Differential flatness-based ADRC scheme for underactuated fractional-order systems

This article mainly studies the fractional-order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional-order systems (FOSs). The FOADRC framework for linear FOSs-based fractional proportion integration differentiation is constructed by using the fractional-order tracking differentiator and the fractional-order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.