Algebraic differentiator based fractional order controller by high-order fully actuated system approach

This paper considers a problem on the design of algebraic differentiator based fractional order controller by using the high-order fully actuated (HOFA) system approach. First, the considered nonlinear system is transformed into a HOFA system model. Second, a fractional order controller involving the Riemann-Liouville fractional sequential derivatives is directly written out for the HOFA system model in the framework of the closed-loop fractional order linear time invariant (LTI) system. Then, the algebraic integral formulas of the unknown derivatives are derived by applying the modulating functions method. Finally, an example is provided to illustrate the efficiency of the proposed method with noisy observation.