aware scenario, the velocity trajectory shall be actively controlled by a human driver. Modelling such driving characteristics is a field of active research. One commonly accepted approach is to model the driving characteristics using stochastic process with the Markovian property (Eqn. (12) and (13)) as in (Lee et al., 2011). xi stands for specific realization of the stochastic state variables Xi and π indicate transition probability between states. π(xn |xn−1 , ..., x2 , x1 , x0 ) = π(xn |xn−1 ) (12)   πij = Π(Xk+1 = j|Xk = i) = 1 (13) j

j

3. MPC BASED PHEV EM The EM controller computes torque demand with predicted information about velocity and road grade, which is to be realised by the specific component level controllers.

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Hence EM serves as supervisory controller providing set point values for the subordinate component specific controllers. 3.1 Problem Formulation PHEV EM aims to minimise the fuel consumption mf maintaining the SoC (the system state SoC shall be denoted by x) within prescribed limits. In comparison to hybrid powertrains the reference value of SoC , xref can be different from its initial value x0 for PHEV, which is offvehicle chargeable. For a specific driving situation xref is the SoC value around which the battery shall be operated. On discretization of the continuous time optimization problem minimising the fuel consumption over a finite time horizon length N results in, N −1  δmf (14) min uUf

i=0

where Uf denotes the feasbile input set. Owing to computational complexity and difficulty in obtaining accurate nonlinear models, the EM problem is formulated as linear MPC with a quadratic cost function and polytopic constraints. The EM-OCP problem is constrained by battery SoC and actuator limits. There exisits approaches to track a SoC, reference value using a quadratic deviation cost of the actual SoC, this paper handles the constraints explicitly as discussed below. From the parallel configuration of CEA PHEV powertrain follows Eqn. (15) assuming both the clutches in closed condition. (15) TICE + TET M = TGB TET M,min (ω) ≤ TET M ≤ TET M,max (ω) (16) (17) TICE,min (ω) ≤ TICE ≤ TICE,max (ω) TICE (k + 1) − TICE (k) ≤ ∆(T ICE,max ) (18)

Eqn. (16) and (17) constrains the torque limits. Torque rate constraints based on the current value of torque set value Eqn. (18) which constrain the set torque only for the next sampling instant. The resulting torque limits for the combustion engine and electric machine are denoted by T ICE and T ET M respectively. Combining Eqns. (15), (16),(17), (18) result in : TET M,min = max(T ET M,min , TGB )−T ICE,max ≤ T ET M ≤ min(T ET M,max , TGB − T ICE,min ) = TET M,max (19) Using the approximations for ICE and ETM from Eqn. (8), (9) together with terminal constraint for SoC and inequality path constraints of SoC for a prediction horizon of length N results in the optimization problem: 

 N opt  TET M (.|k) = argmin m˙ f · Ts sopt ICE (.|k)

(20)

i=0

s. t. x(k) + Ts ·

N 

x(k ˙ + i|k) ≥ xref

(21)

x(k ˙ + i|k) ≤ xmax

(22)

m˙ f = a0 + a1 · (TICE ) + a2 · (TICE )2

(23)

xmin ≤ x(k) + Ts ·

TET M,min

i=0

N −1  i=0

x˙ = b0 + b1 · TET M ≤ TET M ≤ TET M,max

SoC path constraints limiting SoC at every time instant have been included explicitly as in (22). The above mentioned optimization problem computes the optimal ICE/ETM torque split and the on/off state of ICE, a boolean variable. This problem is handled as two subproblems: one convex and another boolean using the procedure described in Algorithm 1. The engine state can be solved using approaches such as branch and bound, convex relaxations or explicit handling of boolean variables. Here an approach based on heuristics of value function (Vi ) as shown in (26) is used as a stopping criterion for the boolean subproblem. An example of such an heuristic rule would be to request combustion torque if the torque demand is nonnegative and the speed at gearbox input is greater than the engine idling speed ensuring a feasible initialization. def

H(Vi ) = |V (i) − V (i − 1)| ≤ 

(26)

Algorithm 1 Iterative method to solve MI-LCQP 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19:

procedure Iterative procedure for joint optiopt mization of sopt ICE (.|k) and TET M (.|k) Input: Tg (.|k) , ωg (.|k) if (21), (22), (25) then opt sopt ICE (.|k) ← 0; TET M (.|k) ← TGB (.|k) opt return siICE (.|k), TET M (.|k) end if init: siICE (.|k) while (i) do

boolean subproblem while (j) do

convex subproblem opt Solve convex QP to get TET M (.|k) end while Compute Value function Vi,j if H(Vi,j ) then opt return siICE (.|k), TET M (.|k) end if Update si+1 ICE (.|k) end while opt Output: siICE (.|k), TET M (.|k) end procedure

Solution method for the convex sub-problem There exists different solution approaches for the convex QP. A tailored real-time capable active set solver was presented in (Vadamalu et al., 2015). In this publication, the convex subproblem of computing the optimal torque split between ICE and ETM is solved using qpOASES (Ferreau, 2012). qpOASES is a self-contained implementation of online active set method for solving convex QPs, specifically designed for solving parametric QPs arising in MPC. QPs can be solved without phase I feasibility step using coldstart (or) hot-start methods reducing effort for internal matrix factorizations. The resulting Karush-Kuhn-Tucker (KKT) system is solved using null-space approach. 3.2 Markov Chain (MC) for driving characteristics

(24) (25) 160

Using velocity and acceleration as states, the procedure described in Algorithm 2 is used to determine the transition probability matrix (TPM) and maximum likelihood estimates of the change in acceleration (A(i, j)) and velocites (V(i, j)) respectively for every state. The discretization and the limits of velocity and acceleration are

IFAC IAV 2016 June 29 - July 1, 2016. Messe Leipzig, Raja Sangili Vadamalu et al. / IFAC-PapersOnLine 49-15 (2016) 157–162 Germany

19: 20: 21: 22: 23:

procedure Markov Chain generation Input:Drive cycle velocity and acceleration discretize using limits as in (27), (28), (30), (31) init: Π ← zeros(Ax , Vx ) while (i) do  Parse driving cycle Add submatrices with vx and ax to Π end while while (j) do  Parse Π S1 ← Submatrices of state transition S2 ← Unique submatrices of state transition while (k ← |S2|) do  Parse submatrices Compute π(j) as in (29) Append π(j) to entry of S2 end while end while init:V,A ← zeros(Ax , Vx ) while (l ← |S2|) do  Parse submatrices i∗ ← argmaxi{0...|S1|} π(i, j) V(i, j) ← Vx (i∗ ) A(i, j) ← Ax (i∗ ) end while Output:Matrices Π, VA end procedure

(Vadamalu and Beidl, 2016) uses the MC predictor for a prediction horizon length of 3 with Explicit MPC controller, but this publication extends the approach for a prediction horizon length of 50 in tandem with the activeset QP solver. Based on the current velocity and the computed change in velocities, prediction can be constructed for the horizon length. Using Eqn. (6) and (7) gearbox input torque and speed vectors of prediction length can be computed in line with the MPC structure in Fig. 2. 4. RESULTS AND DICUSSION The optimization routine is integrated with the nonlinear vehicle model to analyse its performance using simulations. The results of EM controller in Charge Depletion (CD) and Charge Sustaining (CS) modes have been discussed, followed by results in driver-aware scenario. Fig. 3 presents the results of the EM controller in CD operation using the NEDC driving cycle. It can be observed that the controller behaviour differs for different settings of SoCmin . In case of a lower value for the minimum SoC, ICE is never switched on as the lower bound does not turn active. However in the other case, with the same initial SoC, ICE is switched on 161

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given by Eqn (27) and (28). The cardinality of Ax and Vx (denoted by |Ax | and |Vx |) influence the representativeness of the Markov chain based approach. The transition probability is computed as in Eqn.(29) based on submatrices S1 and S2 for each transition. v(k) + v(k + 1) vmax |Vx | = +1 (27) vx (k) = 2 vres v(k) − v(k + 1) |a|max ax (k) = |Ax | = 2 · + 1 (28) Ts ares π(i) = |(S1 == S2(i)|/|S1| (29) (30) Vx  {0, vres , 2 · vres , ...} Ax  {..., 0, −ares , 0, ares , 2 · ares , ...} (31)

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Fig. 4. EM operation in Charge Sustaining mode, N = 50 to maintain its minimum level above 0.58. This condition emulates a scenario before entering an urban zone where pure electric driving is legally mandatory, hence requiring a minimum level of battery charge. Further the on/off state sICE of ICE and the number of iterations required by the active set method have also been depicted. Iterations here correspond to the number of active set changes performed. Due to violation of SoC limits during pure electric driving, the torque split optimization is triggered around 700 s. Before every ICE start, a relative peak in the number of iterations can be observed as this involves reconfiguration of the optimization problem from electric drive mode to tandem ETM-ICE operation. The CS operation for different values of SoC reference value SoCref is presented in Fig. 4. Beginning with the same initial value of 0.2, in one case the SoC value is maintained around the same value. In constrast, the second case requires the SoC value to reach a higher level 0.3 at the end of the cycle. To reach the higher level of battery charge, the ICE is switched on to charge the battery. Such an operation would be undesired from efficiency perspective but is necessary to maintain battery charge level due to forecasted activation of auxiliary electric load (airconditioner driven by an electric compressor). Operation in blended mode (gradual discharge of the battery during driving) can be realized by tuning the parameters SoCref , SoCmin and SoCmax during operation. Fig. 5 shows the values of the change in acceleration and velocity for the discretized state space for the driving

IFAC IAV 2016 June 29 - July 1, 2016. Messe Leipzig, Raja Germany 162 Sangili Vadamalu et al. / IFAC-PapersOnLine 49-15 (2016) 157–162

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scenario of Fig. 6. Discretization resolution of 1 km/h and 0.1 m/s2 is been selected for velocity and acceleration respectively. In V matrix, over the defined band of velocities positive value of acceleration result in positive change of velocities. Likewise deceleration results in negative velocity change. The matrix A stores information about the change in acceleration in subsequent sampling instant. As it can be observed from the driving cycle, there are two different regions of positive acceleration and deceleration in the upper and lower sections of velocity band respectively. Further at low velocities high deceleration values due to deceleration to standstill can also be observed. Results from driving scenario are displayed in Fig. 6, the discussed change in velocity and acceleration matrices are employed for prediction. The first plot depicts the actual vehicle velocity for both the prediction possibilities. The second and third plots show ICE set torque and speed values in guidance (deterministic predictor) and driver-aware scenario (MC predictor) respectively. In both cases a prediction horizon of N = 20 was employed. Fuel consumption of the guidance scenario based on better prediction was 15g. Whereas fuel consumption in drive-aware scenario amounted to 16.7g. Despite poor prediction in case of MC based approach in comparision with deterministic prediction, for a prediction horizon of length 50, the fuel consumption values lie close to each other. Dynamic controller manages the gearshift process, by making the powertrain torque-free during gear change. This can be observed along with fall in ICE speeds during up-shift.

Fig. 6. Results from driving scenario for deterministic and MC predictors, for prediction horizon N = 20

5. CONCLUSION An online optimizing EM strategy based on MPC has been presented for a PHEV. The strategy considers dynamic change in the constraints, adapting its behaviour to varying driving scenarios. Such self-tuning feature reduces calibration effort avoiding scenario-specific calibration of the developed functionality. The performance of the EM controller was analysed in simulation for different driving scenarios. Future work shall focus on robustification of the EM algorithm against parametric and signal uncertainity. Furthermore, benchmarking the solution with other QP solution methods, such as interior point methods, might be studied in the future. 162

REFERENCES Beidl, C., Buch, D., Hohenberg, G., Bacher, C., Hammer, J., and Kufferath, D.A. (2012). Effizienter EFahrzeugantrieb mit dem kompakten CEA-Konzept Combustion Engine Assist. Der Antrieb von morgen. Diehl, M., Bock, H., Diedam, H., and Wieber, P.B. (2005). Fast direct multiple shooting algorithms for optimal robot control. Fast Motions in Biomechanics and Robotics. ECOMOVE, C. (2009). eCoMove: Annex i Description of Work of the eCoMove project. Ferreau, H. (2012). qpOASES User’s Manual (Version 3.0 beta). Optimization in Engineering (OPTEC) and Department of Electrical Engineering, KU Leuven. Lee, T.K., Adornato, B., and Filipi, Z. (2011). Synthesis of Real-World Driving Cycles and Their Use for Estimating PHEV Energy Consumption and Charging Opportunities: Case Study for Midwest/U.S. IEEE Transactions on Vehicular Technology. Maurer, M., Gerdes, J.C., Lenz, B., and Winner, H. (2015). Autonomes Fahren : Technische, rechtliche und gesellschaftliche Aspekte. Springer Open. Rawlings, J.B., Angeli, D., and Bates, C.N. (2012). Fundamentals of Economic Model Predictive Control. IEEE Conference on Decision and Control. Sciarretta, A. and Guzzella, L. (2007). Control of Hybrid Electric Vehicles. IEEE Control Systems Magazine. Vadamalu, R. and Beidl, C. (2016). Explicit MPC PHEV Energy Management using Markov Chain based Predictor: Development and Validation at Engine-In-TheLoop testbed. European Control Conference. Vadamalu, R., Buch, D., Xiao, H., and Beidl, C. (2015). Energy management of hybrid electric powertrain using predictive trajectory planning based on direct optimal control. 16th IFAC workshop on Control Applications of Optimization. Wahl, H.G., Holzaepfel, M., and Gauterin, F. (2014). Approximate Dynamic Programing Methods Applied to Far Trajectory Planning in Optimal Control. IEEE Intelligent Vehicles Symposium (IV).