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Zzzzz... ramblings on the infamous TPS
The set-up of your bike from the previous owner was fine... once you install
a DP ECU (included with all the Termi exhaust packages), the closed-loop
fuel injection mode is disabled, and so the O2 sensor can be removed and
capped off. Now that you have a full system (which removes the exhaust
catalyzer and the flapper valve), you definitely would not want to go back
to the stock ECU and the O2 sensor set-up. The bike is no longer emissions
compliant, but it should perform better, with more HP and improved throttle
response (although having somewhat less fuel mileage than a totally stock
Hyper would have).
The zero position of the Throttle Position Sensor is stored in the ECU, so when
you replace the ECU it is necessary to "teach" the new ECU where zero is with
a "TPS reset". It's a very simple procedure and can be done in your own garage
if you have the right electronic tool (either a TechnoResearch VDST software
package/$195, or the much more expensive Ducati diagnostic shop tool).
The "zero" position of the throttle plate "butterflies" is set to 3.2 degrees open
at the factory, and this is allows enough airflow past the throttle plates for the
engine to idle properly. None of these mechanical settings need to be messed
with when you are changing the exhaust, typically. The TPS reset merely
stores a number in the ECU which is the reading from the TPS with the
throttle plates at their zero position.
Since the ECU only "knows" what the throttle opening is by the voltage read
from the Throttle Position Sensor, it is very helpful to have a calibrated
starting point! Once the amount of throttle opening is known by the ECU,
it uses that number in determining what the fuel injection duration and timing
should be. A small error in the zero position, while not significant at wide
open throttle, can be very significant at small throttle openings. A typical
fuel injection map has an increasing number of changes to the settings table
as throttle position drops below 15% or so, to keep the engine (and the rider!)
happy at part throttle, no easy task on some machines.
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'08 Hyper "S" w/ a few tweaks 
'05 Yammie WR-Supermoto conversion
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