idle speed comparison

*Corresponding author. Tel.: #44-1232-274-147; fax: #44-1232-661-729.

Control Engineering Practice 8 (2000) 519}530

A comparison of idle speed control schemes

M. Thornhill!, S. Thompson!,*, H. Sindano"

!School of Mechanical and Manufacturing Engineering, Queen's University of Belfast, Ashby Building, Stranmillis Road, Belfast BT9 5AH, UK"SAGEM, Research and Development, Birmingham, UK

Received 2 December 1998; accepted 25 October 1999

Abstract

This paper examines the idle speed regulation control problem in multi-point spark ignited petrol engines. Several possiblesolutions are presented, including proportional plus integral control, fuzzy logic control, adaptive fuzzy logic control, adaptive fuzzylogic control in conjunction with Smith prediction and dynamic matrix control. All of the controllers are compared in simulation and,where possible, on a production vehicle. The performance measures used for comparison purposes were mean-square error andmaximum error. It is shown that there are several possible alternatives to the existing proportional plus integral control used on theair bypass valve of production vehicles. ( 2000 Elsevier Science ¸td. All rights reserved.

Keywords: Idle speed regulation; PI control; Fuzzy logic control; Adaptive fuzzy logic; Adaptive fuzzy logic with Smith prediction; Dynamic matrixcontrol; Mean-square error; Maximum error

1. Introduction

Idle speed control (ISC) represents one of the mostgeneric and basic automotive control problems confront-ing automotive control researchers and practitioners.Engine idle speed refers to engine operation under closedthrottle conditions; on average, vehicles consume about30% of their fuel in city driving during idling (Jurgen,1995). It is therefore important to try and optimise ve-hicle and powertrain operation at idle, especially withrespect to the often con#icting requirements of improvedfuel economy, good noise, vibration and harshness qual-ity, and reduced emissions.

The complete ISC problem, in order of importance,encompasses three di!erent operational phases:

1. Idle speed regulation. At idle the engine speed is nevertruly constant (see Section 1.1 and Fig. 8). Therefore,the controller must be capable of maintaining enginespeed close to the set point (selected target idle speedvalue) with as little deviation as possible (the enginemust run smoothly). Essentially, the better the idlespeed regulation the lower the selected idle speedvalue can be set, subject to some allowance for distur-

bance rejection and entry/exit to idle speed. Ideally,idle speed regulation would be performed solely by theair bypass valve.

2. Rejection of known disturbances. Idle speed distur-bance rejection tests are a popular test to perform inan engine test cell. Most modern dynamometers per-mit load adjustments and the data logging equipmentpermits appropriate traces to be collected. In a vehiclethe disturbances are due to electrical loads (switchingon of air conditioning, window heating, lighting, etc.)or for a vehicle with power steering, low-speedmanoeuvring. These are events which, when they oc-cur, may cause the engine to stall or mis"re. Typically,the solution to the problem requires several feed for-ward control loops using accessory load information,and other ad hoc compensation schemes for temper-ature, barometric pressure and other environmentalconditions. Often these would act on both the airbypass valve position and the spark advance.

3. Entry and exit from/to idle speed. Very little researchhas been reported in this area. However, any stepchange from a high-speed level to the set point idlespeed can cause a speed undershoot and the engine tostall. One solution is to provide a smooth targettransition speed that the controller is required to follow.

Further, the order of these operational phases alsoindicates the order of increasing di$culty in performing

0967-0661/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 9 6 7 - 0 6 6 1 ( 9 9 ) 0 0 1 9 0 - 2

Nomenclature

ABV air bypass valveB(s) predicted plant outputBTDC before top dead centrepli

width of triangular membership function l forinput i

DMC dynamic matrix controlc learning ratem vector of fuzzy basis function valuese error signalE(s) error signal in the frequency domainEMS engine management systemf (x) non-linear functionFlii

fuzzy set lifor input i

#ops #oating point operationsFIR "nite impulse responseFLC fuzzy logic controlGc(s) controller transfer functionGp(s) plant transfer functionG(s) delay-free plant modelI integralISC idle speed controlki

integral gainkp

proportional gainl rule numberkF

lii

membership grade of fuzzy set Flii

max maximum functionM number of rules

MSE mean-square errorME maximum errorn number of inputs to fuzzy logic system or

number of sample points (MSE and ME)N

ispeed (rpm) at sample point i

Nrefi

reference speed (rpm) at sample point ih vector of output membership function valuesPI proportional, integral.PRBS pseudo-random binary sequenceR(s) reference signal in the frequency domainrpm revolutions per minuteSA spark advanceSP Smith predictiont timetri triangular membership functionq system delayu controller outputvars. variableswl weight of rule lx system state variablex system state vectorx6 li

centre of triangular membership function l forinput i

y plant outputy6 l output membership function l value>(s) output signal in the frequency domain

vehicle tests and in obtaining controller performancemeasures. Since this paper sets out to compare severalpossible idle speed controllers only the baseline regula-tion tests are considered in detail.

In order to satisfy the baseline regulation problem,current ISC strategies use both spark and air control;even though spark control is required for other functions.When only air control is used to maintain idle speed it isdi$cult to achieve satisfactory performance. The argu-ment is that the geometry of the inlet manifold introducesa delay in the air to speed loop. Therefore, since it can bedemonstrated that changes in spark advance will pro-duce rapid changes in speed, then this delay should becompensated for using spark control.

Typically, a production ISC strategy includes PI con-trol for the air loop and proportional feedback controlfor the spark loop. Since the primary objective of the ISCsystem is to track a constant desired speed by manipula-ting the air bypass valve (ABV) the integral portion of thePI controller is considered to be the core of the ISCstrategy.

Controller gains are normally tuned by hand, usingtrial and error, to obtain best performance. This method

of tuning can be inaccurate since the idle speed system isnon-linear and the engine characteristics change over itslifetime. When combined with short term environmentalchanges, or changes in fuel type, it can be seen that a "xedcontrol scheme cannot be optimal at all times.

This paper presents a comparison of several ISCschemes, all of which use the air bypass valve (ABV) as anactuator. The control schemes that are compared are:

(1) PI control, this is the standard production control-ler.

(2) Fuzzy logic, as it is capable of controlling non-linearsystems.

(3) Adaptive fuzzy logic, as it is capable of controllingtime-varying, non-linear systems.

(4) Adaptive fuzzy logic with Smith prediction, as it iscapable of controlling time varying, non-linear sys-tems with time delays.

(5) Dynamic matrix control (DMC), as it is also capableof dealing with systems with time delays.

All of these control schemes can be designed withoutthe need for a formal mathematical model and tuning, forthe non-adaptive schemes, can be performed on-line.

520 M. Thornhill et al. / Control Engineering Practice 8 (2000) 519}530

Fig. 1. Inputs, outputs and disturbances to the idle speed system.

When used, the spark controller remains unchangedfrom that supplied on the production vehicle. Air}fuelratio control is enabled for all tests and is necessary forthe entry to idle speed tests.

Three sets of tests were performed in order to comparethese control schemes for the regulation of idle speed:

(1) Simulation with constant spark advance. (This simu-lation tests the system integrity, i.e. in the event ofspark control failure what is the residual ISC).

(2) Engine test with constant spark advance.(3) Engine test with proportional spark control. Al-

though spark control may not appear necessary forthe regulation tests, it may be essential for entry andexit from/to idle speed and therefore is included inthe regulation tests.

Two performance measures were used to compare thecontrol schemes, namely mean-square error (MSE) andmaximum error (ME). The MSE gives a feel for howsmooth the engine idles as perceived by the driver of thevehicle. The ME determines the largest deviation fromthe target idle speed. At low target idle speeds a large MEcan cause the engine to stall. Due to engine managementsystem (EMS) limitations on the vehicle tested, the DMCalgorithm and the adaptive fuzzy logic controller withSmith prediction could not be tested.

1.1. The idle speed system

Fig. 1 shows a representation of the idle speed systemwith the physical inputs and outputs shown.

Of the factors which a!ect engine speed, the enginecontroller only has control over the fuel, air, re-circulatedexhaust gas and spark timing. The other factors a!ectingengine speed are either part of the engine design or area function of atmospheric conditions.

In this paper, the vehicle tested had a spark ignitionengine with port fuel injection, a stepper motor thatadmits auxiliary air, variable spark timing and exhaustgas re-circulation all controlled by the engine manage-ment system which had a sample time of 0.032 s. As usual

with ISC the engine speed was controlled using a combi-nation of spark and air control so that the engine speedtracks a reference idle speed. The reference idle speed ispre-set by the engine designer at a speed that givessmooth running of the engine while maintaining accept-able fuel economy. Engine fuel control is reserved foremission control purposes. In all tests exhaust gas re-circulation was disabled and the fuel control enabled.For the constant spark advance tests, the spark advancewas held constant at 103 BTDC.

An internal combustion engine running at idle speed ischaracterised by various problems (Abate & DiNunzio,1990; Nishimura & Ishii, 1986; Washino, Nishiyama& Ohkubo, 1986; Hrovat & Sun, 1996):

1. A trend to trigger speed oscillations with a period ofaround 2}5 s in fuel-injected engines. This is caused bya positive reaction that is inherent in the engine and isrelated to its functioning mode and constructioncharacteristics.

2. A drop in the number of revolutions because of theapplication of a braking torque. There may be variousreasons for this torque, such as switching on of anelectrical load, switching on of air conditioning systemor activation of the power steering.

3. Poor running of the engine as it is operating in a low-speed and low-torque area for which the design hasnot been optimised. Particularly in the case in whichthere is a tendency to lower the target engine rotationspeed (deliberately or because of the above-mentionedbraking torques), this leads to bad combustion of thefuel or failure to burn the fuel. In view of the low valueof the torques involved, this irregularity of operation,if not appropriately compensated, causes #uctuationsin engine speed with high-frequency spectrum charac-teristics with a period more or less aligned to that ofengine phase duration and random distribution. Thisdisturbance is therefore di!erent from that outlined inproblem 1 above. The problem described here isheightened further when the engine is cold so thatfriction is greater and combustion more irregular.

4. The idle speed of an engine is also subject to slowlyvarying changes due to changes in operating condi-tions or engine condition. These slow changes may bedue to the conditions under which the engine operates,like ambient temperature and pressure, fuel quality,lubricant temperature, etc. In addition, the conditionof repair of the engine and the state of wear changeslowly over the life of an engine.

5. Induction to power stroke delay, this delay is variableand is a function of engine speed. This delay is cited asbeing the dominant dynamic e!ect in the idle speedcontrol problem.

In summary, the idle speed system is non-linear andtime varying with variable time delays.

M. Thornhill et al. / Control Engineering Practice 8 (2000) 519}530 521

Fig. 2. Input membership functions used in the fuzzy controller.

Fig. 3. Output membership functions for the fuzzy controller.

2. Control schemes tested

The following control schemes were tested for theirability to regulate the idle speed to a value of 864 rpm inthe presence of the non-linearities described in Section1.1. The parameters in each control scheme were usedboth in simulation and on the engine tests.

2.1. PI control

The gains used here were the production controllergains of 0.03 on both the proportional and integral gains.The production controller uses the formula

u"kpe#k

iPe dt, (1)

to calculate the controller output.

2.2. Fuzzy logic control

The fuzzy logic controller demonstrated here (Takagi& Sugeno, 1985) is the simplest type of fuzzy controller inthat there is only one input and one output. The onlyinput to the fuzzy controller was the error between en-gine speed and idle reference speed. Five fuzzy sets werede"ned on this input universe of discourse (see Fig. 2).The "ve linguistic fuzzy sets de"ned are large negative(ln), small negative (sn), zero (ze), small positive (sp) andlarge positive (lp). These "ve fuzzy sets provide completecoverage of the input space (i.e. for every value of speederror at least one fuzzy set has a non-zero value), forvalues less than !200 rpm (relative to the set point),ln"1 and for values greater than 200 rpm, lp"1.

As there was only one input to the fuzzy controller and"ve fuzzy sets for this input, there were only "ve controlrules.

Rule base 1 shows the rules used for the fuzzy control-ler, the antecedent part of the rule refers to the inputmembership functions shown in Fig. 2, and the conse-quent part of the rule refers to the output membershipfunctions shown in Fig. 3.

Rule base 1. Rules for the fuzzy controller.

IF error is lp THEN change in stepper position is outmf1IF error is sp THEN change in stepper position is outmf2IF error is ze THEN change in stepper position is outmf3IF error is sn THEN change in stepper position is outmf4IF error is ln THEN change in stepper position is outmf5

Defuzzi"cation obtains a crisp numerical value fromfuzzy inputs, the Takagi}Sugeno fuzzy system has beenused exclusively throughout this paper. For a real-valuedinput vector x"(x

1, 2, x

n)T, the output y( x ) of Takagi

and Sugeno's fuzzy system is a weighted average of theyl's

y( x )"+M

l/1wlyl

+Ml/1

wl, (2)

where the weight wl implies the overall truth value of thepremise of rule ¸(l) for the input and is calculated as

wl"n

<i/1

kF

li(x

i). (3)

The output from the defuzzi"cation stage is the "nalcrisp output of the fuzzy logic controller. Fig. 3 showsthat the output membership functions range from !0.5to 0.5 steps, while the ABV can only move in discretesteps. However a #oating point value of ABV is constant-ly added to or subtracted from in the controller, this#oating point value is then rounded to the nearest integerto give an integer number of ABV steps.


Fig. 4. The overall scheme of direct adaptive fuzzy control.

Fig. 5. Input membership functions used for engine speed input.

Note that the output of the fuzzy controller is thechange in stepper position. That is, the stepper position isconstantly added to or subtracted from and this producesintegral action in the controller.

2.3. Adaptive FLC

Non-adaptive fuzzy logic controllers rely on experts tode"ne the input/output membership functions and rules.A more optimal controller would be one that adapts toerrors between desired output and actual output toachieve `optimala control.

There are many adaptive fuzzy logic schemes thatadapt input/output membership functions or the rulebase in the fuzzy logic controller (Procyk & Mamdani,1979; Lee, 1991). The method used in this paper is takenfrom Wang (1994), since Wang's direct adaptive fuzzycontroller is demonstrated to have excellent trackingproperties (even for non-linear systems) and so waschosen as an appropriate control strategy.

In this application, the output membership functionsare adapted so that the fuzzy logic controller is tuned tominimise the error between engine speed and the idlereference speed. That is the controller is a direct adaptivefuzzy controller (Wang, 1994), with adaptation of outputmembership functions only (see Fig. 4). The parametersof the block labelled fuzzy controller in Fig. 4 are de-scribed in Section 2.3.1.

Fig. 4 shows a supervisory control scheme as part ofadaptive fuzzy logic. Supervisory control is used byWang (1994) to maintain stability of the controller duringlearning. Supervisory control switches on when the signalto be controlled has exceeded a pre-speci"ed value thatthe designer has set. To enable analysis of `controllerlearninga these blocks have been neglected during thedesign of direct adaptive fuzzy idle speed controllers.

The formula for the fuzzy controller is as follows:

u(x)"+M

l/1y6 l[<n

i/1tri(x

i!x6 l

i(h),pl

i)]

+Ml/1

[<ni/1

tri(xi!x6 l

i,pl

i)]

. (4)

In the fuzzy logic system used, only the yl (outputmembership function) values are adapted using a least-mean-squares algorithm. Again, the output membershipfunction values correspond to ABV positions.

The input membership function could also be adaptedbut this would require a non-linear adaptation scheme(such as back-propagation), which would necessitate ad-ditional computation time. Careful selection of the inputmembership functions was required so that the inputspace was fully covered, see Fig. 5.

The adaptive law used is based on a least-means-squares formulation.

hQ "cem( x ). (5)

The fuzzy basis function vector is de"ned as follows:

m(l1 ,2,ln )( x )"<n

i/1kF

lii(x

i)

+m1l1 2+mn

ln/1(<n

i/1kF

lii(x

i)). (6)

The learning rate c is a crucial tuning factor in thissystem. A large value of learning rate causes the control-ler to learn quickly but may also lead to instabilityduring learning, a smaller value of learning rate causesslower but more accurate learning.

2.3.1. Parameters of adaptive FLCOnly one input to the fuzzy controller is used, namely

engine speed. Fig. 5 shows the input membership func-tions used for the input engine speed, these membershipfunctions provide total coverage of the input space andwere selected to be most dense around 700 rpm, which isbelow the constantly desired idle speed.


Fig. 6. The Smith predictor arrangement.

Five rules were obtained from the output from eachfuzzy set. One output membership function was assignedto each rule. These output membership functions weregiven initial values of 30 (steps) at the start of eachsimulation, but could be given any value. Weighted aver-age defuzzi"cation was used, see Eq. (2). During simula-tion the position of each output membership functionwas adapted to minimise the error between engine speedand idle reference speed at each simulation time step.

2.4. Adaptive FLC with Smith prediction

Adaptive fuzzy logic control with Smith prediction wastested as adaptive FLC alone resulted in unstable controlwhich was thought to be due to signi"cant delays in theair}speed control loop.

Smith proposed the control scheme shown in Fig. 6(Dutton, Thompson & Barraclough, 1997). Ignoring thedashed lines, what happens in Fig. 6 is that a delay-freemodel of the plant is used to generate the output signalwhich would exist if the delay were absent (assuminga good model). This delay-free signal is then used in theusual feedback loop (via B(s)), instead of the plant output.To help account for errors in the delay-free model, thedelay itself is also modelled, and used to generate whatshould be a model of the actual plant output, includingthe delay e!ect. The dashed lines show how this is thencompared with the actual output, >(s), so that a model-ling error is also fed back into the control loop via B(S).In this way, the e!ects of errors in the model of G(s) arereduced.

The stability of the closed-loop system is identical tothat obtained if the plant's time delay had originally beenignored. However, the closed-loop transfer function con-tains a time delay in its numerator (since G

p(s)"

G(s)e~qs) and this will modify the response of the systemcompared with that of the time delay free plant. How-ever, this technique depends upon an accurate plantmodel (particularly, an accurate model of the delay(Dutton et al., 1997)).

To achieve adaptive fuzzy logic control with Smithprediction, the adaptive fuzzy logic controller described

in Section 2.4 is inserted in the block labelled Gc(s) in

Fig. 6. One of the advantages of fuzzy logic is that it ismodel-free, however the Smith predictor arrangementnegates this advantage in that it requires a model. For thesimulation and practical tests, the models used in theSmith predictor were the same experimentally obtainedFIR model, see Section 4, with the (assumed) delay trun-cated for the delay-free model.

In the actual system the dynamics of the system varyover the input space and so no one model would beoptimal. A method to overcome this problem would beto use an adaptive LMS "lter (Widrow & Wallach, 1996),so that the model for the Smith predictor would beoptimal at all times. This however requires more com-putational load as the system model is being adapted atall times.

2.5. Dynamic matrix control

Dynamic matrix control (Cutler & Ramaker, 1980) isa time-domain-based control algorithm. The basic idea isto use a time-domain step response model of the processto calculate the future changes in the manipulated vari-able required to minimise some performance index.

DMC is included in order to provide a widely used andgenerally accepted alternative controller. Note that thestep response used for calculating the controller matrix isobtained from the FIR plant model. Therefore, the simu-lation results should give the best possible control. Inpractice there would be some plant-model mismatch andan inevitable deterioration in the expected performance.

3. Performance measures

To compare the performance of the di!erent controllerschemes, the following performance measures were used:

(1) The mean-square error (MSE):

MSE"

+ni/1

(Ni!Nref

i)2

n. (7)

Eq. (7) is only used with idle speed regulation tests, i.e.the dynamic response at steady state. In real terms theMSE gives an indication of the smoothness of idle asapparent to the driver of the vehicle e.g. the MSE for theproduction idle speed controller is 203 rpm2 which feelssmooth to the driver of the vehicle. For this study it willbe assumed that an acceptable upper bound on the MSEwill be 203 rpm2.

(2) The maximum error (ME):

ME"max(N!Nref ). (8)

This performance measure is used only with idle speedregulation tests. The maximum error performancemeasure indicates the band around the idle reference


Fig. 7. Finite impulse response on air-to-speed loop.

Fig. 8. Idle speed regulation, PI control, P"0.03, I"0.03.

Table 1Comparison of control schemes in simulation with constant sparkadvance

Type of control scheme Mean-square error(rpm2)

Maximumerror (rpm)

PI (P"0.03, I"0.03) Unstable UnstableFuzzy 140 40Adaptive FL Unstable UnstableAdaptive FL#SP 11 14DMC 3 5

speed within which the idle speed is maintained. In thecase of low idle speed, this band is critical as a large dropfrom the reference speed could cause the engine to stall.The production idle speed controller produced a max-imum error value of 50 rpm for the test shown, this valueis used as the acceptable upper bound.

4. Simulation

4.1. Idle speed model for simulation

For the purposes of testing the adaptive fuzzy logicalgorithm, a "nite impulse response (FIR) 6.4 s in lengthwas calculated using pseudo random binary sequence(PRBS) tests on the air bypass valve (ABV) and measur-ing the resulting speed output (Thornhill, 1998). Notethat this is a "nite impulse response since it is limited toa "nite number of samples de"ned over a "nite range oftime intervals.

The calculated FIR is shown in Fig. 7. The y-axis inthis "gure has been scaled to give the change in speed foran impulse of magnitude 1 step on the AB valve steppermotor. The idle speed oscillations described in Section1 can be seen to have a period of about 2s, these oscilla-tions do not die away with time.

This FIR was used in Matlab/Simulink simulations asthe vector in a discrete "lter block.

4.2. Comparison of control schemes using MSE and ME

Fig. 8 shows a typical idle speed regulation test resulton an engine for PI control of the ABV and sparkadvance with P"0.03 for both loops and I"0.03 forthe ABV loop. The top graph of Fig. 8 shows the speedresponse, the middle graph shows the ABV motion and

the bottom graph shows the spark advance. Similar testswere performed for all the aforementioned controlschemes. The MSE and ME were calculated for each testand are tabulated in Table 1.

Table 1 shows the MSE values calculated from idlespeed regulation tests in simulation. The MSE values ofPI control and adaptive FLC control are not shown asunstable control resulted in simulation. Instability result-ed for PI control as the gains were tuned for operation inconjunction with spark control. The instability that oc-curred without spark control demonstrates poor loopintegrity. Instability in the case of adaptive FLC wasfound to be a result of the system time delay in the inletmanifold air to speed loop. The MSE values for adaptiveFLC with Smith prediction (SP) and DMC are excellentand well within the speci"ed 203 rpm2 value. From thesesimulation results it appears that fuzzy logic control,adaptive fuzzy logic with SP and DMC possess goodcontrol integrity, i.e. acceptable idle control will resulteven in the presence of constant spark advance.


Table 2Comparison of computation and memory requirements for each con-trol algorithm in simulation

Type of control scheme Floating pointoperations

Number ofvariables

PI (P"0.03, I"0.03) 10 3Fuzzy 31 32Adaptive FL 52 34Adaptive FL#SP 1045 438DMC 374204 6802

Table 3Technical speci"cations for the test vehicle

Engine 1.8i 16 valve

Capacity (cc) 1761Cylinders 4 in lineBore and stroke (mm) 83]81.4Max power DIN (hp/rpm) 112/5500Max torque (lb ft/rpm) 114/4250Cooling system Liquid with electric cooling fansFuel system Multipoint electronic fuel injectionTransmission 5-speed manual

Table 1 also shows the maximum error values cal-culated from simulation. The trends observed in the MSE"gures are repeated. The PI control and adaptive FLCare unstable control and the other results are well withinthe speci"ed upper 50 rpm ME bound for smoothrunning.

4.3. Comparison of memory requirements and computationtime

Due to the limitations of the vehicles engine manage-ment system microprocessor, memory and computationtime requirements were calculated for each controlscheme using MATLAB. Table 2 shows the comparisonof memory and computation time for each controller.Computation time refers to the number of Floating PointOPerations (#ops) required by each control algorithmduring each sample interval.

The memory requirements shown in Table 2 are takenfrom simulation studies based upon the simulation re-sults shown above.

It should be noted that the number of variables can beincreased or decreased for some of the above controlschemes. Therefore, the values quoted are the ones thatproduced the simulation results reported in the previoussimulation sections.

4.4. Summary of simulation results

The results of the simulation work support the litera-ture (Hrovat & Sun, 1996) in that it shows that theexisting PI control used in production automobiles canbe improved upon. The advantage to be gained fromimproved ABV control is that less control e!ort will berequired from spark advance (SA) which in turn, can beset at the MBT value and so o!er better fuel economyand improvements in idle stability. The trade-o! is theneed for additional EMS memory and an increase in#ops.

Surprisingly, these simulation studies have shown thatWang's adaptive FLC is not suitable for idle speed con-trol. However when used in conjunction with Smithprediction this technique has been shown to produce

good performance indices (see Table 1). Elsewhere, it hasbeen shown that this adaptive FLC with Smith predic-tion, when used for idle speed control, is robust to model-ling errors in the delay model used for Smith prediction(Thornhill, 1998). This suggests that the closed-loop sys-tem is bene"ting from some phase advance in addition todelay compensation (Santacesaria & Scattolini, 1993).

On the basis of these tests the DMC results appearsuperior to all the other controllers. This is not surprisingin that there was an exact match between the plant andthe model. However, at the moment the memory require-ments and number of #ops required would not make theDMC a practical alternative.

5. Engine tests

The following engine test results, taken from test ve-hicles, were performed on fully warmed up engines. Forthe tests, which included spark advance, the existingproduction spark controller was used. This consisted ofa simple proportional controller with the proportionalgain set at 0.03.

Due to memory and speed limitations of the enginemanagement system (EMS), it was impossible to test theadaptive fuzzy logic controller with Smith prediction orthe DMC controller.

In all the tests the objectives are to "nd foreach controller the performance measures detailed inSection 3.

5.1. The test vehicle

The test vehicle was a standard production vehiclecommonly found in Europe and having the technicalspeci"cations given in Table 3. A Sagem s2000 Develop-ment Engine Management System was used for the de-velopment of all controllers.

5.2. Comparison of control schemes using MSE and ME

Table 4 shows the MSE values calculated from enginetests using constant spark advance. This table shows


Table 4Comparison of control schemes during engine testing with constantspark advance

Type of control scheme MSE ME

PI (P"0.03, I"0.03) 42575 487Fuzzy 815 83Adaptive FL Unstable Unstable

Table 5Comparison of control schemes during engine testing in conjunctionwith proportional spark control

Type of control scheme MSE ME

PI (P"0.03, I"0.03) 203 50Fuzzy 176 50Adaptive FL (start) 363 47Adaptive FL (end) 168 39

Fig. 9. Simulation responses for disturbance rejection of the fuzzycontroller with constant spark advance.

exactly the same trends as the simulations (Table 1) withthe exception that marginally stable control is achievedfor PI control of the ABV. Adaptive FLC with Smithprediction and DMC are not shown, as it was notpossible to code the control algorithms due to EMSlimitations.

Table 4 also shows the maximum error values cal-culated from engine tests. The same trends as seen insimulation (Table 1) are shown here with the exceptionthat PI control does not go unstable but remains margin-ally stable, this is probably due to the use of a linear modelin simulation to represent the nonlinear idle speed system.

Table 5 shows test results from the aforementionedcontrol schemes in conjunction with the spark controlscheme provided with the production vehicle tested. Nosimulation results for these forms of control are available.Although the adaptive FLC controller went unstablewith constant spark advance, once tuned it outperformedthe production controller. The di!erence between theadaptive FLC value for MSE between the start and end is50 s of adaptation. However, there is no guarantee thatthis value would continue to improve (or stability bemaintained) but this form of control looks promising, asno on-line tuning is required.

Table 5 also shows the maximum error values cal-culated from engine tests. The values shown are verysimilar with the lowest maximum error value showntaken from the end of the Adaptive FLC test.

5.3. Disturbance rejection and entry to idle tests

This paper is primarily concerned with the comparisonof the ABV element of an IS controller. However forcompleteness it seems appropriate to brie#y considerdisturbance rejection and entry to idle, which addition-

ally require spark advance control and various feed for-ward loops. In all of the engine tests performed there wasno attempt to retune the proportional spark advancecontroller supplied with the vehicles EMS or modify anyof the feed forward loops.

On the vehicle the disturbance rejection tests provedproblematic. Since all the controllers performed well itproved impossible, from the available traces, to identifywith any certainty the initiation of a disturbance or theresulting transient.

The simulation model is only valid for a constantspark advance set at 100 BTDC. Therefore the onlycontroller that could be tested using simulation was thefuzzy logic controller. Fig. 9 shows the fuzzy logic con-trollers ability to reject a sudden drop in speed of100 rpm, and Fig. 10 shows its ability to track a referencesignal into idle. Using linear controllers, if the enginespeed is suddenly required to drop from some high levelto idle (step input) then the speed will invariably under-shoot unless the controller is heavily overdamped. Toavoid this some smooth curve, like the decaying referencespeed shown in Fig. 10, is normally produced and thesystems ability to track this curve examined.

Fig. 11 shows the response of the production vehiclesPI controller on entry to idle. In this test the throttle wasdepressed and released suddenly. The speed response isthen allowed to decay naturally to 1500 rpm, at whichspeed the idle reference speed starts and decays linearlyto the nominal idle speed of 864 rpm. A similar test wasperformed with the fuzzy logic controller and producedthe responses shown in Fig. 12.

Some comments on the disturbance rejection andentry to idle tests:

1. In the experimental test the PI controller when com-bined with the proportional spark advance controller


Fig. 10. Simulation responses for entry to idle of the fuzzy controllerwith constant spark advance.

Fig. 11. Engine responses for entry to idle of the PI controller.

Fig. 12. Engine responses for entry to idle of the fuzzy controller.

clearly performs well. This is to be expected since thesystem was tuned for this controller combination.However, the results would suggest that this controlleris at the limits of its development in that in order toachieve the indicated performance loop integrity hasbeen compromised (that is failure in the spark loop,resulting in a constant spark advance, may cause idlespeed regulation instability).

2. The fuzzy logic controller, Figs. 9 and 10, appears tohave good disturbance rejection and tracking proper-

ties even without spark advance control. This suggeststhat a production ISC using a fuzzy logic controllerwould be less dependent on spark advance and havebetter loop integrity.

3. Although the simulation results shown in Fig. 10 havebeen produced by the linear FIR model described inthis paper the results have been checked using a neuralnetwork model validated over the engines operationalrange. Both models show similar trends.

4. The experimental results for entry to idle using thefuzzy logic controller, Fig. 12 are inconclusive. Theproblem appears to be that the air bypass valve wasnot resetting itself and therefore most of the controle!ort is being provided by the spark advance loop.Similar results and a similar problem were encoun-tered when testing the adaptive fuzzy logic controller.Note that the simulation results in Fig. 10 have as-sumed that the air bypass valve is reset.

5.4. Summary of engine test results

Due to excessive memory and speed requirements (seeTable 2), it was found that some of the controllers couldnot be tested on the engine.

The controllers tested were PI, fuzzy, and adaptivefuzzy. Observations made during the tests and presentedin this paper indicate that:

1. The idle speed system at open loop naturally oscil-lates; the frequency and amplitude of speed oscilla-tions are dependent on the engine speed.


Table 6Comparison of controllers from simulation results

Best control Adaptive Localmemory

Humanknowledge

Comp.simplicity

Modelrequired

Integrity ofcontrol

PI 5 1Fuzzy 3 Y 2 YAdaptive FLC 6 Y Y Y 4Adaptive FLC#SP 2 Y Y Y 5 Y YDMC 1 6 Y Y

2. Of the control schemes tested on the vehicle withconstant spark advance, only fuzzy control providedacceptable idle speed control (as predicted by simula-tion), from the point of view of idle speed regulation.Given that the fuzzy logic controller is stable withconstant spark advance it was surprising that theadaptive FLC was not.

3. Of the control schemes tested in conjunction withspark control, all algorithms performed well withfuzzy control and adaptive fuzzy control outperform-ing the production controller in the baseline regula-tion tests (see Table 5).

4. In simulation, fuzzy control, adaptive FLC with Smithprediction and DMC showed integrity of control withregard to failures in the spark loop that would causea constant spark advance signal.

5. The results from engine testing showed good agree-ment in their general trends with the simulation re-sults, giving con"dence in those simulations that couldnot be tested on the vehicle e.g. adaptive FLC withSmith prediction and DMC.

6. Discussion

As only some of the proposed controllers could betested on the vehicle, and the simulation and test resultscorrelated well, the following comparison is based onsimulation results. The simulation performance of eachcontroller, summarised in the above sections, are com-pared in Table 6 under the following headings:

Best control: The controllers are ranked from best (1) toworst (6) based on simulation results of ABV control.

Adaptive: All controllers that possess adaptation char-acteristics are marked with Y.

Local memory of controller: All controllers that possesslocal memory (Thomas & Armstrong-HeH louvry, 1995)are marked with Y. This corresponds to adaptive con-trollers only.

Incorporation of human knowledge: Whether or nothuman rules can be included in the controller (e.g. fuzzylogic).

Computational simplicity/ memory required: Controllersare ranked from the simplest (1) to the most complex (6).

Model required: If the controller requires a model of thesystem, it is marked with an Y.

Integrity of control loops: Whether the control withconstant spark advance is acceptable (Y).

Based upon Table 6, DMC control is cited as the bestcontrol scheme based on the mean-square-error andmaximum error values calculated from simulation (seeTable 1). However in a real system, adaptive FLC withSP would be the preferred control scheme, see advant-ages of adaptive FLC with SP listed in Table 6 that DMCdoes not possess. Fuzzy control would also be a viablealternative to the production controller (particularly ascomputational simplicity is required with the currentEMS).

Further, fuzzy logic is a more natural scheme to dealwith non-linear systems due to its ability to approximatenon-linear functions to arbitrary accuracy (Wang, 1994).The local memory of adaptive fuzzy logic allows verydi!ering control e!orts to be applied at di!erent areas ofthe input space without a!ecting the control learnedelsewhere, this prevents unlearning of previous informa-tion as di!erent regions of the input space are entered. Itwas found during training of adaptive fuzzy logic systemsthat it was necessary to use triangular input membershipfunctions as Gaussian input membership functionsspread over the entire input space causing unlearning ofinformation through leakage e!ects (i.e. every inputmembership functions was always "red to some degree).The local memory property ensured that the controlquality always improved over time. In conjunction witha temperature input, the entire control surface for allengine-operating temperatures could be learned adap-tively.

Based on test results obtained from the engine withconstant spark advance, fuzzy control achieved the bestperformance indices (see Table 1). This result however isbased solely on the particular choice of output member-ship functions that were used for testing.

For test results in conjunction with spark control, theadaptive FLC outperformed all other controllers andwas improving throughout the engine test. This wasa surprising result in that the same controller was unsta-ble with constant spark advance (see Table 5).


7. Conclusions

f Five control schemes (PI control, fuzzy control, adap-tive FLC, adaptive FLC with SP, Dynamic MatrixControl (DMC)) have been tested in simulation andcompared in terms of performance for idle speed regu-lation. The results of these comparisons are shown inTable 1 using mean square error and maximum erroras performance measures.

f Application of adaptive fuzzy logic to control of theABV is presented. Use of adaptive fuzzy logic anda constant spark advance results in unstable controlfor all controller learning rates.

f Control of the ABV using adaptive fuzzy logic inconjunction with proportional (P) control of the sparkadvance results in superior control of idle speed regu-lation relative to the production controller on enginetests.

f Actual vehicle results comparing fuzzy logic, conven-tional PI control and adaptive FLC (with constantspark advance and with proportional spark control)are presented and shown to broadly agree with thesimulation results.

f A novel control scheme based on adaptive fuzzy logicand Smith prediction is introduced, this scheme showsexcellent promise in simulation.

f Using state of the art EMS technology, it was deter-mined that DMC and adaptive FLC with SP couldnot be programmed in this instance due to excessivememory and speed requirements.

Acknowledgements

The authors wish to thank SAGEM, Birmingham forsupporting this research project.

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