Combining fractional order operators and adaptive passivity-based controllers: An application to the level regulation of a conical tank

In this paper, fractional order (FO) operators and adaptive passivity-based controllers (APBC) are combined. The main aim is to explore possible advantages of combining FO operators and APBC over the use of integer order APBC. The proposed technique is experimentally applied to the level regulation of a conical tank. For comparison purposes, integer order (classical) Proportional Integer (PI) controller and FO-PI controller are also experimentally applied and studied. Results showed that the design of FO-PI controller is simpler than classical PI controller design, since it uses a single set of parameters for the whole operational range of the plant; whereas three different set of parameters were adjusted for the classical PI controller. The design of FO-APBC and APBC is similar, and simpler than FO-PI and classical PI controllers design, not needing to know the plant parameters. Moreover, the proposed FO-APBC is more robust than APBC under plant parameter variations.