Transient Control of Variable Geometry Turbineon Heavy Duty Diesel Engines

Anders Ekdahl

Abstract— In this paper a closed loop controller for Vari-able Geometry Turbine (VGT) control during transient boostpressure build-up is presented.

The controller is a state feedback controller with boostpressure, exhaust pressure and turbo speed as inputs. Boostpressure and turbo speed are measured states while the exhaustpressure is estimated using an observer. A constant feed-forward term is added to the output signal for optimal workingpoint selection.

The controller has less parameters than the current openloop solution, but still shows comparable performance results.By using a model based approach the tuning is simplified andmade more intuitive.

I. INTRODUCTION

A number of novel technologies have been introduced onheavy duty diesel engines with the advent of more stringentemission level legislations. Today, engines with advanced in-jection control using high injection pressure and multiple fuelinjection pulses, exhaust gas recirculation (EGR) systemstogether with variable geometry turbines (VGT) and variousexhaust gas after-treatment systems are sold on the market.Within a few years the engines are likely to be equipped withnew technologies such as variable valve timing (VVT) andhomogenous charge compression ignition (HCCI).

These new solutions are introduced to reduce emissions,while the possibility to improve the engine dynamic be-haviour is often a secondary target. However, for the endcustomer the driving performance and fuel economy areoften the most significant parameters when selecting a newvehicle, especially on the heavy truck market.

This paper explores the possibility to improve the enginedynamic torque behaviour by using the VGT for efficientboost pressure build-up. The work is based on the modelpreviously presented in [1]. Analysis of this model, whencontrolled by a map-based controller, has been evaluatedin [2] and the experiences from that exercise have influencedthe design choices presented in this paper.

Many authors (see for instance [3] or [4]) have reportedusing boost pressure as an input for VGT control, often inconjunction with air inlet mass flow [5]. Some solutions usethe exhaust manifold pressure also [6], [7], but this pressureis often ignored in the control loop.

In this paper a controller with feedback from boost pres-sure, turbo speed and exhaust manifold pressure is presented.These three states are the predominant states for turboperformance. The reason for including the exhaust manifold

The author is with the Engine Product Development Dept.,Volvo Powertrain Corp., SE-405 08 Goteborg, Sweden. Email:anders.j.ekdahl@volvo.com

Net torqueon crankshaft

Time

Requested torque

Actual torque

Maximize generated energy by minimizing this surface.

Fig. 1. Target function for optimal response.

pressure in the feedback loop is to control pumping losses,which reduces the available torque on the engine crankshaft.

By introducing a measurable criterion for optimal response(see Fig. 1) the total engine performance is evaluated. Thecriterion function corresponds to a maximisation of the totalenergy generated by the engine and transferred into thevehicle. By integrating the difference between demanded andactual crankshaft torque the energy loss is defined (assumingconstant engine speed) as

Θ =∫ tf

t0

(MR(t) − Mcrank(t)) dt (1)

Here t0 is the beginning of the torque request and tf thetime where actual engine crankshaft torque, Mcrank is equalto requested torque, MR. Note that this area is dependingboth on engine hardware, smoke limiting strategies and VGTcontrol strategies.

II. ENGINE MODEL

The engine model used as reference for this work haspreviously been presented in [1]. The model is a mean valuemodel primarily based on steady state data. Steady stateproperties are matched well with the real engine while tran-sient properties deviate somewhat. The transient propertiesare however accurate enough in order to evaluate the controlalgorithms in question.

The model contains six states; inlet manifold pressure andgas mass Pinl, minl, exhaust manifold pressure and gasmass Pexh, mexh, turbo rotational speed ωtbo and EGRtemperature TEGR. Note that the model in [1] does nothave any states in the exhaust manifold volume, but dueto numerical accuracy problems in the turbine mapping the

Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

WA2.5

0-7803-9354-6/05/$20.00 ©2005 IEEE 1228

ωtbo

Mcomp Mturb

ωeng, Mcrank

minl, Vinl

Pinl, Tinl Pexh, Texh

mexh, Vexh

Pcomp, Tcomp

Pamb, Tamb Pturb, Tturb

φVGT

φEGR

TEGR

EGR cooler

Charge air cooler

Fig. 2. Engine with inputs and outputs.

exhaust manifold volume is now modelled in the same wayas the inlet manifold.

Engine speed is often treated as a state in many enginemodels, but is considered to be constant in this model.This approximation is done since the engine normally doesnot accelerate significantly during the short boost pressurebuild-up time, which is up to two seconds for most drivingconditions. The approximation is valid for a fully laden truck(20 to 60 tonnes) driving on a high gear, or going uphill. Thisis equivalent to a very high rotational inertia which reducesthe rotational speed derivative according to

ω =M

J(2)

In order to simplify the model the number of states arereduced to three, Pinl, Pexh and ωtbo, where both Pinl

and ωtbo are assumed to be measured states on the specificengine. The gas mass states in the manifolds are eliminatedby assuming the same temperature on incoming and outgoingmass flows. The EGR temperature state is ignored since theEGR valve is closed during heavy transient fuelling steps,in order to reduce smoke. Hence the EGR gas temperaturedoes not have any impact on the inlet manifold temperature.

The reduced model is described as follows:

Pinl =TambRairγair

Vinl(mcomp − Pinl ˙meng) (3)

Pexh =TexhRexhγexh

Vexh(Pinl ˙mexh − mturb) (4)

ωtbo =1

Jtbo ωtbo

{Cp,exhmturbTexh ×

ηturb(BSR, φV GT )

(1 −

(Pexh

Pamb

) 1−γγ

)

− Cp,airmcompTamb ×(1 −

(Pinl

Pamb

) 1−γγ

)

ηcomp

(fmcomp

(ωtbo,

Pinl

Pamb

), Pinl

Pamb

)}

(5)

where

mcomp = fmcomp

(ωtbo,

Pinl

Pamb

)Pamb√Tamb

(6)

mturb = fmturb

(Pexh

Pamb, φV GT

)Pexh√Texh

(7)

˙meng =Vdωengηv

4πTambRair(8)

˙mexh =Vdωengηv

4πTambRair

1 + AFR

AFR(9)

BSR =ωtbo Dturb

2

√2 TexhCp,exh

(1 −

(Pexh

Pamb

) 1−γγ

) (10)

The notation ˙m indicates massflow factors where the chosenstate variables are omitted, in order to find the relationshipbetween the states.

The turbine is mapped with efficiency ηturb and correctedmass flow, fmturb. The compressor is mapped in a similarway with ηcomp and fmcomp, but with a different set of inputvariables. The engine is characterised using current enginespeed, ωeng and the volumetric efficiency at that speed, ηv.Smoke limiting strategies are represented using air to fuelratio, AFR. Finally, BSR is the blade jet speed ratio andDturb equals the turbine diameter.

The engine crankshaft torque is defined from the chosenstate variables as

Mcrank = Pinl

(A ˙meng

AFR+

Vd

πωengNcyl

)

−PexhVd

πωengNcyl(11)

where A is the total fuel conversion efficiency including thefuel lower heat value and combustion efficiency, Vd is thedisplacement volume and Ncyl equals number of cylindersin the engine.

The reduced model is suitable for controller design sinceall states are possible to measure on a real engine. The modelcan be tuned and verified against measurements for all states.The reduction in number of states makes the model lessaccurate, but the impact is marginal.

III. CONTROL ALGORITHM

A. Controller selection

Following elementary control theory, the first control ap-proach was to use regular linear theories. In order to do

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this, the model was linearised. It was soon found that thelinearised dynamics contained gradients from the turbineand compressor maps that are hard to quantify accurately.Also, the linear model is only valid around a local operatingpoint, since the dynamics change significantly with respectto current operating point. These implications rejected theapproach to use a simplistic linear controller.

More advanced methods such as optimal control path orexact linearisation are difficult, not to say impossible, to usesince the non-linearities are map-based and hard to quantifynumerically with sufficient accuracy.

One feasible solution is to use Model Predictive Control(MPC). This would benefit both from the non-linear modeland deal with the problem of actuator saturation in anintegrated way. However, implementing an MPC controllerwould not be possible using the current control unit’s com-puting power and would mostly be of theoretical interest.There exist some published attempts in the area [8] withgood performance, but the major drawback is found to bethe computing power needed. It is however obvious thatthe expanding computing power in automotive control unitsincreases the interest for MPC (or similar) solutions in anear future, especially for complex control problems such asVGT/EGR control.

Another solution would be to use a Linear ParameterVarying (LPV) model [9], where inlet and exhaust mani-fold pressures are used as scheduling variables. As statedin the referenced paper, many approximations have to bedone. Considering that the presented model is a light-dutyengine with corresponding low manifold pressures theseapproximations become even less valid for a heavy dutyengine. Modifying the presented model, or beginning fromscratch would be time-consuming. Since the theories for LPVare immature this approach is currently not considered asfeasible, altough the area is developing fast.

Studying previously published work [3], [4] [10], [11],regarding VGT control, indicated that a common solutionis to use a map based Pinl demand as input to the VGTcontroller. But controlling Pinl only (often using a PI(D)controller) using the VGT position is quite insensitive sincethe VGT position primarily affects Pexh and not Pinl.

When looking at the exhaust side the connection betweenφV GT and Pexh is more direct. Here a more aggressive con-troller can be chosen without any major stability concerns.Note once again that this is a linearised description of themodel and as such only valid in a local surrounding near thelinearisation point.

The exhaust pressure state is in contemporary papers oftenused for stabilising the EGR flow [6], [7], which means thatthe focus for controlling the exhaust pressure is controllingthe EGR flow and not the turbo response itself. This impliesthat the performance focus is in emission optimisation andnot transient engine performance.

An interesting model-based design has been publishedin [12], but the implementation details are unclear. Here amodel over the engine is used for generating feed-forwardcontrol signals to the EGR and VGT.

Pexh estimatorTexh, mexh

φVGT

Pexh trajectory estimator

Pinl trajectory estimator

ωturb trajectory estimator

ωturb

ωengine

Pinl K φVGT

φVGT

Fig. 3. Controller block diagram

B. State feedback controller

The controller evaluated was a state feedback controllertracking boost pressure, exhaust pressure and turbo speedtrajectories, see Fig. 3. This is an approach similar to [13]in the sense that the optimal control paths can be evaluatedoff-line and in advance on a desktop computer. The resultingcontrol paths are then used as reference input to the actualcontroller.

The trajectories were parameterised as constant slopes inorder to minimize the parameters needed. The dynamics inPinl and ωtbo motivated the addition of a first-order low-pass filter in series with the trajectory generator to enable theaddition of a short time delay before the turbo responds. Thefilter is not used on Pexh since the exhaust manifold pressureis almost immediately changed when the VGT position isvaried.

Pinl,tr (t) = Pinl,d

(t − t0 + tPinl · e−

t−t0tP inl

)+

+Pinl (t0) (12)

Pexh,tr (t) = Pexh,d (t − t0) + Pexh (t0) (13)

ωtbo,tr (t) = ωtbo,d

(t − t0 + tωtbo · e−

t−t0tωtbo

)+

+ωtbo (t0) (14)

In the equations above the subscript tr indicates desiredtrajectory for the three states and the subscript suffix d thedesired increase rate in kPa/s and rad/s2 respectively. Thefilter time constants are tPinl and tωtbo respectively. Thereference trajectories are initialised to the current state valuesat the beginning of the transient step, t0. This makes thecontroller aware of the initial states.

Since the controller only has three inputs and one outputthe control law

u = −Kx, (15)

where K is the state gain matrix, is equivalent with thefollowing control law that defines the VGT position demand,φV GT,dem,

φV GT,dem = φV GT − {k1 (Pinl,tr − Pinl) +k2 (Pexh,tr − Pexh,e) +k3 (ωtbo,tr − ωturb)}, (16)

where φV GT is a constant, time-invariant VGT position forthe specific engine speed.

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2150

200

250

300

350

400

Time [s]

Pex

h [kP

a]

Fig. 4. Pexh with (solid) and without (dash-dot) exhaust pressure feedback

The controller has in total nine parameters that haveto be tuned. The three feedback gains are independent ofengine speed while the five estimated trajectory parameters(Pinl,deriv , Pexh,deriv, ωtbo,deriv, tPinl, tωtbo) and the VGTmid point position (φV GT ) depend on engine speed.

C. Exhaust manifold pressure estimator

In order to be able to control the exhaust manifold pressurean estimator was designed since no actual sensor is mountedon the engine. The estimator is based on rewriting (7) into

Pexh,e =mturb

√Texh

fmturb

(Pexh,e

Pamb, φV GT

) . (17)

Pexh,e can not be explicitly solved in (17) since Pexh,e isneeded for calculating the pressure ratio over the turbine. Inorder to solve this a low pass filter with a short time constant,together with a delay of one calculation tick is added to breakthe algebraic loop. This filtered and delayed pressure is usedas input to the mass flow map, fmturb.

The exhaust gas mass flow (mturb) and exhaust gastemperature (Texh) are estimated outputs from calculationsin the existing engine control unit strategies. It is assumedthat the mass flow generated by the engine is identical withthe mass flow through the turbine. This assumption is true formost working conditions except very short transient intervalswhen Pexh is changed rapidly. For this application the errorintroduced is negligible.

An analysis was performed regarding omission of theexhaust pressure in the feedback loop. The impact of theexhaust pressure is visible in Fig. 4. Here, there are visible ef-fects that the introduced exhaust pressure feedback stabilisesthe pressure significantly. The actuator control signal is alsomore active when the feedback is omitted in the design,which increases wear on the actuator.

D. Controller tuning

The controller has been designed for intuitive and straight-forward tuning. Here, the working order is presented when

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2100

200

300

400State feedback estimated control paths @ espd=1400rpm

Boo

st p

ress

ure

(kP

a)

Modelled boost pressureDesired trajectory

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

4

6

8

10x 10

4

Tur

bo s

peed

(rp

m)

Modelled turbo speedDesired trajectory

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2100

200

300

400

Exh

aust

pre

ssur

e (k

Pa)

Modelled exhaust pressureCalculated exhaust pressureDesired trajectory

Fig. 5. Estimated and modelled state trajectories

tuning the controller using computer simulations. The work-ing order is similar when tuning the algorithm in conjunctionwith a real engine. All optimisation is done using theoptimality criterion in (1) in conjunction with the Matlaboptimiser fminsearch.

1) First the optimal constant VGT position without feed-back is found. This defines φV GT .

2) The three reference trajectories are then tuned to matchthe measured and estimated state trajectories. This isdone manually during the first tuning iteration.

3) Finally, the three gains in K are tuned for optimalresponse.

4) The reference trajectories and the gains are tunediteratively in order to find the optimum setting.

The reason for retuning the reference trajectories is that theresponse (hopefully) improves when the feedback loop isactivated.

During the tuning process it was found that the feedbackgain could be set independent of engine speed. Simulationswere done in the engine speed range of 1000rpm to 2000rpmwith 100rpm steps. Gain for Pinl was set to 1%/kPa, Pexh =0.5%/kPa while ωtbo = 10−3 %/[rad/s].

The optimal reference trajectory constants varied signif-icantly within the engine speed interval. Pinl,d ∈ [30 115]kPa/s, Pexh,d ∈ [20 150] kPa/s, ωtbo,d ∈ [10 45] krad/s2,tPinl ∈ [0.1 0.8]s and tωtbo ∈ [0.1 0.6]s. This motivates theuse of engine speed dependent trajectories.

E. Controller performance, simulated

The controller developed has been tested together with theengine model with good performance. As an example thebehaviour for the controller is presented when the enginerotates at 1400rpm and the torque demand is a step fromzero to maximum torque. During this step the controller isactive in approximately 1.6 seconds, and after that time thesteady state strategies take control over the VGT actuator.

The state trajectories and their estimated control paths areplotted in Fig. 5. As seen in the lowest part of Fig. 5

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−15

−10

−5

0

5

10

15

20State feedback controller output @ espd=1400rpm

Boost pressure contributionTurbo speed contributionExhaust pressure contribution

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 230

35

40

45

50

55

φ VG

T

Fig. 6. VGT position controller output (simulated environment). Individualcontributions (upper) and resulting control signal (lower)

Pexh,e has a significant difference from the modelled Pexh.This is mainly due to differences in exhaust temperature inthe model compared to the estimated temperature from theengine controller algorithms. Note that this temperature isrecognised as quite inaccurate in the model used since itlacks relevant temperature nodes (primarily heat exchangewith the surrounding manifold material). Unfortunately, norelevant exhaust pressure or temperature measurements on areal engine were available at the time of writing.

In Fig. 6 the individual contributions are displayed to-gether with the resulting VGT control signal, φV GT,dem. Thepredominant term is depending on the boost pressure whilethe turbo speed contribution is only minor in amplitude.

F. Controller performance, experimental

The controller has been tested on an engine installed invehicle. The main implications with in-vehicle testing arenon-steady engine speed in conjunction with less sensor data.For instance neither crankshaft torque nor exhaust pressurewere measured on the specific vehicle. Nevertheless, theexperiences drawn during the experiments were valuable forcontinuing work.

The exhaust pressure estimator was evaluated on the en-gine by comparing with the corresponding inlet pressure. InFig. 7 are inlet pressure (measured) and exhaust pressure (es-timated) displayed. Note that the exhaust pressure estimatoris well-behaved and generates reasonable results both duringthe torque step and when reaching steady state. In order toverify the estimator, comparisons with measurements wouldhave to be performed.

The state trajectories and their respective control paths aredisplayed in Fig. 8. Comparing these with the modelled be-haviour in Fig. 5 it is seen that the boost and exhaust pressuretrajectories match quite well, but the measured turbo speeddiffer from the modelled one. The small difference in boostpressure when using the model has almost disappeared whenusing the measured signal. The exhaust pressure follows the

0 5 10 15 20 25 30 35100

150

200

250

300

350

400

450Boost pressureExhaust pressure (estimated)

Time [s]

Pres

sure

[kPa

]

Fig. 7. Boost and exhaust pressure during transients measured duringin-vehicle tests.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2100

200

300

400State feedback control paths @ espd=1330rpm

Boo

st p

ress

ure

(kP

a) Measured boost pressureDesired trajectory

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24

6

8

10x 10

4

Tur

bo s

peed

(rp

m) Measured turbo speed

Desired trajectory

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2200

250

300

350

400

Exh

aust

pre

ssur

e (k

Pa)

Calculated exhaust pressureDesired trajectory

Fig. 8. Estimated and measured state trajectories

desired trajectory quite well except for a small offset, but thesignal is well behaved.

Since the measured signals are noisier than the modelled,the gains have to be reduced in order not to be too noisesensitive. Also, since the boost pressure and exhaust pressuresignals track their respective control trajectories well, thecorresponding control signals are more or less constant, asseen in Fig. 9. The controller is phased out in favour ofsteady state strategies after approximately 1s. The closing ofthe VGT in later phases is therefore not actuated since otherstrategies are in control of the VGT actuator.

Comparing the test results with the modelled ones inFig. 6 both the initial closing and later opening phase havedisappeared. Since both the boost and exhaust pressure arestable, it is hard to estimate how well the controller can dealwith balancing the pressures.

G. Comparison with current map based strategy

In the current VGT control implementation the transientVGT position is controlled using a two-dimensional map

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−15

−10

−5

0

5

10State feedback controller output @ espd=1330rpm

Boost pressure contributionTurbo speed contributionExhaust pressure contribution

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220

25

30

35

40

45

50

φ VG

T

Fig. 9. VGT position controller output. Individual contributions (upper)and resulting control signal (lower)

with engine torque and speed as inputs. The controllerproposed in this paper shows results similar in performancewhen compared with the map based solution. The mainreason for introducing the feedback controller is the reducednumber of parameters and the awareness of the states initialvalues.

IV. CONCLUSIONS AND FUTURE WORK

A. Conclusions

In this paper a state feedback controller for boost pressurebuild-up using VGT control has been presented. Three statesare used for feedback; inlet and outlet manifold pressure,and turbo speed. Inlet pressure and turbo speed are measuredstates while the outlet pressure is estimated using an observerbased on the turbine mass flow maps.

Simulations and initial experimental results show goodresults although there are many unsolved issues. Performanceis comparable with the current, map based implementationwhile the number of parameters are reduced significantlyand also more intuitive and easy to tune. Due to the strongnon-linearities in the turbo system it is difficult to developa complete solution without using complex algorithms suchas MPC or similar.

B. Future work

By letting φV GT be found dynamically, the controllershould be able to improve performance during varying work-ing conditions. One approach is using MPC-like methodsto find the optimal φV GT , as well as the reference statetrajectories. This could be done at a lower sample ratethan the actual state feedback loop in order to reduce thecomputing power needed.

An issue of high importance is the inclusion of othertorque demands than a full step from zero to maximum inone tick. Especially slower ramps have to be analysed andtaken care of in a production-ready solution.

V. ACKNOWLEDGEMENTS

This work was partially financed by the Swedish Agencyfor Innovation Systems, VINNOVA.

The author wishes to thank his supervisors at ChalmersUniversity of Technology, Bo Egardt and Stefan Pettersson.The support and comments from various colleagues at VolvoPowertrain Corp. is also gratefully acknowledged.

NOMENCLATURESymbol Description unitT Temperature [K]P Pressure [kPa]PR Pressure ratio -M Torque [Nm]J Moment of inertia [kg m2]ω Rotational speed [rad/s]m Mass [kg]m Mass flow [kg/s]ρ Density [kg/m3]V Volume [m3]η Efficiency -R Gas constant [J/(kg K)]γ Specific heat ratio -cp Specific heat at constant pressure [J/(kg K)]φ Control signal -t Time [s]

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