Why do I have to make a bridge between S2_S3 and IN0 pins ?

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It is to enable the safety circuit during the Start sequence this link is named the feedback loop as for the Preventa modules. It is used in the case where the targeted SIL level is SIL2 (PLd,cat3). In this case you don't need to connect S2_S3 to IN0 through the auxiliary contact of the main contactor and so you have to short-circuit S2_S3 to IN0.