This is a great solution to the PSP's nub being so small and having such a bad grip. Don't worry however, you can convert PS2's nub for your PSP.
What you need
An old PS2 controller, original fot best plastic's quality.
Note: You will end up destroying a PS2 controller.
1. Take a broken PS2 controller or one that you'll never use. You won't be able to turn it back into a regular controller.
2. Take out the small screws in the back of the controller.
3. Rip apart everything inside the controller but keep track of the Analog sticks.
4. Choose what stick you'll use but keep the other one just in case.
5. Look on the inside of the stick. Where that square hole is, that's where the stick connects to the controller and PSP.
6. Now take your grinding tool and grind the outer circular part on the bottom of the stick down as much as you can. Then grind down the little things that stick out diagonally from the square hole. Don't grind the hole though.
7. Now remove your PSP's analog nub. It's easy. Just pull up and it comes right off. No, it doesn't void your warranty. It was made to come off.
8. Now place on the Analog stick where the nub just was and move it around. If it feels to stiff, take out that grinding tool again and do some more.
Now you can easily switch between the nub and stick whenever you want.