By JORDAN LEVIN

Wilco leader Jeff Tweedy is negotiating with the unexpected again. On this recent weekday morning, his 10-year-old son’s school has closed due to a water-main break, so Tweedy is driving him back to their Chicago home, juggling an interview with a reporter and other demands of being a famous rock artist while dealing with his youngest son’s sudden liberation. “Yeah, he’s having the best day of his life,” Tweedy says. “We had to rearrange everything.”

Then again, Tweedy and Wilco — who play the Fillmore Miami Beach on Monday — have been rearranging their music for more than 10 years, against a dramatic and sometimes controversial history. That story has included being lauded as indie champions of artistry, after being dropped by their label for refusing to change their music. Tweedy has kicked addictions to alcohol, marijuana and painkillers for crippling migraines, as well as even more crippling depression and panic attacks. Last year, his former creative partner in Wilco, Jay Bennett, sued him for breach of contract, then died of an accidental overdose of painkillers, an eerie echo of Tweedy’s struggle.

So if Tweedy, 42, is a tad defensive about Wilco’s latest self-titled album’s sounding mature, he’s got his reasons. “If you say that it’s a record made by people who are grown up, I think that’s a revolutionary act in rock music,” he says. “Growing up is absolutely maligned in rock music. But I’m here to tell you it’s not so bad.”

For Tweedy, growing up doesn’t mean losing his creative edge — just that it doesn’t need to be quite so jagged. “You have a better ability to concentrate and work and keep things in perspective,” he says. “You have a deeper comfort level with ambiguity and not knowing.

“I still feel as curious and interested in exploring other approaches to music making as I’ve ever felt.”

Chicago Tribune pop music critic Greg Kot, who wrote the book Wilco: Learning How to Die in 2004, says the group has never stopped experimenting.

“The great downfall of a lot of bands is once they find the formula for success, they repeat the formula,” Kot says. “Wilco has made seven studio albums, and not one sounds like the other.”

Kot says he believes the key to that continuing creativity is Tweedy’s musical curiosity (he’s a fan of everything from 1960s folk rock to experimental electronic music) and emotional honesty.

“There’s an insight in his songs,” Kot says. “Every song is about him but is also able to find a universal thread.”

Tweedy’s musical journey started in the early ’90s, when he co-founded the seminal alternative country band Uncle Tupelo. That group broke up in 1994, and Tweedy started Wilco, garnering attention with the band’s second album, 1996′s Being There.

But it was 2002′s Yankee Hotel Foxtrot that put Wilco on the musical and cultural map. Its label, Reprise, dropped the group after the band refused to remake Foxtrot, which was filled with dissonant experimentation and pained, haunting lyrics, into something more commercially palatable. Wilco streamed the album on its website before signing a new deal with its current label, Nonesuch — a now-common move that was controversial at a time of intense debate over music sharing on the Internet.

Foxtrot became Wilco’s biggest success, selling more than half a million copies and earning critical raves. And Wilco has been under pressure since then, from critics and music fans who expect the group to keep pushing the envelope.

Meanwhile, in the years surrounding Foxtrot, Tweedy’s migraines, which he’d had since childhood, got so bad he had to keep a bucket offstage so he could throw up between songs. In 2004, he ended up in rehab to kick the painkillers and to deal with the closely related, longtime issues of depression and panic attacks.

“I don’t know what my music would have been like if I had continued,” Tweedy says. “There probably wouldn’t have been any.”

Kot says that before rehab, Tweedy was close to collapse. “I’d see him onstage looking absolutely wrung out, 15 years older than he was,” Kot says. “Fans who say the music hasn’t been as good since he got off drugs and got normal, they root for that myth of strung-out desperation as what rock ‘n’ roll has to be.”

Tweedy says he still deals with the notion that rock creativity is fueled by abuse. “People usually look at it as somehow the drugs are where the inspiration, the feeling comes from,” he says. “That’s absolutely misguided.

“There was an old assumption that my problems were part of who I was creatively. I feel like I created in spite of those things. . . . I’ve gotten more comfortable with being in my skin, and that has allowed me to be more comfortable with doing what I do well.”

The mood on Wilco (the album) is far more accepting than despairing. Darkness may lurk in “Bull Black Nova”, in which the protagonist has committed some mysteriously terrible act, but most songs, if not outright hopeful, acknowledge that love and determination can compensate for a lot of inevitable pain and surprise.

“Remember to show gratitude,” Tweedy sings in “Sonny Feeling”. “The darkest night is nothing new.” In “You Never Know”, such lines as “Come on children; you’re acting like children; every generation thinks it’s the end of the world,” seem to be his response to young critics who demand permanent musical rebellion. But on “Wilco (the song)”, he has some fun offering “a sonic shoulder for you to cry on” to those listeners who “dabble in depression. . . . Wilco will love you baby.”

After all, Wilco has kept Tweedy going.

“There’s worse strategies,” he says, “than turning to your music for consolation.”