I need to learn the detailed step by step wahing machine programmes. Not general knowledge, I made research but could not find any.
There are lots of flowcharts explaining the basic steps. Basically, you are controlling a state machine with a water intake, a drum and a water discharge pump as well as other smaller pumps or valves for detergents etc. As you say, each machine is a bit different. If I were to build a firmware without prior knowledge, I would befriend a good mechanic who services these machines. It is a whole industry on its own. Since it is a big market, some washing machine parts are even used in other industries as they cost a fragment of what it would cost elsewhere.
Having said that, everything has already been very well established and there must be little room for yet another washing machine.