Fractional order active disturbance rejection control with the idea of cascaded fractional order integrator equivalence

An Improved Fractional-Order Active Disturbance Rejection Control: Performance Analysis and Experiment Verification

“…where s is Laplace operator, a i , a 0 and b are real numbers, m and i are positive integers with m representing the maximum order of the system. The differential equation form of system (1) with the external disturbance, denoted by d, is…”

“…Define the quantity q(y (nγ) , y (m) , t) = y (nγ) − y (m) . Equation (2) can be rewritten as follows, (1) , y (2) , • • • , y (m−1) , y, u, t)…”

“…The aim of this paper is to design u such that the system output tracks a sufficiently smooth reference trajectory r and the ultimate tracking error stays in the neighborhood of the origin, i.e., lim t→∞ y(t) − r(t) < , when the reference signal and its derivatives, i.e., r, ṙ, r, • • • r (m−1) , r (nγ−m+1) , are bounded. As inspired by FO-ADRC in [1], we propose the tracking controller as follows…”

“…F RACTIONAL calculus has been applied to different fields in recent years [1], [2], [3], [4]. With a deep understanding of the system, there is a growing need for fractional-order control and modelling [5], [6].…”

“…Thirdly, the stability criteria of the IFO-ESO and the IFO-ADRC closed-loop system are given when the disturbance is assumed to be bounded. Unlike the stability analysis of the ESO and the closed-loop system in [1] and [22], the stability criteria of the high-order ESO and high-order ADRC closedloop system in this paper are given.…”