A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation. (27th February 2018)

• Record Type: Journal Article
• Authors: Kidambi, Krishna Bhavithavya; Ramos‐Pedroza, Natalie; MacKunis, William; Drakunov, Sergey V.
• Other Names: Fridman Leonid guestEditor.; Poznyak Alex guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 3(2019)
• Page Start: 779
• Page End: 792
• Publication Date: 2018-02-27
• Subjects: nonlinear control -- robust control -- sliding mode estimation; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4070
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.