Air-Fuel Ratio Control in Spark-Ignition Engines

Presented to: Dr. Riadh Habash, Fouad F. KhalilPresented by: Ziad El Kayal, Hassan Fakih Umar Qureshi, Marc Topalian

How it Works Air and the fuel enter

the carburetor, then through the engine and finally past a senor

Using a sensor to measure the oxygen content of the engine's exhaust, the system keeps the fuel-air ratio very close to the proportion for chemically perfect combustion

References

“Air-Fuel Ratio Control in Spark-Ignition Engines Using Estimation Theory” Chen-Fang Chang, Nicholas P. Fekete, Alois Amstutz, and J. David Powell

“Development of a Transient Air Fuel Controller for an Internal Combustion Engine” Stewart P. Prince

“Digital Control of an Automobile Engine Air-Fuel Ratio System” Martin J. Dubois, Robert P. Van Til, Nicholas G. Zorka

“Individual Cylinder Air-Fuel Ratio Control with a Single EGO Sensor” Jessy W. Grizzle, Kelvin L. Dobbins, and Jeffrey A. Cook

“Design and Development of an ECU and its Air-Fuel Ratio Control Scheme” Myomgho Sunwoo, Hansub Sim and Kangyune Lee

Requirements

The controller must keep a fuel to air ratio of 1:14.7 (0.068)

The overshoot at the output must not be greater than 16%.

The settling time must be less than or equal to 10 seconds.

Required Characteristic Equation From the IEEE article, the maximum overshoot

required is 16% and the maximum settling time was 10 seconds.

Required Characteristic Equation: s2 + 2wnζs + 2wn

Through calculation we found ζ (damping factor) = 0.5 wn=0.8 rad/s

Therefore, set s equal to zero and find the poles, using the quadratic equation: s1=-0.4 + 0.4√3 i s2=-0.4 - 0.4√3 i

Open Loop Transfer Function

We needed to find a transfer function we could use to plot a root locus diagram

We found the open loop transfer function of our block diagram to get the following formula

(0.5t2Td + 0.5t1Td)s + Td

T1t2s2 + (t1 + t2)s + 1

Using constants from IEEE references we were able to plot the following root locus diagram The diagram allowed us to find the roots and poles of the transfer

function

From the diagram we were able to design the lead compensator

Root Locust Diagram

Design of Lead Compensator

Required Formula

Gc(s)= (s+z) / (s+p)

The zero is found from the previous calculations, z = 0.4 Use Root Locus method to find the value of the pole.

Draw straight lines from s1 to all the poles and zeros found on the root locus No need to use s2 because it is just a complex conjugate Find the angle at which the pole is located

∂1= 177 degrees∂2= 50 degrees)∂3= 5 degrees)∂4= 1 degree∂ = 19 degrees

Using +∂ -∂1 -∂2 -∂3 -∂4 -∂d=-180 degrees   ∂d=65 degrees

Using this we were able to find the pole which we used to design our lead compensator

Gc(s)= (s+0.4) / (s+0.6)

Open Loop Transfer Function Diagram

Closed Loop Transfer Function Diagram

Simulink Design

Simulink Closed Loop Transfer Function Diagram

Conclusion

Through research, we were able to design a controller to regulate the fuel to air ration in a spark-ignition engine with an overshoot of 11% and a settling time of 10 seconds.

We were able to accomplish the emission standards by adjusting the fuel to air ratio required by the IEEE paper.