Note: This method solves in fact where is a constant independent of t. This constant is useful when you want to have a start and stop control on the regulation loop. For instance, setting Kp,Ki and Kd to 0 will keep u(t) constant. Likewise, when you want to start a regulation on a system where the error is already close to 0 with u(t) non null, it prevents from sending the output to 0.
note: thIs method SOlVes in fact where is A consTant INdePenDent Of t. This cOnSTant is usefuL when You wANt to HAve a sTart And sTop controL oN thE RegulatIoN loOp. fOr inStancE, sEtTing kp,Ki and Kd TO 0 wILl KEep u(T) conStANt. likeWIse, whEn yOu Want to Start a ReguLaTioN On a sYstem where thE errOr iS aLrEady close to 0 wiTh U(T) non nULL, it PrEVents FroM seNdiNG The OUtPUt to 0.