Led Zeppelin

Led Zeppelin singer Robert Plant just bought himself a stairway to stalker-free heaven -- because the obsessed fan he accused of following him around the world has just been ordered to stay the hell away.

TMZ broke the story ... Plant obtained a temporary restraining order against 40-something-year-old Alysson Billings earlier this month, requiring her to stay 100 yards away from the singer at all times.

But today, a judge made the restraining order permanent, ordering Billings to stay even farther away -- 300 yards -- for the next three years.

Plant claims Billings has been harassing him for the last 3 years -- showing up at his concerts around the globe, sending him bizarre gifts and increasingly threatening messages.

He says the woman believed they were in a relationship ... even though they never met.

Led Zeppelin legend Robert Plant says a delusional, love-struck, female fan is a threat to his safety ... and he just got a temporary restraining order to keep her as far away as possible.

It's pretty nuts ... in docs Robert says Alysson Billings has been harassing him for three years -- all because she believes they're in a relationship ... even though he's never met her.

Specifically, Robert says Alysson leaves hotel keys for him, sends flowers, random packages and constantly shows up to his concerts all over the world.

But it gets worse ... Robert says ever since he started dating his new girlfriend, Patty Griffin, Alysson's obsession has taken a dark turn ... sending him increasingly threatening messages:

-- "Your betrayal with another woman still stabs my mind."

-- "She's got you so p***y whooped and henpecked, it makes me want to puke ... and I'm telling you that rotten crotch is ruining you."

-- "This woman is literally evil for you and your life ... you are about to fall for that dirty old crotch. And I'm not joking, I cannot, will not, shall not live this way anymore."