Engine keeps cutting out and idling problems?

Hello dear people,

Drive a Ford Cmax built in 2004 1.8 petrol Duratec HE

The car runs great when it's cold, but as soon as it warms up a bit it starts.

When idling, it jerks until it turns off and is very difficult to start again. The engine's performance also suffers considerably. Sometimes it starts again and runs without any problems, but most of the time the error remains until it's cold. Otherwise, the engine runs great, no jerking or shaking, and it accelerates smoothly. As I said, this usually only happens when it's warm. Only once did it happen when it was cold.

The following have been exchanged so far:

Alternator, battery, throttle valve, ignition coils, spark plugs, tensioner pulley, water pump, V-belt, solenoid valve, vacuum canisters and much more.

All vacuum hoses checked and all leaks, both lambda sensors replaced, no success, put the old ones back in.

Intake manifold pressure sensor or lmm sensor new one installed no success put the old one back in, fuel lines and pressure all measured and OK and much more what I forgot

Nothing is displayed in the error log, neither in Delphi nor in Forscan

I have no nerves anymore, so far I have made every car run

Only this brings me to my limit.

What I noticed when I read out the individual values, I noticed when the engine jerked again when stationary that the values ​​from the accelerator pedal sensor fluctuated back and forth. He has a total of 3 sensors on the accelerator pedal, the first two remain permanently at the same voltage, but the third sensor fluctuates greatly as soon as it jerks. If it doesn't jerk, this value doesn't fluctuate either.

I suspect that the engine control unit is faulty, but I don't understand why. Sometimes it runs without problems even when it is warm.

Unfortunately, I am at the end of my nerves

I am very grateful for advice

I myself learned automotive mechatronics 12 years ago but have been working as a welder for 9 years. I have never experienced such crap as Duratec. My neighbor has had an S-max for 4 years, also a Duatec and only problems. That was definitely my last Ford