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so I have a turbo 89 mk3 supra and it's the block is na everything esle turbo and the harness is a different year than the engine and body., im running into the issue of my supra having a rough idle and I think it could be crankshaft timing because me and my father have changed the messed with the cps and got the best result so far before hand the turbo would pull 8lbs of boost but whenever the wastegate open the car doesn't make anymore power as if the wastegate acted like a rev limiter and it was limiting around 3500-4000 rpm and had a high idle. After we adjusted the cps it would pull the same 8lbs but this time it would limiter after 5000-5500 rpm but now it has a rough idle.
 

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Disconnect the battery. Then set the engine to TDC on the cam gears, then pull the spark plug on #1 and verify piston TDC on cyl #1. You can use a long screwdriver down the spark plug hole, and rotate the engine via a ratchet or breaker bar on the crank pulley bolt a few times to visually observe exactly the middle of where it tops out at TDC. Compare that to 0* marked on your crank pulley. If you're within 2-3* of 0 you're not a tooth off on the timing belt, it'll be WAY off if it's off at the crankshaft. If it's off somewhat less, it might be a tooth off at the cam gears. It will be visually obvious to compare TDC #1 with the screwdriver and TDC on the cam gears when you're on that cycle of the engine's rotation (cams spin once for every 2 rotations of the crank).

Assuming the cam gears are at an obvious TDC with the notches on the backplate and the #1 piston is obviously at TDC, then you need to set base timing with the CPS. Jumping pins T1 and TE1 in the diagnostic block will allow you to use a timing light on cyl #1 and verify base timing, It should be 10* BTDC. If you can't adjust the CPS physically to 10* BTDC and still bolt it to the head, you need to pull the CPS and re-stab it into the engine. Do this at TDC on the cams and there's notches in the CPS to align for base timing.
You can look up the Toyota style procedure in the Cygnusx1 TSRM if you Google that.

Given that you've changed the behavior with CPS adjustments, I'm fairly sure it's related to mechanical timing and CPS setting as you've already figured. I just hope your CPS isn't wildly advanced or anything and resulted in insane amounts of timing advance, which in turn would potentially fry your engine even at 8psi.
 
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