I dont think pulse and cheap belong in the same sentence!
It depends what you class as cheap? Brand new wont be less than a couple of ££££ but you could get a decent set second hand for around £1000-£1800. I actually bought a cebora 2035m pulse mig earlier this year six months old for £750 but believe me it took some searching and patience for one to come up at that price
According to my experience,there are three Suggstion:.One is using Tapping machine"Transformer type" which is very stable model in the world. The seond one ,if you need about 200Amp output welding current,I recommend one mode FortuneWeld MIG200P that worths £ 888. The third one,I suggest you buy TIG200PAC-DC as replacement as this model have fantastic performance for Aluminum welding.I hope my views do help to you.
I've had no complaints selling the EWM Pico Puls 180, I've not sold many to DIYers though. But for those that can stretch to it it makes the welding so easy it's almost cheating as you don't actually learn to set up a decent arc condition for yourself.