  This paper presents an active disturbance rejection control (ADRC) scheme
with an improved fractional-order extended state observer (IFO-ESO).Based on
the new ADRC scheme, the open-loop transfer function of a high-order system can
be approximately rendered to a so-called Weighed Bode's ideal transfer
function, whose closed-loop performance is less prone to the controller
parameter variations. The design of the IFO-ESO helps reduce the number of
system states to be estimated and improves the performance of closed-loop
system over %the previously proposed the fractional-order active disturbance
rejection control (FO-ADRC) in the literature. Compared with the integer-order
active disturbance rejection controller (IO-ADRC) and FO-ADRC, the auxiliary
tracking controller of IFO-ADRC has a simpler form. Frequency-domain analysis
shows that IFO-ESO has better estimation performance than fractional-order ESO,
and time-domain simulation demonstrates that the proposed ADRC has better
transient performance and is more robust against the parameter variations than
FO-ADRC and IO-ADRC. The proposed ADRC is applied to permanent magnet
synchronous motor (PMSM) servo control system and demonstrates its capability
in a real-world application.
