Model Predictive Control of a Diesel Engine with Turbo Compound and Exhaust After-Treatment Constraints

5th IFAC Conference on 5th IFAC Conference on Engine Powertrain Simulation and Modeling 5th IFACand Conference onControl, Engine and Powertrain Control, Simulation and online Modeling Available at www.sciencedirect.com Changchun, China, September 2018 and Modeling 5th IFACand Conference onControl,20-22, Engine Powertrain Simulation Changchun, China, September 20-22, 2018 Engine and Powertrain Control,20-22, Simulation Changchun, China, September 2018 and Modeling Changchun, China, September 20-22, 2018

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IFAC PapersOnLine 51-31 (2018) 349–354

Model Predictive Control of a Diesel Model Predictive Control of a Diesel Model Predictive Control of a Diesel Engine with Turbo Compound Exhaust Model Predictive Control ofand a Diesel Engine with Turbo Compound and Exhaust Engine After-Treatment with Turbo Compound and Exhaust Constraints Engine After-Treatment with Turbo Compound and Exhaust Constraints After-Treatment Constraints After-Treatment Constraints J. Dahl ∗∗ , H. Wass´ en ∗∗

J. Dahl en ∗ ∗∗ ∗∗ ∗ , H. Wass´ ∗∗ ∗∗ O. ,, M. Herceg Lansky , D. Pachner ∗∗ J. Dahl , H. Wass´ en,, ∗J. ∗∗ , L. ∗∗ ∗∗ O. Santin Santin ∗∗ M. Herceg , L. Lansky J. Pekar Pekar ∗∗ ∗ ∗∗ ∗∗ ∗∗ ∗∗ , D. Pachner ∗∗ J. Dahl , H. Wass´ e n O. Santin ∗∗ , M. Herceg ∗∗ , L. Lansky ∗∗ , J. Pekar ∗∗ , D. Pachner ∗∗ ∗ Santin O. , M. Herceg , L. Lansky , J. Pekar , D. Pachner ∗ Volvo Group Truck Technology, Goteborg, SE 40508 Sweden (e-mail: ∗ Volvo Group Truck Technology, Goteborg, SE 40508 Sweden (e-mail: Volvo Group Truck Technology, [email protected]). Goteborg, SE 40508 Sweden (e-mail: [email protected], [email protected], [email protected]). ∗∗∗ Volvo Group Truck Technology, Goteborg, SE 40508 Sweden (e-mail: Honeywell, Transportation Systems, Prague, [email protected], [email protected]). ∗∗ Transportation Systems, Prague, 14800 14800 Czech Czech Republic Republic ∗∗ Honeywell, [email protected], [email protected]). (e-mail: [email protected], [email protected], Honeywell, Transportation Systems, Prague, 14800 Czech Republic (e-mail: [email protected], [email protected], ∗∗ Honeywell, Transportation Systems, Prague, 14800 Czech Republic [email protected], [email protected], (e-mail: [email protected], [email protected], [email protected], [email protected], (e-mail: [email protected], [email protected], [email protected]) [email protected], [email protected], [email protected]) [email protected], [email protected], [email protected]) [email protected]) Abstract: In In this this work work we we consider consider air air path path control control of of aa Volvo Volvo Heavy Heavy Duty Duty 13L 13L Diesel Diesel engine engine Abstract: equipped with three air path actuators Exhaust Gas Recirculation Valve (EGV), Intake Throttle Abstract: In this work we consider air path control of a Volvo Heavy Duty 13L Diesel engine actuatorsairExhaust equipped with threework air path Gas Recirculation Valve Duty (EGV), Intake Throttle Abstract: Inturbocharger this weWastegate consider path and control of a Compound Volvo Heavy 13L Diesel engine Valve (ITV), (ITV), (WG), a Turbo Turbo (TC). The purpose of the the equipped with three air path actuators(WG), Exhaust Gas Recirculation Valve (EGV), Intake Throttle Valve turbocharger Wastegate and a Compound (TC). The purpose of equipped with three air path actuators Exhaust Gas Recirculation Valve (EGV), Intake Throttle Valve (ITV), turbocharger Wastegate (WG), and a Turbo Compound (TC). The purpose of the TC device is to recover the waste heat energy to improve fuel efficiency. Thus, the motivation TC device is turbocharger to recover theWastegate waste heat(WG), energy to aimprove fuel efficiency. Thus, motivation Valve (ITV), and Turbo Compound (TC). The the purpose of the is to todevice control the air path path system and inenergy particular the exhaust exhaust energy toThus, achieve satisfaction TC is the to recover thesystem waste and heatin to improve fuel efficiency. the motivation is control air particular the energy to achieve satisfaction TC device is the toAfter-Treatment recover thesystem waste heatinenergy torequirements improve fuel and efficiency. Thus, the motivation of the Exhaust System (EATS) assess the fuel economy. For is to control air path and particular the exhaust energy to achieve satisfaction of thecontrol Exhaust After-Treatment System requirements and assesstotheachieve fuel economy. For is to the air path system and industrial in(EATS) particular the exhaust energy satisfaction this purpose a commercially available tool for Model Predictive Control (MPC) has of the Exhaust After-Treatment System (EATS) requirements and assess the fuel economy. For this purpose a commercially available tool for Modeland Predictive Control (MPC) For has of the Exhaust After-Treatment Systemindustrial (EATS) requirements assess the fuel economy. this purpose aThe commercially available industrial toolinfor Model Predictive Control (MPC) has been applied. designed controller is integrated a production Engine Electrical Control been applied.aThe designed controller is integrated a Model production EngineControl Electrical Control this commercially available both industrial toolin for (MPC) has Unitpurpose (EECU) and tests are performed performed in engine engine test bench Predictive and on-road. on-road. The results results show been applied. and The designed controller is integrated intest a production Engine Electrical Control Unit (EECU) tests are both in bench and The show been applied. The designed controller is integrated in a production Engine Electrical Control that by coordination of the air path actuators utilizing advanced MPC framework it leads to Unit (EECU) and tests are performed both in engine test bench and on-road. The results show that by coordination of are theperformed air path actuators utilizing advanced MPC framework it leads to Unit (EECU) and tests both in engine test bench and on-road. The results show improvements in the exhaust energy conversion which was measured by fuel reduction of 0.3% that by coordination of the air path actuators utilizing advanced MPC framework it leads to improvements in the exhaust energy conversion which was measured by fuel reduction of 0.3% that coordination oflevels the air path actuators utilizing advanced MPC framework it leads to improvements in NO the xexhaust energy conversion whichTransient was measured by fuel reduction of 0.3% with by maintained in a World-Harmonized Cycle (WHTC) compared to levels in a World-Harmonized Transient Cycle (WHTC) compared to aa with maintained NO x improvements in NO the xexhaust energy conversion whichTransient was measured by fuel controller reduction of 0.3% Proportional Integral Derivative (PID) control scheme. The designed MPC reached levels in a World-Harmonized Cycle (WHTC) compared to a with maintained Proportional Integral control scheme. The designed MPC controller reached levels in and a (PID) World-Harmonized Transient Cycle (WHTC) compared to a with maintained NOx Derivative mass production maturity level had a similar margin to the EU6 emission regulation as the Proportional Integral Derivative (PID) control scheme. The designed MPC controller reached mass production maturity level and had control a similarscheme. marginThe to the EU6 emission regulationreached as the Proportional Integral Derivative (PID) designed MPC controller compared PID scheme. mass production maturity level and had a similar margin to the EU6 emission regulation as the compared PID control control scheme. mass production maturity level and had a similar margin to the EU6 emission regulation as the compared PID control scheme. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. compared PID control scheme. Keywords: Diesel Diesel engines; engines; Engine Engine control; control; Model Model Predictive Predictive Control; Control; Air-path; Air-path; Aftertreatment Aftertreatment Keywords: Keywords: Diesel engines; Engine control; Model Predictive Control; Air-path; Aftertreatment Keywords: Diesel engines; Engine control; Model Predictive Control; Air-path; Aftertreatment 1. INTRODUCTION INTRODUCTION The calibration calibration of of the the control control strategies strategies of of this this kind kind of of 1. The 1. INTRODUCTION The calibration of the coupled control strategies ofcould this be kind of systems with multiple actuators very systems with multiple actuators ofcould very 1. INTRODUCTION The ofwhen the coupled control strategies this be kind of systems with multiple coupled actuators approaches could be very time calibration consuming using traditional traditional as time consuming when using approaches as systems with multiple coupled actuators could be very Design and control of diesel engines and Exhaust Aftertime consuming when using traditional approaches as open-loop or multiple single-input single-output control Design and control of diesel engines and Exhaust After- open-loop or multiple single-input single-output control time when single-input using traditional approaches as Design and System control (EATS) of diesel have engines and Exhaust After- open-loop Treatment become more difficult difficult single-output control loops. consuming Thisorhas hasmultiple motivated to increased increased MPC applications Treatment System have become more loops. This motivated to MPC applications Design and control (EATS) of of diesel engines and Exhaust Afteropen-loop orhasmultiple single-input single-output control Treatment System (EATS) have become more difficult with the introduction stricter regulations, resulting in loops. This motivated to increased MPC applications in the automotive (Borrelli et al. (2010), Pekar et al. with the introduction of stricter regulations, resulting in in the automotive (Borrelli et al. (2010), Pekar et al. Treatment System hardware (EATS) have becomethat more difficult loops. has et motivated toSantin increased MPC applications with introduction of stricter regulations, resulting in in need the for increased increased complexity adds more the This automotive et al. et(2010), Pekar et al. (2012), Khaled al.(Borrelli (2014), al. (2016)) where it need for hardware complexity that resulting adds more Khaled et al. (2014), Santin et(2010), al. (2016)) where it with the introduction of stricter regulations, in (2012), in the automotive (Borrelli et al.suited Pekar etwith al. need forofincreased hardwareforcomplexity that adds more degrees freedom available control. On the engine side (2012), Khaled et al. (2014), Santin et al. (2016)) where it has been shown that MPC is well for dealing degrees of freedom available for control. On the engine side beenKhaled shownetthat MPC isSantin well suited for dealing with need forofGas increased hardware adds more (2012), al. (2014), etinherently al. (2016)) where it degrees freedom available forcomplexity control. Onthat the engine side Exhaust Recirculation (EGR) is traditionally traditionally used to has has been shown that MPC is well it suited for dealing with multivariable actuation because supports Exhaust Recirculation (EGR) is used to actuation because it inherently supports degrees ofGas freedom available for control. On the engine has been shown that MPC is well suited for dealing with Exhaust Gas Recirculation (EGR) isTypical traditionally usedside to multivariable reduce the engine NOx emissions. configuration multivariable actuation because it inherently supports constraints and the control goals can be transformed reduce the engine NOx emissions. configuration and the control goalsit can be transformed Exhaust Gas Recirculation (EGR) isTypical traditionally used to constraints multivariable actuation inherently supports reduce the engine emissions. Typical configuration of EATS EATS consists ofNOx Diesel Oxidation Catalyst (DOC), constraints and the control can befunction. transformed into particular particular terms of because MPCgoals objectives This of consists of aa Diesel Oxidation Catalyst (DOC), into terms of MPC objectives This reduce the engine NOx emissions. Typical configuration constraints andintuitive the control goals can befunction. transformed of EATS Particulate consists of aFilter Diesel(DPF), Oxidation Catalyst (DOC), a Diesel and a Selective Catinto particular terms of MPC objectives function. This then offers an way of calibration based on the aof Diesel Particulate Filter (DPF), and a Selective Catthen offers an intuitive of objectives calibrationfunction. based onThis the EATS consists (SCR). of aFilter Diesel Oxidation (DOC), into particular terms of way MPC aalytic Diesel Particulate (DPF), and Catalyst aand Selective CatReduction The DPF traps oxidize the then offers an intuitive way of calibration based on the importance of the goals. alytic Reduction (SCR). The DPF traps oxidizeCatthe importance of the goals. aParticulate Diesel Particulate Filter (DPF), and aand Selective then offers an intuitive alytic Reduction (SCR). The DPF and oxidize Matter (PM). The NOxtraps conversion occursthe in importance of the goals. way of calibration based on the Particulate Matter (PM). The NOx conversion occurs in To achieve achieve optimal optimal management of of the the EATS EATS and and waste waste alytic Reduction (SCR). DPF traps and oxidize the importance of the goals. Particulate Matter (PM).The The NOx conversion occurs in To the SCR, where an injected urea water solution is used as management the SCR, where an injected ureaNOx water solution is used as To achieve optimal management of the EATS and waste heat recovery, it is of interest to maintain exhaust temParticulate Matter (PM). The conversion occurs in the SCR,agent. whereToanfulfill injected urea regulation water solution is used as heat recovery, it is of interest to maintain exhaust temreactive the NOx NOx it is is important important reactive agent. Toanfulfill the regulation it To achieve optimal management ofmaintain the EATS and below waste heat recovery, it is of interest to exhaust temperature above certain minimum limit and NOx the SCR, where injected urea water solution is used as reactive fulfill the NOx regulation high it is important that the theagent. SCR To temperature is sufficiently sufficiently and that that perature above certain minimum limit and NOx below that SCR temperature is high and heat recovery, itcertain is of interest to maintain exhaust temabove minimum limit NOx below maximum limit. These constraints have and been considered reactive To fulfill the NOx regulation it is important that theagent. SCR temperature is sufficiently high and that the input NOx level is not too high. The requirement of perature maximum limit. These constraints have been considered the input NOx level is not too high. The requirement of perature above certain minimum limit and NOx below maximum limit. These constraints have been considered in Stewart and Borrelli (2008); Karlsson et al. (2010); that the SCR temperature is sufficient sufficiently high and that the input NOxEATS, level isneeding not too high. The requirement of in Stewart and Borrelli (2008); Karlsson et al. (2010); highly efficient high temperature, highly efficient EATS, high temperature, maximum These have us been considered Stewart and Borrelli (2008); Karlsson et al. (2010); Zhao et al. al. limit. (2014) whichconstraints have motivated towards MPC the input NOx level isneeding not toosufficient high. The requirement of in highly efficient EATS, needing sufficient high temperature, have driven the engine hardware to also include devices to Zhao et (2014) which have motivated us towards MPC have driven the engine hardware to also include devices to in Stewart and Borrelli (2008); Karlsson et al. (2010); Zhao et al. (2014) which have motivated us towards MPC application. In particular, the work in this article is aa highly efficient EATS, needing sufficient high temperature, have driven the engine hardware to also include devices to maintain EATS EATS heat heat such such as as Intake Intake Throttle Throttle Valve Valve (ITV) (ITV) application. In particular, the work in this article is maintain Zhao et al. (2014) which have motivated towards MPC In particular, the work in us this articleand is isa step towards optimal engine and EATS operation have driven the(WG) engine hardware to also include devices to application. maintain EATS heat such as to Intake Throttle Valve (ITV) and Wastegate leading fuel economy losses caused step towards In optimal enginethe andwork EATS operation and and Wastegate (WG) leading to fuel economy losses caused application. particular, in this is is towards optimal and EATS isa a continuation continuation of the engine work presented presented in operation Gelsoarticle andand Dahl maintain EATSused heattosuch asup Intake ThrottleAs Valve (ITV) and Wastegate (WG) leading to fuel losses caused by the the energy heat the economy EATS. a mean mean of step astep of the work in Gelso and Dahl by energy used to heat up the EATS. As a of towards optimal engine and EATS operation and is a continuation of the work presented in Gelso and Dahl (2016); E. and J. (2017). The differences comparing to and Wastegate (WG) leading to fuel economy losses caused by the energy to heat up the EATS. a recovery mean of (2016); E. and J. (2017). The differences comparing to improving fuel used consumption different waste As heat improving fuel consumption different waste heat recovery a continuation of the work presented in Gelso and Dahl andis:J. (2017). The differences comparing to previousE. work by the energy used to heat up the EATS. As aattention mean of (2016); improving fuel consumption different waste heat recovery systems, e.g. Turbo Compound (TC), are gaining previous work systems, e.g. Turbo Compound (TC), are gaining (2016); E. andis: work is:J. (2017). The differences comparing to improving fuel consumption different waste heatattention recovery previous systems, e.g. Turbo Compound (TC), are gaining attention (Payri et al., 2015). (Payri ete.g. al., Turbo 2015).Compound (TC), are gaining attention previous work is: systems, (Payri et al., 2015). (Payri et©al., 2015). 2405-8963 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Copyright © 2018 IFAC 382 Copyright 2018 responsibility IFAC 382Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 382 10.1016/j.ifacol.2018.10.072 Copyright © 2018 IFAC 382

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J. Dahl et al. / IFAC PapersOnLine 51-31 (2018) 349–354

• New engine setup that features WG and TC unit for waste heat recovery. • The control objectives of the previous work is extended by adding constraint on engine out NOx. • Modeling, MPC design, and integration in EECU is based on industrial commercial tool Honeywell’s OnRAMP Design Suite, Honeywell (2018).

estimate of CO2 in the inlet manifold gas, and expressed as a dry mole fraction.

Furthermore, the designed controller has been experimentally tested in a engine test bench as well as on-road including live traffic.

• Tracking of BGF setpoint. This is a mean to control the engine out NOx and as the NOx and PM is related to each other it also controlling the PM level. • Air-Fuel Ratio (AFR) should be above a soft limit. This is a mean to avoid excessive smoke and to improve the response time when driver press on the pedal (demands an increase of engine power). • N Ox should be below a soft limit. This is a mean to secure emission fulfillment. The limit changes based on the NOx levels the EATS currently can convert. • Texh should be above a fixed soft limit. This is a mean to achieve required EATS temperature for high NOx conversion efficiency. • Nturb should be below a soft limit. This is a mean to prevent the turbine from over speeding which may cause mechanical breakdown. • Penalization of actuator positions from preferred feedforward actuator position. This is a mean to adjust the impact of feedforward and feedback control actions. • Actuators rate of change is penalized to prolong actuators life and eliminate fast changes which might have impact to drivability.

The engine description and the objectives are presented in Section 2. The modeling part is revealed in Section 3. The formulation of the control problem is given in Section 4. Section 5 describes the experimental results obtained at an engine test bench and on-road in truck. Finally, the conclusions of the article are discussed in Section 6. 2. ENGINE DESCRIPTION In this paper, we consider the air-path control problem of a Volvo 13L heavy duty Diesel engine (Fig. 1) where the following actuators are controlled; EGV, WG and ITV. The engine has a fixed geometry turbo, TC, Charge Air Cooler (CAC) and EGR cooler. Available sensors are inlet manifold pressure (Pim ), inlet manifold temperature (Tim ), exhaust manifold pressure (Pem ), engine speed (Neng ), turbo wheel speed (Nturb ), AFR, exhaust NOx (N Ox ) and exhaust temperature (Texh ). The engine out NOx sensor measures both AFR and NOx and is mounted after the DPF in the EATS, hence there is transportation delay of the sensor measurement. The engine exhaust temperature sensor is mounted on the intake of the EATS. The engine system has no dedicated sensor for measuring EGR flow or air flow. Instead the EGR flow is estimated by a virtual sensor using sensor fusion of three different models using above listed available engine sensors, Dahl et al. (2018). There is no EGV or WG position sensor, hence it is assumed that these actuators are at the demanded positions.

2.1 Control objectives The overall control objectives are considered as follows:

3. ENGINE MODELING The grey-box, control oriented, mean-value model has been developed in OnRAMP Design Suite (Honeywell, 2018) using the first principles combined with the empirical model parts for NOx emissions. Both steady-state and transient experimental data, collected within 2 days, have been processed and the engine parameters were identified using a process as suggested in (Pachner et al., 2012) formulating the identification as nonlinear optimization problem. To allow identification of individual physical components (e.g. EGV), the engine has been instrumented with additional sensors during data collection on test cell. In particular the Venturi tube based measurement of EGR mass flow and pressure and temperature sensors upstream and downstream the compressor and turbines. To model the TC connected to the camshaft we neglect the dynamics of interconnection, hence we assume that the wheel speed is related to the engine speed with a fixed ratio. Achieved steady-state fit of the model against the measured data sets (marked by different color) depicted in Fig 2. It shows that the model represents the engine in a wide range of operating conditions with accuracy of > 95% for the critical model outputs used by the controller.

Fig. 1. Schematic of the engine In this work Burned Gas Fraction (BGF) is selected as a control objective due to its strong relationship to NOx emissions, Heywood (1988). The BGF is determined by an 383

Formally, the fitted mean value model of the air path for the engine can be written in state space form ˙ x(t) = f (x(t), u(t), d(t)) (1a) y(t) = g(x(t), u(t), d(t)) (1b) that express the relation between the model inputs u(t) ∈ Rnu , measured disturbances d(t) ∈ Rnd , model states

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351

temperature to SCR in order to maintain its high NOx conversion efficiency. Table 1. Operating points definition. Name Neng τind

Unit rpm Nm

Values 600 200

800 400

1000 900

1400 1400

2000

4.2 Problem Formulation

Fig. 2. Resulted steady-state model fit. x(t) ∈ Rnx , and the model outputs y(t) ∈ Rny via the continuous mapping functions f (·), g(·) in time domain t. Based on the control problem formulation defined in Section 2, the model inputs are u(t) = [EGV(t), WG(t), ITV(t)], d(t) = [Neng (t), τind (t)] and y(t) = [Texh (t), BGF(t), AFR(t), N Ox(t), Nturb (t)] where τind is indicated torque [Nm]. 4. CONTROL PROBLEM The nonlinearities arising in the plant are handled via scheduling approach where the scheduling variables are selected by the user. According to many authors Del Re et al. (2010), the injection quantity and the engine speed are preferred scheduled variables for air path control of diesel engines. Therefore the indicated torque τind is transformed into demand of fueling inside the model for the purposes of controller scheduling.

For the purpose of control design, the set of local linear models of (1) is discretized in time using the zero order hold with the sample time Ts = 20 ms. To achieve offsetfree tracking, the models are augmented with the step type of additive disturbance state w ∈ Rny affecting the outputs. That is utilized to capture the difference between the piecewise affine approximation and the nonlinear model (1). The additive disturbance states w are estimated by the linear Kalman filter using Unknown Input Observer technology as described in Fattouh et al. (1999). The model used for MPC design (Stewart and Borrelli, 2008) is at time step k given as xk+1 = Ad,i xk +B d,i uk +E d,i dk +E w,i wk +f d,i (2a) (2b) wk+1 = wk (2c) dk+1 = dk y k = C d,i xk +D d,i uk +F d,i dk +wk +g d,i (2d) OP is a polyhewhere i ∈ 1, . . . , nOP , dk ∈ Ri and {Ri }ni=1 dral partition of the scheduled disturbance space. The matrices Ad,i , B d,i , E d,i , C d,i , D d,i , F d,i are the discretetime equivalents of the local linearization matrices of (1). The terms f d,i , and g d,i contain the linearization equilibria after some algebraic manipulation from local linearization matrices of (1).

The constrained finite time optimal control problem representing the control objectives from Section 2 is defined as follows np −1 1  J(y k , y ref,k , uref,k , , ∆uk ) (3a) min u0 ,...,unp −1 , 2 k=0

4.1 Model Linearization and Scheduling

s.t.:

The scheduling domain was divided into a set of operating points where the model (1) is approximated by local linear models around corresponding stable equilibria as done in Stewart and Borrelli (2008). At each operating point local linear MPC and Kalman filter have been setup. The bump-less switching between the controllers is achieved by the parallel run of all the local Kalman filters so that their internal state is being initialized and further by penalization of the rate of change of the actuators in the MPC cost function. It was selected nOP = 20 operating points defined as a rectangular grid of engine speed and indicated torque as shown in Table 1. The steady state equilibria for the inputs, states, and outputs have been determined in the tool using the setpoint optimization with the objective to maximize engine torque, minimize fuel consumption and NOx emission, meet the actuator constraints, and maximum turbo speed limit. The resulted steady state input equilibria leads to fully open ITV and fully closed WG. This setup is possible as MPC offers automatic way of handling the minimum exhaust 384

(2) (3b) (3c) u ≤ uk ≤ u (3d) y −  ≤ yk ≤ y +  ∆uk = uk − uk−1 (3e) x0 = x(t) (3f) u0 = u(t), u−1 = u(t − Ts ), d0 = d(t) (3g) where np is the prediction horizon, u, u denotes the lower, upper limits for u, y, y are the lower, upper limits for y,  is the vector of slack variables to enforce output constraints. The reference signals y ref , uref and the scheduled and the unmeasured disturbances d, w are assumed to be constant over the prediction horizon. The cost function J(y k , y ref,k , uref,k , , ∆uk ) in (3a) is given by J = (y k − y ref,k )T Qy (y k − y ref,k ) + T Q +

∆uTk R∆u ∆uk + (uk − uref,k )T Ru (uk − uref,k ) (4) where R∆u  0, Ru  0, Qy  0, Q  0 and the vector of slack variables  is introduced to deal with output constraints (3d) via quadratic penalty function.

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The reference trajectories y ref and actuator feedforward values uref are determined by linear interpolation of the setpoint lookup tables defined by the scheduled variables d.

BGF (%)

14 y ref y

13 12 1640

1645

1650

1655

1660

1665

1670

1675

1680

The controller was integrated in a production EECU and results were gathered in both engine test bench and in a truck on road. The Combined Gradient/Newton Projection algorithm introduced in Santin et al. (2016) has been used as a Quadratic Programming (QP) solver for problem with 16 optimization variables. The engine test bench measurements were collected from a WHTC, whereas the truck measurements were from an In-Service Conformity (ISC) cycle run in cold ambient conditions. The achieved MPC controller performance reached mass production level maturity and several benefits over the production PID strategy have been observed as described below. In the followings, several interesting parts are examined in details to show the overall controller performance. To save space, the actuators that stay at their constant preferred positions during the showed experiments are not plotted in the following figures.

u

0 1640

1645

1650

1655

1660

1665

1670

1675

1680

(Nm / rpm)

3000 τind

2000

Neng

1000 0 1640

1645

1650

1655

1660

1665

1670

1675

1680

Time (s)

Fig. 3. BGF tracking in engine test bench. BGF (%)

10 y ref

8

y

6 6700

6710

6720

6730

6740

6750

6760

6770

6780

6790

6800

EGV (%)

100 u ref u

50 0 6700

6710

6720

6730

6740

6750

6760

6770

6780

6790

6800

(Nm / rpm)

3000 τind

2000

Neng

1000 0 6700

6710

6720

6730

6740

6750

6760

6770

6780

6790

6800

Time (s)

Fig. 4. BGF tracking in truck. in steady state and Fig. 4 in transient situations. The BGF tracking is achieved primarily by EGV actuator and therefore other actuators are not shown because they stay close to their preferred positions. The larger tracking errors seen (Fig. 4 at 6715 s and 6755 s) are caused by constraints prioritization over the tracking objective. This is explained in the next section. 5.2 Air-Fuel Ratio Constraint 50 y min

AFR (-)

5. EXPERIMENTAL RESULTS

u ref

50

y

0 1382

1382.5

1383

1383.5

1384

1384.5

1385

1385.5

1386

1386.5

1387

20

BGF (%)

The tuning of the MPC was done in a frequency domain to define the controller bandwidth while fulfilling the robustness stability and performance criterion individually for particular operating point region. This has been done via shaping of the control sensitivity function of the local MPC controller related to unconstrained case of the explicit solution (i.e. region CR0 ) via multiplicative factor of R∆u . The controller robust stability has been achieved by the small gain theorem during the design assuming a defined level of unstructured model output uncertainty. The recursive feasibility of the MPC problem solution is guaranteed by consideration of output constraints as soft and existence of only bound constraints on the actuators. The frequency bandwidth of the controller was set as decreasing function of τind from 1-0.4 Hz to slow down BGF tracking on higher τind to prevent unwanted large reaction of EGV to disturbances. Further, as there are three actuators (EGV, ITV, WG) but only one setpoint (BGF) the control problem is regularized by attracting WG and ITV to their feedforward values. The associated weights RuW G and RuIT V were selected relatively low compared to weight QT , while RuIT V > RuW G to allow exh opening of WG with the slower closing ITV in case of too low Texh to maintain high SCR conversion efficiency. For τind < 300 Nm, the EGV is attracted to feedforward value as the inaccuracy of BGF increases for low flows. The prediction horizon was selected to 3 s to allow controller to see the main plant dynamics and part of dynamic response of Texh .

y ref

10 0 1382

y

1382.5

1383

1383.5

1384

1384.5

1385

1385.5

1386

1386.5

1387

100

EGV (%)

4.3 Tuning Details

EGV (%)

100

u ref

50 0 1382

u

1382.5

1383

1383.5

1384

1384.5

1385

1385.5

1386

1386.5

1387

(Nm / rpm)

4000

5.1 Burned Gas Fraction Tracking The results show tracking performance of BGF setpoint in Figs. 3 and 4. Note that BGF is affected by a noise especially in low engine speed area due to the low delta pressure over the EGV. Fig. 3 depicts tracking of BGF 385

τind

2000 0 1382

Neng

1382.5

1383

1383.5

1384

1384.5

1385

1385.5

1386

1386.5

Time (s)

Fig. 5. AFR constraint control in engine test bench.

1387

IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018

J. Dahl et al. / IFAC PapersOnLine 51-31 (2018) 349–354

that the maximum limit on the NOx contraint is satisfied, and the small limit violations are the result of NOx constraint softening.

50 y min

AFR (-)

353

y

0 5410

5412

5414

5416

5418

5420

5422

5.4 Exhaust Temperature Constraint

BGF (%)

50 y ref y

Texh (°C)

400

0 5410

5412

5414

5416

5418

5420

5422

EGV (%)

100

1050

u

5412

5414

5416

5418

5420

5422

2000

1150

1200

1250

1300

1350

1400

1450

1500 y ref

20

y

10 0 1050

τind

1000

Neng

EGV (%)

5410

5412

5414

5416

5418

5420

5422

Time (s)

1200

1250

1300

1350

1400

1450

1500 u ref

50

u

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

5.3 NOx Flow Constraint

u ref

50

u

0 1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

ITV (%)

100 u ref

50

u

0 1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

4000

(Nm / rpm)

The AFR constraint has the most preference over other constraints, in order to achieve fast dynamical response from the engine. This is visible in Fig. 6 around 5410 s where fast acceleration of the engine is demanded. Sudden increase in torque causes AFR constraint to become active which leads to closing EGV. The BGF setpoint is no longer tracked because of AFR limit is active. After 5412 s, when the AFR limit is not active, the BGF is tracked again.

WG (%)

100

The controller is quickly responding to any decrease in AFR by closing EGV (Figs. 5 and 6). AFR level is kept at a minimum due to a smoke limiter, handled externally to the MPC controller, which is actively limiting the maximum injection quantity based on measured air flow.

τind

2000

Neng

0 1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Time (s)

Fig. 8. Texh constraint control in engine test bench. Texh (°C)

250

0.4

NOx (g/s)

1150

0

Fig. 6. AFR constraint control in truck.

y max

0.2

y min

200 150 5200

y

y

5250

5300

5350

5400

5450

5500

684

685

686

687

688

689

690

691

BGF (%)

30

0 683

692

y

y ref

20

y

10 0 5200

y ref

10

5250

5300

5350

5400

5450

5500

0 683

684

685

686

687

688

689

690

691

692

100

EGV (%)

100

u ref

50

u ref

50 0 5200

u

u

5250

5300

5350

5400

5450

5500

100

0 683

684

685

686

687

688

689

690

691

692

3000

WG (%)

BGF (%)

20

EGV (%)

1100

100

0

1000 683

Neng

684

685

686

687

688

689

690

691

u ref

50 0 5200

τind

2000

u

5250

5300

5350

5400

5450

5500

100

692

ITV (%)

(Nm / rpm)

1100

30

BGF (%)

5410

y

0

u ref

50 0

(Nm / rpm)

y min

200

Time (s)

u ref

50 0 5200

Fig. 7. NOx constraint control in engine test bench.

u

5250

5300

5350

5400

5450

5500

The NOx flow constraint is important for eliminating the peaks in the NOx flow generation. One of such peaks is shown in Fig. 7 for torque demand above 2500 Nm. The NOx flow constraint takes preference over BGF tracking but is less important than AFR constraint. Fig. 7 shows 386

(Nm / rpm)

4000 τind

2000 0 5200

Neng

5250

5300

5350

5400

Time (s)

Fig. 9. Texh constraint control in truck.

5450

5500

IFAC E-CoSM 2018 354 Changchun, China, September 20-22, 2018

J. Dahl et al. / IFAC PapersOnLine 51-31 (2018) 349–354

Handling of exhaust temperature minimum limit of 200◦ C is visible in Fig. 8. The controller responds to the Texh constraint by opening the WG and closing the ITV, thus narrowing the air flow for low load conditions and increasing the energy coming to EATS. Activation of the exhaust temperature constraint has a consequence that the BGF setpoint is not tracked because waste heat energy management has a higher priority. The experimental data from the truck shown in Fig. 9 show that WG and ITV react immediately when the exhaust temperature limit is reached, which is visible in between 5350-5415 s. In this interval the BGF setpoint is not tracked. It may happen at lower torque/injection quantity region, that the requested exhaust temperature for the EATS may not be achieved. This can be mitigated by adjusting the exhaust temperature constraint with margins to the desired EATS temperature. For instance, note in Fig. 9 that the minimum exhaust temperature limit is varying. 5.5 Comparison to a baseline PID control scheme The designed MPC controller was compared with a baseline which consisted of a traditional PID control scheme that used several engine modes. The Brake Specific Fuel Consumption (BSFC) was decreased by 0.3% with the same engine out NOx (Table 2) by a better thermal management of EATS via WG and ITV control to satisfy the Texh limit. Both the MPC and the baseline PID scheme fulfilled, with similar margin, the EU6 WHTC emission regulation levels. It was also noted that the MPC resulted in lower fuel consumption variation between different driving cycles, compared to the baseline PID control scheme. It is expected that the proposed controller will reduce the calibration time compared to traditional designed PID control scheme. Table 2. Changes relative to baseline PID on WHTC. BSFC -0.3%

BSTC -0.2%

NOx 0.0%

PM -11%

avg Texh -3.4%

6. CONCLUSIONS An MPC controller for the engine air path system, with EATS inlet NOx and temperature explicitly constrained, have been designed. The controller have been integrated in a production EECU and verified in both test bench and onroad in a Volvo truck. Results from WHTC in test bench and ISC on-road shows that the controller is able to track the demanded BGF setpoint and control towards fulfillment of the soft constraints. The designed MPC reached mass production maturity level and further decreased the fuel consumption with 0.3% compared a baseline PID control scheme, where both controllers fulfilled the emission regulation with similar margin. In future, the work can be expanded to also include fuel injection system and EATS control, current and historical emissions, and using preview information (e.g. GPS and map data). A way of handling this complex problem could be to separate the problem into two levels, where an MPC on top level acts as a supervisor for the engine and EATS and generates the demands and constraints for the controllers on engine and EATS level. 387

REFERENCES Borrelli, F., Baoti´c, M., Pekar, J., and Stewart, G. (2010). On the computation of linear model predictive control laws. Automatica, 46(6), 1035–1041. Dahl, J., Wassen, H., Idelchi, A., Lubomir, B., Pachner, D., Santin, O., Herceg, M., and Lansky, L. (2018). RealTime EGR and Air Flows Estimation for Heavy-Duty Engine. In Symposium for Combustion Control. Del Re, L., Allg¨ower, F., Glielmo, L., Guardiola, C., and Kolmanovsky, I. (2010). Automotive model predictive control: models, methods and applications, volume 402. Springer. E., G. and J., D. (2017). Diesel engine control with exhaust aftertreatment constraints. In 20th IFAC World Congress, 8921–8926. Elsevier. Fattouh, A., Sename, O., and Dion, J.M. (1999). An unknown input observer design for linear time-delay systems. In Proceedings of the 38th IEEE Conference on Decision and Control, volume 4, 4222–4227 vol.4. Gelso, E.R. and Dahl, J. (2016). Air-path control of a heavy-duty egr-vgt diesel engine. IFAC-PapersOnLine, 49(11), 589 – 595. 8th IFAC Symposium on Advances in Automotive Control AAC 2016. Heywood, J. (1988). Internal combustion engine fundamentals. Mcgraw-Hill, New York. Honeywell (2018). OnRAMP Design Suite. http://www.honeywellonramp.com/. Karlsson, M., Ekholm, K., Strandh, P., Johansson, R., and Tunest˚ al, P. (2010). Multiple-input multiple-output model predictive control of a diesel engine. IFAC Proceedings Volumes, 43(7), 131 – 136. 6th IFAC Symposium on Advances in Automotive Control. Khaled, N., M., C., Pekar, J., Fuxman, A., and Santin, O. (2014). Multivariable control of dual loop egr diesel engine with a variable geometry turbo. SAE Technical Paper 2014-01-1357. Pachner, D., Germann, D., and Stewart, G. (2012). Identification Techniques for Control Oriented Models of Internal Combustion Engines, 257–282. Springer, London. Payri, F., Luj´an, J., Guardiola, C., and Pla, B. (2015). A challenging future for the ic engine: New technologies and the control role. Oil & Gas Science and Technology - Rev. IFP Energies nouvelles, 70(1), 15–30. Pekar, J., Garimella, P., Germann, D., and Stewart, G.E. (2012). Experimental results for sensor selection and multivariable controller design for a heavy-duty diesel engine. IFAC Proceedings Volumes, 45(30), 122 – 129. Santin, O., Pekar, J., Beran, J., D´Amato, A., Ozatay, E., Michelini, J., Szwabowski, S., and D., F. (2016). Cruise Controller with Fuel Optimization Based on Adaptive Nonlinear Predictive Control. SAE Int. J. Passeng. Cars Electron. Electr. Syst., 9(2), 262–274. Stewart, G. and Borrelli, F. (2008). A model predictive control framework for industrial turbodiesel engine control. 47th IEEE Conference on Decision and Control, 5704–5711. Zhao, D., Liu, C., Stobart, R., Deng, J., Winward, E., and Dong, G. (2014). An explicit model predictive control framework for turbocharged diesel engines. IEEE Transactions on Industrial Electronics, 61(7), 3540–3552.