AUTHOR=Xingqi Hu , Guolian Hou , Wen Tan 

TITLE=Tuning of PIDD2 controllers for oscillatory systems with time delays

JOURNAL=Frontiers in Control Engineering

VOLUME=3

YEAR=2023

URL=https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.1083419

DOI=10.3389/fcteg.2022.1083419

ISSN=2673-6268

ABSTRACT=<p>Proportional–integral–derivative (PID) control is a durable control technology that has been widely applied in the process control industry. However, PID controllers cannot achieve satisfactory performance for oscillatory systems with long time delays; thus, high-order controllers like the proportional–integral–double derivative (<inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>P</mml:mi><mml:mi>I</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) can be adopted to enhance the control performance. In this paper, we propose a tuning formula for the <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>P</mml:mi><mml:mi>I</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> controller for oscillatory systems with time delays and its practical implementation <italic>via</italic> an observer bandwidth-based state-space <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>P</mml:mi><mml:mi>I</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. Simulation results show that the state-space <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>P</mml:mi><mml:mi>I</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> controller tuned from the proposed formula trades-off among robustness, time domain performance, and measurement noise attenuation and can arrive at a better control effect than PID for oscillatory systems.</p>