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MegaMeet 2009 Atlanta. X-Tau Transient Fuel Compensation Bowling & Grippo. Transient Enrichments ??. Transient Enrichments . When an Internal Combustion (IC) Engine is operating at the same RPM for a given period of time, this is known as “Steady-State” operation.
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Transient Enrichments • When an Internal Combustion (IC) Engine is operating at the same RPM for a given period of time, this is known as “Steady-State” operation. • When the RPM changes, or the load changes, the period of time to get the final steady-state point is known as a “Transient” – a.k.a. acceleration or deceleration….. • Transients occur very frequently in the operation of an IC engine. • Engine transients require different control methods compared to steady-state operation….. And they are tricky to adjust….
Transient Enrichments • When the throttle is opened up, or there is an increase in load, the engine experiences a momentary “lean” condition that last for a fraction of a second or longer. • Conventional methods (i.e. carburetor) would compensate for this by squirting in extra fuel – remember the “accelerator pump”?
Transient Enrichments • The carburetor has an “accelerator pump” circuit which has a lever operated off of a cam that is attached to the throttle shaft. • The lever actuates a diaphragm that acts on a reservoir of fuel, this fuel is pushed up a tube to the nozzles. • There are squirter nozzles that inject the fuel into the airstream. • To adjust the accelerator pump, you need to: • Change the cam profile (squirt profile) • Change the spring on the accelerator pump lever (duration) • Drill out the squirter nozzles (quantity of fuel for squirt).
Transient Enrichments • With the introduction of electronic fuel control systems, fuel can be controlled much more accurately than with pumps, levers, and squirters. • With EFI, there is still the need for adding additional fuel during an acceleration event. • In a similar fashion, during deceleration situations it is desirable to reduce the fuel delivered. • The computer needs to determine when to apply the additional fuel (or reduced fuel), and how much to do so. • Traditional ECUs employ methods that simulates accelerator pump circuit on the carburetor. This is known as Acceleration Enrichment and Decel Fuel Cut.
Acceleration Enrichment • Traditional Acceleration Enrichment Ramp: Fuel (ms) Time Ramp Up Duration Decay • Event is triggered either by a throttle change or MAP change. • Decel is the opposite of above. • Temperature dependent….
Transient Enrichments • But…. You have to ask the following question: Why do you need extra fuel when you accelerate?
Transient Enrichments • Investigations into the reasons for acceleration enrichments were a hot topic for many years, along with much speculation. • In 1981, Charles Aquino published a paper in a SAE journal entitled “Transient A/F Control Characteristics of the 5 Liter Central Fuel Injection Engine (SAE 910494). • This innocuous paper outlined a simple algorithm for the effects of wall wetting of fuel as it leaves a fuel injector. • The algorithm in the paper used two symbols, X and Tau, to denote the parameters used in the algorithm – hence the name. Much simpler than the Shoot more fuel method used in conventional acceleration enrichment. • This paper is the beginning of Model-Based Control Methodology of Internal Combustion Engines.
Wall Wetting • When fuel is injected, the goal is for the complete “shot” to enter the cylinder. • The reality is that some fuel clings to the intake port runners, valve, etc., on every injector shot of fuel…..
Wall Wetting • Fuel clings to the runner, producing puddles…. • For every shot, part of it gets into the cylinder, and the rest of it just clings…. • The part that clings in the puddle on every injector shot is called “X”
Wall Wetting • So for every injection a certain percentage clings to the walls and the rest get into the cylinder: Minjected = (1 – X) * Msquirted • Where Minjected is the actual fuel that gets into the cylinder on this squirt, X is the percent of fuel that clings to the walls, and Msquirted is the amount of fuel that the fuel injector delivers. • Example – assume X is 30% and Msquirted is 10 milligrams of fuel from the injector: Minjected = (1 – 0.3) * 10mg = 7mg Less fuel actually got in!
Wall Wetting • OK – then this means that on every shot, the puddle must have: Mpuddle = X * Msquirted • Where Mipuddle is the fuel puddle mass, X is the percent of fuel that clings to the walls, and Msquirted is the amount of fuel that the fuel injector delivers. • Example – assume X is 30% and Msquirted is 10 milligrams of fuel from the injector: Mpuddle = 0.3 * 10mg = 3mg • The mass of fuel in the puddle must be accounted for (known as Conservation of Mass) – and with fuel prices the way they are today every drop matters!
The Puddle • Great - we know how much fuel gets into the cylinder on every shot and how much clings in the puddle. But here is a question: Where does all of the fuel in the puddle go? • Conservation of mass applies here – the puddle does not just disappear, it eventually evaporates back into the airstream and back into the cylinder. • This is the genius of the Aquino method – it keeps track of how much fuel is in the puddle, and how much is getting added on every injector squirt, and how much is evaporating back in the air.
The Puddle…. • Fuel clings to the runner, producing puddles…. • The puddle will evaporate back into the airstream… • The time it takes for the fuel deposited in the puddle to evaporate is “Tau”.
Puddle Mass • On every injection event, along with the fuel that gets into the cylinder, some additional fuel is added from the puddle that is evaporating: Minjected = Mpuddle/(Tau/dt) • Where Minjected is the additional fuel that gets into the cylinder on this squirt from the evaporating puddle, Mpuddle is the mass of fuel in the puddle, and dt is the time elapsed since the last injection pulse. • Example – assume Tau is 0.4 sec, Mpuddle is 10 milligrams of fuel, and dt is 0.2 seconds: Minjected = 10 mg / (0.4/0.2) = 5 mg
The Entire X-Tau Model • We now have all contributions to the X-Tau Model • First, the part that gets in the cylinder: Minjected = (1 – X) * Msquirted + (Mpuddle / (Tau/dt)) • Next is the part that is in the puddle after the squirt: Mpuddle_after = X * Msquirted - (Mpuddle/(Tau/dt)) • This is the complete model, in discrete form. It indicates that on each squirt part of the fuel gets in the cylinder and the rest (amount X) goes to the puddle. At the same time, the puddle evaporates and goes back into the airstream (at a time rate Tau).
The Entire X-Tau Model How do we know that the puddling of fuel really happens?
A Few Things to Note: • The X-Tau wall-wetting algorithm is strictly a fuel-only operation. It operates on commanded changes in injector pulsewidth. There is no air dependence. • There are logical X and Tau pairs which are stable… if the X is too large (meaning most fuel clings to walls in every shot) or Tau is too long (it never evaporates) then there can be a runaway situation where the puddle mass grows and grows. See the MegaManual for good settings to keep out of these non-physical situations. • There are threshold values where the change in injector pulse (from the previous one) has to exceed before the algorithm is used – this is due to errors in fuel calculations, bit-noise, round-off errors, accumulation errors, etc.
The X-Tau Model OK – How do I come up with the X and Tau values for my engine? • First - before determining X and Tau, you must have your entire Volumetric Efficiency (VE) table calibrated (tuned). • Second – go back and make sure the VE table is tuned Your VE Table MUST BE TUNED before attempting to calibrate ANY transient accel/decel condition.
X = 0.3 Tau = 0.4 seconds X-Tau Tuning • It turns out that for many cases, a good starting point for a warmed up engine is: • Cold engines and higher RPMs will change the values of X and Tau. • There are several different rules of thumb on the effects of RPM, temperature, etc. depending on researcher…. • Rate of throttle opening is not a big effect on values.
X-Tau Tuning • Shayler (SAE #950067) came up with a set of curves that illustrate X and Tau dependence on engine coolant and engine RPM. Also has dependence on AFR. • Graphs can be used as a good “scaling” tool from the base X and Tau numbers. • Approach is to offset the number on the graph by what you determined X and Tau to be at fully warmed-up situation.
Variation in X as function of coolant and different AFR setpoints
Variation in Tau as function of coolant and different AFR setpoints
Throttle-Stomps • The throttle-stomp method can be used to implement the transient variations and allow the effect of different X and Tau values to be determined. • Semi-rapid acceleration and deceleration events are invoked while monitoring the O2 reading. • Adjust X and Tau to minimize excursions in AFR. Adjust ONE VALUE AT A TIME and note the effect. • Note that there are other effects that will fight you, most notably manifold filling/emptying effects (be sure come to the next MegaMeet to learn about the “air side” of things…). • Finally UEGO sensors will not react fast enough for radical stomps. Since throttle rate does not affect X and Tau very much, use slower opening rates….
Step-Fuel Perturbation • Step-fuel Perturbation mode is where the pulsewidth is increased by a certain amount for a given time, then restored to original value. • The step-fuel increase and decrease in pulsewidth triggers the X-Tau algorithm. • Using exhaust O2 readings the amount of deviation in AFR can be visualized. • Change X and Tau to minimize the excursions. Change one variable at a time. • Step-fuel Perturbation is a mode within MSII software. • Throttle stomp method may be easier with limited diagnostics.
Notes on UEGO Sensors • Everybody just loves their Wideband O2 sensors (UEGO) and they treat the O2 readings as gospel…….. • However, keep in mind that there inherent delays and inaccuracies in any UEGO setup…. • Tune to the deviations in AFR during transient correction, not the absolute value of the reading. Minimize the deviations. • Deviations in a narrow-band O2 sensor’s voltage can also be used, and may react faster as compared to UEGO.
