A Double-$r$ $fhan$ Algorithm for Tracking Differentiator of Active Disturbance Rejection Control
Peilin Liu, Tao Wang, Zhiyuan Chai, Chuang Liu, Xuezhong Zhu
Abstract
Discrete-time optimal control tracking differentiator (DTOC-TD) based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> algorithm is widely used in active disturbance rejection control (ADRC) for motor drive, which can not only arrange the transition process for setpoint jump but also filter out the noises of the input signal. However, for the conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> algorithm, only a single <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> parameter is included, which makes it difficult to balance the tracking and filtering capabilities. This paper proposes a double- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ra, rb</i> ) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> -DTOC-TD (briefly noted as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> -TD) to ensure tracking and filtering simultaneously. A different operating sequences of the two r parameters are designed and compared. Simulation results verify the excellent step signal tracking and noise filtering performances of double- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> -TDs. Experiments are conducted on an electric forklift driven by a four-phase 16/12 switched reluctance motor (SRM). By replacing the conventional TD with the proposed double- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fhan$</tex-math></inline-formula> -TDs in the ADRC of SRM control, the system tracking performance can be obviously improved.