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I think they are actually weeds but the roots are edible - dense and high caloric . When the bolsheviks were starving the Ukrainians back in the 1930’s , they stole all of their harvests , especially all of the potatoes . Apparently the Jerusalem artichokes were wild so the bolsheviks didn’t steal them or dig them up and many Ukrainians survived on them . There is a problem with storage however - I leave them in the ground until just  before the first frost and put them in buckets and cover them with sand - weird , I know but it’s the only way to keep them.the plants also have pretty yellow flowers at the end of August . Mine are about 6 feet tall.
Actually they taste good , but are pretty gassy! I think it’s a common complaint . I look at them as survival plants . They just grow and grow like weeds

It is a real struggle, I empathize with you! I really struggled in the garden when my oldest 3 who are very close in age were very little.

With the baby this year, I have learned never to discount what can be done in 5 to 10 minutes. Recently I canned some pickles. It was an all day ordeal. Pick in the morning when her and I are the only ones up. Nap. Wash cucuмbers while she naps. Stop to cook everyone breakfast. Eat breakfast, feed and play with baby. Nap. Cut the ends of the cucuмbers while she naps. She wakes up early, so I have to hold her for the rest of the nap, then pack cucuмbers into jars for a few minutes until she starts fussing. Etc etc until the pickles come out of the canner at 7 pm.   The ONLY way that I can get any garden work/preserving done is to take the short amounts of time and do the best I can.

Freezing and freeze drying is far less time consuming, but freeze drying is not the best option for everything that comes out of the garden.

Today I threw together a gallon jar of cucuмbers and herbs/spices to make fermented pickles. That is perhaps the fastest (and healthiest) way to preserve the garden bounty.