Identification of a Turbo-Charged Diesel Engine†

CONTROL OF CARS AND ENGINES

IDENTIFICATION OF A TURBO-CHARGED DIESEL ENGINE P. E. Wellstead*, C. Thiruarooran** and D. E. Winterbone** ·Control Systems Centre, University of Manchester Institute of Science and Technology, Manchester M60 1 QD, U. K. ··Department of Mechanical Engineering, UMIST, Manchester M60 1 QD, U.K .

Abstract. The techniques of system identification are applied in order to determine the dynamics of a turbo-charged diesel engine under closed-loop regulation. Three approaches are discussed:- (1) digital frequency response estimation, (2) step response fitting, and (3) parameter estimation of an equivalent discrete time model. The exercise is conducted at a number of operating conditions and leads to an engine model dominated by a single unstable pole which moves as a function of the engine operating point, together with more complex dynamics associated with the turbo-charger loop. Keywords. Closed-loop identification; modelling; spectral analysis; engine testing; parameter estimation. INTRODUCTION

the air pressure at the engine inlet manifold.

Almost one hundred years have elapsed since Rudolf Diesel (1858-1913) proposed the thermodynamic energy cycle which now bears his name, and although the diesel cycle has been embodied in prime mover form for some eighty years, the Diesel engine with which we are familiar today is remarkably similar to the early Busch-Sulzer engines used to power submarines in the First World War. Of course, such similarity is largely superficial since the modern diesel power plant is a highly sophisticated piece of engineering, involving many refinements on the original, both in terms of its construction and the materials used.

Interestingly, each of these diesel engine features involves the closure of a feedback loop. Two of the modifications, namely direct fuel pump drive and turbo-charging are structural changes aimed at improving engine performance and simplifying construction. The third (closure of the speed governing loop) is, however, essentially a stabilizing strategy intended to mitigate the destabilizing influence of the structural feedback loops. One of the aims of this paper is to apply the techniques of closed-loop identification to determine the dynamics of a turbo-charged diesel engine (and implicitly the influence of the structural loops) while operating, under closed-loop speed regulation. Much has been written of late on closed-loop identification, and in this paper we explor~ albeit in a restricted sense, some of the practical features of closed-loop identification techniques. Three approaches are used:- (1) digital frequency response esti~ ation, (2) step response fitting and (3) pArameter estimation of an equivalent discrete time model. The original aim in applying such a range of techniques was to obtain comparative results for the problem in hand. As it turns out, however, the exercise also reveals some useful, but little known, features of the identification techniques themselves.

As control system analysts it is the constructional features of the modern diesel engine which attract our attention. In particular three refinements to the basic engine are fundamental to the efficient operation of modern dieSel engines, and at least indirectly are responsible for the system identification studies related here. The first advance in diesel engine operation which is of interest to us is the use of fuel pumps driven by the engine output shaft. Second is the use of automatic governors to regulate engine speedt , and third is the application of turbocharging to augment tNote that not all diesel engines are governed, the majority of automotive diesels are essentially open loop.

Overriding the intrinsic interest in comparative identification studies was the need to

361

362

P. E. We llste ad, C. Thirua r oo r an and D. E. Wint e rb one

determine the dynamical properties of a turbocharged diesel engine. In a previous exercise the current authors rWinterbone and others, 1977) have formulated a dynamical model for a diesel engine. However, this model is a complete simulation of the engine and as such unsuitable for control studies. Hence the need for a simple model determined from direct dynamical measurements. In particular, the next generation of engine governors will almost certainly be part of an overall engine management scheme, and in keeping with such integrated engine control strategies is the need for a more detailed knowledge of those aspects of engine dynamics which are relevant to automatic control. Viewed in another light, the exercise reported here is the sequel to our previous studies of autoI:'otive power plant, in particular the automotive gas turbine, (Wellstead and Nuske, 1976). The paper is arranged as follows, section 2 motivates the subsequent discussion of engine dynamics by developing a simple analytical model of diesel dynamics. This is followed by explanations of the engine test configuration, together with information on signal conditioning and basic data preparation. Section 5 contains the main body of the work, being the identification results obtained at various engine loads and speeds. Section 6 concludes the paper by relating the identification results to the physically motivated model of section 2. A SIMPLE ENGINE MODEL In the introduction we made some play of the fact that turbo-charged diesel engines are multi-loop feedback systems. The fact that turbo-charged diesel engines involve three feedback loops is of course wellknown to engine analysts. Nevertheless, it will prove instructive to consider a little more deeply the diesel engine as a multiloopplant First because it provides the basic motivation for our identification studies, and secondly because it is a convenient way of constructing a crude analytical model to which we can relate our identification results. Let us begin with the diesel engine with all loops open. In this form (Fig. I a) the engine input T(t) is the effective torque supplied by the fuel. The usual output variable is angular velocity net) and this is related to the input by a single pole a with gain ke' Where ke and a are jointly determined by the effective inertia of the engine and its load, together with viscous losses. The effective torque T(t) generated by the combustion of the fuel.is a complex function of the fuel flow.rate mf(t), the inlet manifold air flow rate ma(t), the fuel calorific value plus other variables. For the purposes of the current discussion, however, the torque T(t) can be thought of as being a linear function ke of the sum mf + ma as indicated in Fig. lb. Notice that

"9

~J-r-

~ -(
e s+a

net)

(a)

Diesel engine with all loops open

(b)

Diesel engine with fuel system net)

~_k_C_~~L_:_:_a__~~h-~(c)

Turbo-charger loop closed rack position

(d)

n(t), englne speed

Turbo-charger and fuel pump loops closed Fig.

in addition to the functional simplification of the fuel combustion kinetics, we have aloo ignored the fact that the fuel energy is converted to mechanical energy by an impUlsive combustion process. In noting this fact, other authors (Flowers, 1971) have represented the diesel combustion system by a sampled data model. We do not do this because we are dealing with a medium speed, multicylinder engine, which for control purposes can re considered as a continuous system. Consider now the technique of turbocharging. Basically this amounts to supplying the air mass flow rate ~ (t) from a compressor/ turbine driven byathe engine exhaust gases (see Kates (1970) for a more complete physical description). Roughly speaking, the air mass flow rate m (t) delivered by the turbo-charger is propgrtional to the engine speed net), this then forms a positive feedback loop around the basic engine (fig. Ic) and forms the first of the loops mentioned in the introduction. Next consider the fuel system whereby the diesel fuel is pumped by a gear train driven from the output shaft and gated by a rack mechanism. In terms of a simplified model, this can be repr~sented by writing the fuel mass flow rate 1I'.f(t) as the sum of the output speed net) ~modified by a gain k p )

Identi ficatio n of a Turbo-C harged Diesel Engine and the fuel rack positio n u(t) (modif ied by a gain k r ). As shown in fig. Id, this introdu ces an additio nal positiv e feedbac k loop and forms the second feedbac k loop discuss ed in our prelim inary discus sion. Both the turboch arger and the fuel pump loops involve positiv e feedbac k and conseq uently have a destab ilizing influen ce upon the engine dynami cs. An influen ce which is compen sated for by the closure of a final negativ e feedback loop which include s a dynami cal compen sator aimed at regula ting the engine speed and stabili zing the transie nt perform ance (fig. 2). engine speed

Fig. 2 This comple tes our trio of feedbac k loops and with it the simple analyt ical model of the diesel engine . The overal l engine transfer functio n can be comput ed from Fig. I to give k k k n(s) e c r (I) u(s) s+ ex-k k (k +k ) c e

t

p

In fact the diesel engine is much more complex than the above model would imply. For exampl e, the samplin g phenom ena mention ed above could be include d to make the model more repres entativ e. Beyond this a fully dynami c model can be constru cted which include s all system dynami cs and the impulsive nature of the combus tion proces s. Such a model (report ed in Winter bone, 1977) has been develop ed and proven most useful in transie nt simula tion of diesel engine s. Howeve r, the require ments of a dynami cal model for contro l purpos es differ from those for simula tion purpos es, and it was, in part at least, the need to isolate these contro l require ments for diesel engine s which stimulated the identi ficatio n work reporte d here. On the one hand we require d experim ental basis for formul ating a turbo-c harged diesel engine model like the simple model shown here. Corres pondin gly, if a more complex mode l seems justifi ed , some means of justify ing that model and relatin g it to the simulation model was require d. In partic ular, the possib le changes in dynami cs which might occur as the speed and load of the engine varies were of especi al intere st, since this information is require d to (a) tune the parame ters of a dynami cal simula tion model, and (b) assess the suitab ility of govern or design s. This latter point is motiva ted in terms of the simple analyt ical model by noting that signifi cant change s in, say, turboch arger dynami cs with speed would alter coeffic ient k t in equatio n (I) and could alter the diesel from an open-lo op stable system to an open-lo op unstab le plant. Likewi se the

363

windag e compon ent of ex increas es as the cube of speed and has a stabili zing influen ce on equatio n (I) by increas ing ex. TEST BED The engine used in this study was a six cylinder, four stroke , medium speed, turbocharged 6YEX Ruston Diesel engine (Mark 11) manufa ctured by English Electr ic (Diese ls) Ltd. and install ed in the labora tories of the Thermo dynamic s Divisio n of the Departm ent of Mechan ical Engine ering, UMIST. The engine is equippe d with a Holset 4LEV-30S turboch arger of the single stage centrif ugal compre ssor/ radial turbine type. The engine operati ng speed is in the nomina l range 1000 rev/min to 1800 rev/min and a typical loading is 700 Newton metres . The engine is equippe d with dvnamo meter, electro nic speed govern or, and the approp riate instru mentat ion to monito r the signals require d for the identi ficatio n studie s. As indicat ed in fig . 3, these were: demand ed speed r(t), fuel rack positio n u(t) and actual engine speed n (t) • transmis sion shaft

I,

Diesel engine

yna.clomet er

+

r(t)

fuel rack position ,u (t)

engine speed.n( t)

Fig. 3 SIGNAL CONDITIONING Throug hout our studies the engine was run with the govern or loop closed . Variou s test perturbati ons were applied to the demand ed speed input r(t) and both direct and indire ct method s were used to estima te the diesel engine dynami cs. The fuel rack positio n transdu cer gave good undisto rted measur ements of the rack displac ement and was used direct ly. The speed transdu cer signal was, howeve r, not so well conditi oned. In fact, as shown in Fig. 4, in additio n to the spectr al power associa ted with the engine dynami cs, the speed transdu cer autospe ctrum also display ed a number of high frequen cy period icities associated with transm ission shaft modes, and transdu ction phenom ena. The identi ficatio n of shaft resona nt modes has intere st in its own right, but is not relevan t to the identi ficatio n of engine dynami cs, and in order to preven t aliased shaft modes (Wells tead, 1976) interfe ring with the engine respon se, the speed signal was low pass filtere d using a third order Butterw orth filter with 20 Hz cut-of f.

P . E. Wellstead, C. Thiruarooran and D. E. Winterbone

364

....o El'" Q)

;:l ~ ~

Q)

0..

UUl

Q)

0..Q)

(J)

c::

0· ...

~

;:l

bO

c::

<~~~~~~~~-----.-----r~~~--50

100

150

200

250

Frequency (Hz) Fig. 4 Autospectrum of the unfiltered engine speed signal

5un (j w) §

IDENTIFI CATION One of the irritating facts which is at the back of the systems analysist's mind when selecting an identification algorithm for a particular task, is the knowledge that the one algorithm will not tell him all that he wishes to know. Even more irritating is the property possessed by almost all identification techniques of accentuating certain system properties while remaining insensitive to others. In many cases such difficulties are avoided by picking the 'right' algorithm for the right application. However, in applications like the current one, where we seek an overall understanding of the engine dynamics, no such intuitive escape route exists, and we are obliged to apply a representative range of methods to elicit all the required information. For the problem in hand we chose to use a non-parametric direct identification technique (digital frequency response estimation) and verify it by a continuous time parametric method (step response fitting). The techniques were applied at a set of operating conditions and small signal principles applied in order to determine the effective linear model at these conditions. The operating range of the engine is from 1000 rev/ min to 1800 rev/min in speed, with a nominal load range of 200 Newton metres to 800 Newton metres. IH thin this range a number of combinations of load and speed were examined, but for the purposes of the current paper only the following operating points are mentioned. (a) High speed/High load (HSHL)

counterparts, one hopes that this trend will be shortlived, for the modern techniques of digital frequency estimation (Wellstead,1975) coupled with the interactive power of realtime mini computers makes frequency response identification a valuable on-line analysis tool (Wellstead, 1974). However, as with all system identification techniques, certain problems arise when the system under study is operating under closed loop conditions. This difficulty can be readily avoided, however, by replacing the normal estimator of the engine frequency response H(j w) given by

-

1800 rev/ min, 810 Nm

(b) Mid

speed/ Mid load (MSML) - 1400 rev/ min , 620 Nm

(c) Low

speed/ Low load (LSLL) - 100 rev/ min, 210 Nm

DIGITAL FREQUENCY RESPONSE ESTIMATION A natural approach for control engineers to take to system identification is that of direct frequency response estimation. Despite the strong intuitive advantages of frequency response estimates, the technique is currently less fashionable that its parametric

uu

(2)

(w)

where (with reference to Fig. 2) , S (j w) is the cross -spectrum between the racku~osition u(t) and the engine speed net), Suu(w) is the auto spectrum of the rack position u(t), and the circumflex denotes an estimated quantity. A more suitable estimator, which is unbiassed by the feedback loop, is given by the crossspectral ratio Srn C.i w)

(3)

Sru(j w) where Sru(j w) and Srn(jw) are respectively the cross-spectra between the demanded speed r(t) and u(t), and r(t) and net). In equation (3) the demanded speed r(t) can be seen to act (informally speaking) as a frequency domain instrumental variable . Indeed, conditions on r(t) for (3) to be a valid estimator may be formulated in an analogous manner to those pertaining to instrumental estimators . In particular, we require that: (i) r(t) be independent of a disturbance in the system H(s), and (ii) r(t) and u(t) have non-zero cross -spectral power in the frequency band of interest. Using H(j w) as our estimator, the frequency response of the engine between rack position u(t) and actual engine speed net) was estimated at the three primary operating conditions HSHL, MSML, LSLL. The estimates were obtained using the digital techniques described in (Wellstead, 1975) applied to records of r(t), u(t), net); where r(t) was a band limited Gaussian noise source. The estimates obtained in this manner are shown in Fig. 5, where, in addition to the basic estimates the approximate joint 95% confidence intervals are also plotted. The confidence regions are obtained as described in (Wellstead, 1977) by noting that, to a first approximaEion, the confidence regions for the estimator H(j w) may be obtained by a conformal mapping of the corresponding regions for the overall (open loop) transfer function between r(t) and net). In many open loop applications the analyst will not compute exact confidence bands for his spectral estimates but will rely upon the

Identification of a Turbo-Charged Diesel Engine

365

information provided by~the coherency function. However, for estimator H(jw) no ready equivalent of coherency exists, and we are obliged to compute confidence bands. Horeover. these confidence regions prove most useful, since in Fig. 5 they indicate that the estimates become increasingly unreliable at low frequ~ .~

"

. '"

Cl

.

.......

".

k

-.a. ':."... ~

Ccmfideonce Regions Map

.

.!l

.,,-.11

'\w.

"....

.

Interior to Exterlor

a.'",

,

".~""""~

,..,~

Cl

0.05

0.5

0.05

0.5

~

a Estimate

::.

95% Confidence Bounds

5.00

0.5

.

....... ~

50.00

•

-135

5.00

0.5

o

Y ""Q~ 'b~

• Q.

"

-180

:r"

lI')Llfll'

"lr"

-90

Frequency (rads/sec)

0.05

d~ds/scd 50

-45

J:

0.05

Ft"cquency

0 ~

)(

95% Confidence Bounds

)"')."'~ ~~

)r It

~

"le

lr

50.00

K 'AA

Fig. 5c Frequency Response Estimates from rack position to engine speed (low-speed/low-Ioad)

Fig. 5a Frequency Response Estimates from rack position to engine speed (high speed/high load)

cies. Intuitively, this relates to the idea that a tightly controlled plant is difficult to identify, because the successful controller masks the plant dynamics. Practically it arises because the signals u(t) and r(t) have little cross-spectral power at low frequencies (see Fig. 6). 1.0

"<
..

"

-u;-...

•

>-

......r:: o

tJ

.t:: U "Cl

...

0.5

."

::l

C"

'" 0.05

50

0.5

,.

Frequency (rads/sec)

0.05

0.5

50

O~

__

0.05

::

-90 -135

~

J:

"-

~

______

5.00

~

50.00

Fig. 6 Showing the small squared coherency between demanded speed and rack position at low frequencies

-45 ~

________

0.50

Frequency (rads/sec)

0

o~

~L-~

-180

Fig. 5b Frequency Response Estimates from rack position to engine speed (mid speed/mid load)

In terms of the conformal mapping the estimates are approaching the point at which the map switches from interiDr+interior to interiOr+exterior, with a corresponding increase in the H(s) plane confidence circle diameter. The uncertainty at low frequencies tends to

P. E. Wellstead, C. Thiruarooran and D. E. Winterbone

366

mask the dynamical properties which we seek to identify. Nevertheless, Fig. 5 tends to support the following suggestions: (i) at high speed/high load the engine is a single stable pole close to the origin; (H) at mid speed/mid load the engine is a single unstable pole close to the origin; (Hi) at low speed/ low load the engine appears to exhibit a zero close to the origin, although at higher frequencies the results are again consistent with a simple unstable pole. A full discussion of these suggestions will be given later, for the moment we note that they must be considered as tentative because of the relatively low statistical confidence associated with the low frequency estimates. STEP RESPONSE FITTING A discrete time parameter fitting algorithm (Wellstead, 1976) was applied and supported the proposition of a higher order model at low speed/low load, but indicates that the extra dynamics are hardly discernable. For this reason we neglect these minor influences and attempt to estimate the position of the dominant pole and hence quantify our earlier remarks concerning the movement of this pole with operating conditions. In principle, the discrete time model estimated by the conventional techniques can be inverse z-transformed in order to provide estimates of the continuous-time system parameters. However, this transformation is notoriously sensitive and can lead to ambiguous results (Wellstead, 1975), to the extent that we prefer to fit the continuous system parameters directly (provided of course that the complexity of the problem permits) by a non-linear optimization procedure. The precise details of the procedure are given elsewhere (Thirurooran, 1977), but the basic approach is to take a weighted sum of the rack and actual speed response to a step on demanded speed, and adjust the parameters of an engine model until a least square error criterion was satisfied. Mixed into this optimisation is the governor transfer function; however, it is actually known from offline measurements and can thus be handled by fixing certain parameters in the minimization. By repeating this procedure at the three main operating conditions, the diesel engine pole positions were determined and are listed in Table I. TABLE I Diesel Engine Pole Positions Operating Condition

Pole Position

HSHL

-0.33

MSML

0.19

LSLL

0.81

Notice that these estimates agree with the change in dynamics observed from the frequency response estimates. An additional degree of

confidence is lent by the fidelity with which the fitted models track the observed step responses, (see Fig. 7 at the end of the text). THE SIMPLE MODEL REVISITED The identification results support the structure proposed in very simple model of section 2 in a pleasing manner. Moreover, the mobility of the pole can be simply related to changes in the system parameters due to nonlinear speed dependent phenomena. Notably a considerable portion of engine losses increase with the square (or cube) of speed, a fact ,.,hich explains the movement of the engine pole into the left-half plane as speed increases. Despite the apparent suitability of the single pole model, one still remains dissatisfied since the suggestion remains that other dynamical phenomena are active. To see where these might lie, we return to the engine model and reconsider the turbocharger loop. In particular, we note that a zero in the overall transfer function can arise from a pole in a minor feedback loop. Also, notice that at engine low speed the turbocharger will be idling, causing under-aspiration of the engine. It follows that at low speeds the dynamics of the turbocharger (if any) will be particularly noticeable. With this in mind we replace the turbocharger gain k t in Fig. Id by a simple lag kt/(s+8) and reformulate the overall transfer function as n(s)

UCST

(s+a)(s+8)-k k (k +(s+8)k ) e c

t

(4)

p

which contains the required zero. The dynamics of the turbocharger can be argued to be inoperative at high and medium speeds since there is a surplus of air at these conditions. A fact which conveniently explains why we were only able to detect 8 at low speeds. CONCLUSION Diesel was wont to refer to himself as "ein Gluckspliz" and felt in some ways more proud of his social theories than his engineering achievements. However, it takes more than luck to invent an engine which, in spite of refinements of turbocharging, governing and pump drive systems, remains substantially the same as Diesel's original creation. Indeed. seen from a systems viewpoint the diesel engine is remarkably elegant and yet simple to control, being nominally a single pole near the origin. Unfortunately it is doubtful whether controls based upon such simple models will be deemed adequate for much longer. For vehicle emissions legislation combined with the pressing need for better operational efficiency, will inevitably mean that more sophisticated controllers based upon more detailed models will be required in all diesel engine applications. It is in this light that we would wish the work reported here to be seen. Put more explicitly, this

Identification of a Turbo -Charged Diesel Engine is not a self-contained study of diesel engine dynamics, but a contribution to the gener~l body of work aimed at increasing the control engineer's knowledge of prime movers and their efficient use.

2.0

367

1

1.0-

s!::

o. o ~~__~-+-;~~~-·-"~·'~'~'·~--------~-----­

v-

TDIE (S ECO!-mS )

c ""

-1.0

'"' ~

-2.0

Tl'lE (S ECntillS)

-20 . 0 ~.1.l

"'

[;; - 40 . 0

~ -60 .0 '-' z '" -80.0 -100.0

Fig. 7c Step responses of rack and engine speed at low speed/low load (actual response - dotted line, model response - continuous line). REFERENCES Fig. 7a Step response of rack and engine speed at high speed/high load. (Actual response - dotted line, model response - continuous line)

2.0

1.0

z

...c

0.0

2

0

f-.

H tn

0

<>

TIi'1E (SECONDS)

-1.0

'"

u

;2

-2.0

-3.0 20.0 TIMF. (SECONTlS)

-2:::f 0 ~

-40 . 0

~

-60 . 0

~

-80.0 [

~

I

f

0:

-1 00.0

Fig. 7b Step response of rack and engine speed at mid speed/mid load. (Actual response - dotted line, model response - continuous line. )

Flowers, J.O., Hazell, P .A. (1971). Sampleddata theory applied to the modelling and control analysis of compression ign1t10n engines. Int. J. Control, 14, 832. Kates, K.J. (1970). Diesel an~High-Compress­ ion Gas Engine Fundamentals. American Technical Society, New York . Hinterbone, D., Thiruarooran, T. and Wellstead, P.E. (1977). A Wholly Dynamic Model of a Turbo- charged Diesel Engine . S.A.E. International Automotive Engineering Congress, Detroit, U. S .A. Wellstead, P . E. (1975). Aliasing in System Identification. Int. J. Control, 22, 363 . Wellstead, P.E. and Nuske, D. J . (1976~ Identification of an Automotive Gas Turbine Parts 1 and 2 . Int . J . Control, 24, 297 . Wellstead , P . E. (1975). Frequency Domain System Identification, in the S .R. C. Vaction School on Stochastic Processes in Control, University of lolarwick. (Also available as Control Systems Centre Report ~o. 296, University of Manchester Institute of Science and Technology.) lolellstead, P . E., Galley , D. and Koreman, R. (1974) . Interactive Computer-Aided Identification of Engineering Systems , in lEE Conference on Computer-Aided Design, Southampton. Wellstead, P.E. (1977). Reference Signals for Closed Loop Identification. Int. J. Control (to appear) Thiruarooran, C. and others (1977). Diesel Engine Identification Studies. Mechanical Engineering Department Report, UMlST . (Available from the authors.) Wellstead, P.E. (1976). Model Order Testing Using an Auxiliary System . Proc . lEE, 123, 1373.