ISA Automotive & Vehicular Division - 1996 Cleveland Symposium
REGRESSION MODELS FOR REAL-TIME CONTROL
OF INTERNAL COMBUSTION ENGINES
Dr.D.E. Ventzas(MIEEE, SMISA) [1]
Professor of Control & Instrumentation
TEI Lamia - Lamia 35 100 - GREECE
KEYWORDS
Engine, regression, speed,load, air to-fuel ratio, spark advance.
ABSTRACT
The paper presents regression models for internal combustion engines.It relates engine outputs i.e. performance,emissions and fuel economy to the engine, i.e. speed and load, and the real time parameters such as fuel-to-air ratio and spark advance.
INTRODUCTION
Open loop operating carburetor and distributor controls air-to-fuel ratio and spark advance in spark ignition engines. System theory can relate engine outputs i.e. performance, emissions and fuel economy to the engine, i.e. speed and load, and the real time control parameters such as the fuel-to-air ratio and the spark advance.
The above analysis results in closed-loop control of fuel-to-air ratio for modern carburetors, reducing the errors and parameter variations. Sensors nonlinearities result in non-linear effects (limit cycles) eliminated by suitable sensors models linearization. Peak cylinder pressure commands optimum spark ignition timing. Controller sensitivity in fuel-to-air ratio and atmospheric humidity variations is investigated.
CLOSED LOOP CONTROL
The open loop control scheme, closes by an operator, and is given in fig. 1.
wind, friction
disturbances
throttle
VSVeV
OPERATOR ENGINE
DYNAMICSDYNAMICS
Fig. 1. Automotive engine velocity control scheme
The inputs of the engine are:
ofuel-to-air ratioospark advance ospeed
othrottle % ocoolant temperature oheat transfer
ocompression ratioofuel ovalve timing
osurface-to-volume ratio and pistons stroke o ignition quality
oinlet air temperature, pressure and humidity
The outputs of the system are:
opoweroemissions
oexhaust temperatureocylinder peak pressure
oposition at peak pressure
The ranges and corresponding values of:
oengine speed [rpm],
o the ratio of the airflow at the given throttle and engine speed to the
airflow at the same engine speed with atmospheric pressure in the
cylinder [%],
o the fuel-to-air ratio divided by the stoichiometric fuel-to-air ratio, and
othe relative spark advance compared to the minimum advance for best
torque,
form an experimental parameter variation look-up table, for steady state engine steps. For a single cylinder engine, the performance characteristics are given in fig. 2. The scalar output y is difined as (Hubbard, 1975):
where,
a=constant vector (K x 1) f=vector function (K x 1)
x=vector inputs (control variables, engine operating point) (4 x 1)
i.e. with noise ni witth variance ó2
ory0=F . a + n
With least square estimates we get an estimate of a and covariance matrix:
Fig. 2, gives the performance map of a CFR single cylinder machine, at 1200 rpm with optimum spark, it presents dependencies of Brake Mean Effective Pressure (BMEP) and eqivalence ratio (fuel-air ratio/stoichiometric fuel-air ratio) v.s. air and fuel flow rates. r2 is the coefficient of determination at every regression step:
minimum advance for best torque 1200 rpm
3.0 lb/hr 50% airflow 75% airflow 100% airflow
60
fuel flow
rate (lb/hr)BMEP
40
20
1.1
Equivalence ratio
0.7
1.0 lb/hr
20 lb/hr 40 lb/hr
air flow rate (lb/hr)
Fig. 2. Performance characteristics of a single cylinder engine
(Cooperative Fuel Research)
The hydrocarbon concentration vs equivalence ratio at 1200 rpm, is given in fig. 3, (Hansel, 1970).
Fig. 3. Exhaust hydrocarbon vs fuel-air ratio/stoichiometric fuel-air ratio
The NO concentration v.s. equivalence ratio at 1200 rpm is given in fig. 4.
Fig. 4. NOx concentration vs fuel-air ratio/stoichiometric fuel-air ratio
The effective pressure vs equivalence ratio at 1200 rpm is given in fig.5.
Fig. 5. Mean effective pressure v.s. fuel-air ratio/stoichiometric fuel-air ratio
Horsepower
and fuel brake specific
consumption fuel consumption
indicated
horsepower
brake horsepower
friction horsepower
0 30 40 50 60 70 8090
minimum throttle openingthrottle opening
Fig. 6. Engine performance, fuel consumption v.s. throttle opening
The CO2 and CO concentration at the engine’s exhaust gases is measured by pyroelectric sensors, radiation absorption monitoring (Pattas, 1990).
Fig. 7. Radiation for CO2 (4.26 ì) and CO (4.66 ì) band
For the oxygen sensor the Nernst equation suggests that (Stamatellos, 1992):
where,
E=sensor electrodes voltageR= gas constant
T=sensor absolute temperatureF= Faraday constant
PO2=partial pressure of oxygen (ambient, exhaust)
The oxygen sensor step response is given in fig. 8.
Fig. 8. Oxygen sensor step response
The closed loop control scheme with sensors non-linearities is shown in fig. 9 (Wilkie, 1995).
sensor exhaust
output controller system gain time delay equivalence
ratio
sensor statics
sensor lag
Fig. 9. Closed-loop control scheme with non-linearities
A water-cooled pressure sensor is used; its specifications are in Table 1:
PRESSURE TRANSDUCER CHARACTERISTICSPmax / 500 atm
Tmax / 240 o C
Sensitivity / 11.09 * 10 -12 Cb / kp.cm -2
Natural frequency / 100 kHz
Damping / 0.35
Table 1. Pressure transducer characteristics
The spectra of pressure signals and the pressure signals in the cylinder are shown in fig. 10, 11 (Patterson, 1967, Vlachos, 1971).
Fig. 10. Frequency spectra of pressure transducer (a),
charge amplifier (b) and differentiation filter (c) output signals
Fig. 11. Window of derivative action filter applied on
cylinder pressure signal (b) once (c), twice (d) (900 rpm)
Signals differentiation accentuates signal details, but increases noise (that is removed by digital filters); this is usefull for fast signal processing and control.
CONCLUSIONS
The paper monitored the open loop operating controls in spark ignition engines. It related engine outputs i.e. performance, emissions and fuel economy to the engine, i.e. speed and load, and the real time control parameters such as the fuel-to-air ratio and the spark advance.
The above analysis resulted in closed-loop control of fuel-to-air ratio for modern engines, reducing the errors and parameter variations. Peak cylinder pressure commands optimum spark ignition timing. Controller sensitivity in fuel-to-air ratio and atmospheric humidity variations is investigated.
REFERENCES
1.Hubbard, Mont, Applications of Automatic Control to Internal
Combustion Engines, Ph.D, Stanford University, 1975
2.Hansel, J. G, A Turbulent Combustion Model of Cycle to Cycle
Combustion Variations in Spark Ignition Engines, Combustion
Science and Technology, vol. 2, no. 4, December 1970
3.Pattas, K. N, Automotive Technology, vol 1, Applied
Thermodynamics Laboratory, Thessaloniki, 1990
4.Stamatellos, A. M, Internal Combustion Engines, in Greek,
Thessaloniki, 1992
5.Venikov, J, Internal Combustion Engines, Mir Publishers,Moscow,
1982
6.Vlachos, N, A Statistical Analysis of Cyclic Variations in Spark
Ignition Engines, M.Sc. Thessis, Dpt. of Mechanical Eng, Imperial
College of Science and Technology, 1971
7.Patterson, D. J, Cylinder Pressure Variations: a fundamental
Combustion problem, SAE Transactions, 1967, p. 621
8.Wilkie, B. F, Frank R, Suchyta J, Silicon or Software: The
Foundation of Automotive Electronics, IEEE Vehicular Technology
Society News, pp. 17-20, August 1995
APPENDIX 1:Measuring engines parameters
PARAMETER / MEASUREMENTengine speed / 5.0 rpm
spark setting / 0.5 o
fuel flow rate / 0.03 0.07 lb/hr
air flow rate / 0.1 0.4 lb/hr
intake pressure / 0.1 ” Hg
torque / 0.1 ft.lb
intake temperature / 0.5 o F
exhaust temperature / 20 o F
peak pressure angle / 1.5 o
CO2 exhaust concentration / 0.75 %
CO exhaust concentration / 0.25 %
HC exhaust concentration / 6 ppm
NO exhaust concentration / 100 ppm
Table 1. Measuring engines parameters
D.E. Ventzas[2]is Control and Instrument Eng, Professor of Control & Instru-mentation in TEI Lamia, MIEEE, SMISA, MHITEN and his research interests are Process and Biomedical Instrumentation & Control; his recent activities lie in the field of Modelling, Simulation and Fault Tolerant Control Systems.
[1]D.E.Ventzas, Analipseos 124, Volos 382 21, Greec