What is the role of the round counter in the key schedule of PRESENT? Currently I am working on PRESENT block cipher implementation (Hardware) and I am unable to understand the role of round counter in key scheduling part of cipher.

Can some share some insight on round counter and its working?
to prevent self-similarity of key scheduling

The importance of constant addition (not only present cipher) appears in preventing key schedule-based attacks  such as slide attack ,related key attacks and other structural attacks such as: invariant subspace attack , and nonlinear invariant subspace attacks.

paragraph  5.4 Key schedule attacks in original Present Block cipher
answers your questions.