Fractional-Order Model Reference Adaptive Controllers for First-Order Integer Plants

In this chapter, we extend the ideas of the model reference adaptive control (MRAC), developed for integer-order plants with integer-order adaptive laws, to the case of integer-order plants but with fractional-order adaptive laws. Two cases are analyzed in detail; the direct MRAC (DMRAC) and the combined MRAC (CMRAC). In both cases, boundedness of all the signals in the resultant adaptive scheme is theoretically proved and a discussion on the error, and parameter convergence is provided in each case. The study is performed for scalar first-order time-invariant plants, since extensions to the vector case are currently under investigation.