Air-fuel ratio control method based on the modified proportional-integral controller and the Smith predictor

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Abstract

BACKGROUND: To meet modern emission standards for spark-ignition engines, it is necessary to maintain a stoichiometric air-fuel ratio (α=1.000) or an enriched mixture (α=0.995–0.999). To improve the precision of air-fuel ratio (AFR) control, feedback controller utilizing data from a lambda sensor, which is mounted in the exhaust system of the internal combustion engine (ICE), is employed. For stable and fast operation of this controller, the use of a standard proportional-integral (PI) control law is limited. This is due to the significant time delay between changes in the AFR in the ICE cylinder and the lambda sensor response. The time delay leads to over-accumulation of the integral component and, as a result, incorrect operation of the regulator.

AIM: Improvement of the accuracy of maintaining the air-fuel ratio (AFR, α) in the cylinder of the internal combustion engine through closed-loop control using a lambda sensor during transient modes.

METHODS: To achieve this aim, the proportional-integral controller has been modified with an exhaust system model that predicts the air-fuel ratio response to control actions — changes in the fuel supply quantity. This control approach is known as the Smith predictor. The research methodology is comprehensive. The main theoretical provisions were obtained through an analytical review, then verified using computational modeling, implemented for the internal combustion engine control system, and tested during engine test-bench trials.

RESULTS: The main results were obtained for the two spark-ignition engines: 4.4-liter V8 and 1.5-liter 4 cylinder. Both engines equipped by turbocharger and direct injection fuel system. The possible values of the exhaust system’s dynamic properties were demonstrated. For example, the time constant and delay for the operating mode — n=1500 RPM and relative air charge 0.3 can be T=0.23 s and θ=0.21 s. This leads to prolonged transient processes and overshoot when changing the target air-fuel ratio. It was found that thanks to the controller developed during the research, it is possible to eliminate the overshoot completely as well as to reduce the transient process time by 1.6 times.

CONCLUSION: The developed method for controlling the air-fuel ratio has confirmed its functional safety and effectiveness through the engine tests. This method can be utilized for the ICE control system of a vehicle. The results are most relevant for turbocharged spark-ignition engines with a wideband lambda sensor, but they can also be applied to diesel engines or spark-ignition engines with a threshold lambda sensor.

About the authors

Pavel V. Dushkin

Central Scientific Research Automobile and Automotive Engines Institute “NAMI”

Author for correspondence.
Email: pavel_dushkin@inbox.ru
ORCID iD: 0009-0006-2861-7434
SPIN-code: 7814-1836

Cand. Sci. (Engineering), Lead software engineer of the Software Center

Russian Federation, Moscow

Vladislav V. Kremnev

Central Scientific Research Automobile and Automotive Engines Institute “NAMI”

Email: kremnevvlad@mail.ru
ORCID iD: 0009-0006-2982-4785
SPIN-code: 2926-3228

Postgraduate of the Scientific and Educational Center, Software engineer of the Software Center

Russian Federation, Moscow

Sergey S. Khovrenok

Central Scientific Research Automobile and Automotive Engines Institute “NAMI”

Email: khovrenok@yandex.ru
ORCID iD: 0009-0005-8714-5193
SPIN-code: 1202-6843

Postgraduate of the Heat Engineering and Automotive Engines Department, Software engineer of the Software Center

Russian Federation, Moscow

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Supplementary files

Supplementary Files
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2. Fig. 1. Diagram of target air-fuel ratio distribution across operating modes of a turbocharged spark-ignition engine: Мк, engine torque, n, crankshaft rotational speed.

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3. Fig. 2. The necessity of rapid adjustment of the target air-fuel ratio during the exhaust system component overheat protection mode (4.4-liter V8 spark-ignition engine testing): tr, exhaust gas temperature; t, time; α, air-fuel ratio.

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4. Fig. 3. Functional diagram of a basic controller: T, time constant; θ, delay; s, complex variable; αdesired, target air-fuel ratio; αcylinder, air-fuel ratio in the cylinder (formed without delay); αmeasured, measured air-fuel ratio (formed through the first-order plus delay model); PI-reg, proportional-integral controller operating according to equation 1.

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5. Fig. 4. Transient process simulation: α — air-fuel ratio; 1, target air-fuel ratio (αdesired); 2, measured air-fuel ratio (αmeasured) with proportional gain KP=0.1 and integral gain KI=3; 3, measured air-fuel ratio (αmeasured) with proportional gain KP=0.1 and integral gain KI=1; t, time.

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6. Fig. 5. The transient process in a 4.4-liter V8 spark-ignition engine at n=1500 RPM, relative air charge rl=0.3: t, time; α, air-fuel ratio.

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7. Fig. 6. Functional diagram of the modified controller:: αdesired, target air-fuel mixture, mm0, raw (uncorrected) injected fuel mass; mm, final injected fuel mass, αpredicted, air-fuel ratio prediction in the exhaust manifold; αmeasured, measured value by the universal lambda sensor.

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8. Fig. 7. The ring buffer scheme: t1...tM, the time points when the αpredicted_i value is fixed; M, number of array cells.

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9. Fig. 8. Automated model tuning: αdesired, target air-fuel ratio; αpredicted, result of the tunable model operation; αmeasured, experimental data, Tmod; θmod, tunable parameters; t, time.

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10. Fig. 9. The optimization results for the operating point of the 1.5-liter 4-cylinder engine: 1, target air-fuel ratio; 2, simulated air-fuel ratio; 3, measured air-fuel ratio; t, time; α, air-fuel ratio; T, time constant; θ, delay.

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11. Fig. 10. Transient process graphs for the 1.5-liter 4-cylinder engine: a, air-fuel ratio controller off; b, air-fuel ratio controller in normal mode; c, no delay in the Smith predictor model; d, no delay in the Smith predictor model, incorrect time constant; 1, target air-fuel ratio; 2, measured air-fuel ratio.

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