The two most common normalization methods for the old Affymetrix 3’ GeneChips are RMA and PLIER. I have been reading about PLIER in the following reference http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2623311/, and it states that it requires a Perfect Match and Missmatch probess.

However, thew new Affymetrix GeneChip ST microarrays do not have such Perfect Match and Miss Match probes, but they have some control probes that fulfill the same function. Thus, can the PLIER normalization be applied to such arrays? Is there an R package that implements it?

Not really. The RMA algorithm long ago became the default for most people because the differences between RMA and PLIER and GCRMA and affyPLM and whatever else were actually not that big, and were really only of interest to statisticians working in the field. Put a different way, all this was hashed out in the mid 2000s, when people were still trying to figure out the 'best' method for summarizing Affy arrays. These days most people don't care about those old arguments - if you are a PhD statistician trying to make a name, you for sure aren't working on microarrays, and if you are somebody in the trenches analyzing data, you just use RMA because it's good enough, and why bother trying to explain to some reviewer that PLIER is like awesome and stuff when you can just use RMA and they won't bat an eye?