“This is the first time we’ve been here,” proclaimed Cheap Trick guitarist Rick Nielsen Thursday night in Plymouth, “and we’ve been everywhere in the world.”

Since 1974, Cheap Trick has played round the world and regularly in the Twin Cities — from First Avenue to the Minnesota Zoo to Target Center. But this was the first time at Hilde Performance Center, an amphitheater in a hilly city park in the western suburbs.

Since the stage with a roof was constructed in 2004, Hilde has hosted the Minnesota Orchestra annually. Last year, Plymouth tested the rock waters with Colorado’s cult-loved Big Head Todd & the Monsters. And this summer they upped the ante with Cheap Trick, the veteran Rockford, Ill., quartet that was inducted into the Rock and Roll Hall of Fame this year.

These hard-touring Midwesterners mix hard rock, hot guitar licks and humor into a crowd-pleasing show. They come from the School of Rock that says music should be fun, fast and loud — and sound like the Beatles, David Bowie, Led Zeppelin, AC/DC, all your childhood favorites.

“We’re Cheap Trick. We’re too dumb to quit,” said Nielsen, 67, who changed guitars for every song but wore the same ball cap all night long.

Lead singer Robin Zander, 63, changed voices on several songs. He credibly channeled AC/DC (either singer) on “Heart on the Line,” Robert Plant on “Baby Loves to Rock,” Bowie on “Wake Up Tomorrow,” John Lennon on “California Man” and Steve Perry on “The Flame,” Cheap Trick’s only ballad on Thursday and only No. 1 song.

The durable Zander made Dobie Gray’s “The In Crowd” positively Bowiesque and rocked “Ain’t That a Shame” in ways that Fats Domino never intended. But Zander was at his best on Cheap Trick’s big favorites, the pleadingly poppy “I Want You to Want Me,” the trippy “Dream Police” and the power-pop classic “Surrender,” with its twisted lyrics about mom and dad being all right but seeming a little weird.

Indeed, Cheap Trick is lovably weird — from Nielsen and his guitar with five necks (used on the closing “Goodnight”) to Tom Petersson’s 12-string bass to Zander’s pale peach suit with white Zorro hat.

Daxx Nielsen, Rick’s son, has been the drummer since 2010. He’s not as effortlessly crisp as longtimer Bun E. Carlos, who left due to injury and was the subject of now-resolved feuding lawsuits. He is a nonperforming band member.

Ever-chatty, ever-silly Rick Nielsen surveyed the crowd of 3,000 and spotted a T-shirt he liked — “No Bun E, No Problem.”

“That’s the best shirt ever,” Nielsen said to mixed response from the fans.

At least, the concertgoers agreed about the Hilde as a new venue for name concerts. Capacity is 5,000 for these shows, though more than 10,000 attend Minnesota Orchestra concerts here.

“This is better than Rock Fest and HalfWay Jam,” said TaraLynn Magnuson, of Annandale, referring to two area outdoor festivals. “It’s not flat. People in the back can see the stage.”

Her friend, Rena Cloutier of Shakopee, echoed the enthusiasm. “I love this,” she gushed. “It’s beautiful. The trees. The stage is nice and big. Parking is easy and no charge.”

Shawn Nelson, of Watertown, a former musician, was thrilled with the Hilde.

“We’ve been needing an amphitheater forever,” he said. “This is a great night, great venue, great band.”

With three food trucks, a pizza booth and two beer stands stationed in a parking lot next to the park, Nelson found the concessions easy, the prices reasonable. He pronounced the sound good, the sightlines nice and the lighting system park-board quality.

“This place is probably underutilized,” he said.

Hilde, to feature rocker ZZ Ward and popster Eric Hutchinson on July 30, even received praise from the stage.

Gabe Douglas, lead singer of the Twin Cities-based opening act 4onthefloor, who grew up in a small town, couldn’t contain his excitement.

“You guys got a pretty beautiful amphitheater,” he declared.