Design of adaptive systems by using fractional calculus system's approach

The Model Reference Control System (MRACS) is the control system tuning its controller to match the controlled system to the reference model designed in the system adaptively. Conventional MRACS assumed the order of integration or derivative as integer order. By introducing fractional order integration or derivative (Fractional Calculus,) MRACS can use the arbitrary order adaptive control law and control the complex system described by fractional calculus like visco-elastic body. In this paper, we improved the transient response of MRACS and modified MRACS to be able to control the plant even though the model matching condition was not satisfied by applying fractional calculus to adaptive transfer function of MRACS, and we constructed the MRACS for the fractional calculus system.