A comparative introduction of four fractional order controllers

Using the differentiation and integration of fractional order or non-integer order in systems control is gaining more and more interest from the systems control community. In the paper, four representative fractional-order controllers in the literature are briefly introduced, namely, TID (tilted proportional and integral) controller, CRONE controller (controle robuste d´ordre non entier), PI^λD^μ controller and fractional lead-lag-compensator. The basic ideas and technical formulations are presented with some comparative comments. The major purpose of the paper is to draw attention to the non-conventional method of robust control based on fractional order calculus.