Backstepping control of ODE/wave PDE cascaded systems with dynamic boundary conditions. Issue 6 (3rd June 2022)

• Record Type: Journal Article
• Authors: Cai, Xiushan; Wan, Liguang; Yang, Qingsheng; Wu, Jie; Liu, Leipo
• Is Part Of: International journal of control. Volume 95:Issue 6(2022)
• Page Start: 1625
• Page End: 1633
• Publication Date: 2022-06-03
• Subjects: Cascaded system -- wave dynamics -- predictor control -- backstepping transformations; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2020.1866214
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : We consider backstepping control for ODE/wave PDE cascaded systems with dynamic boundary conditions. The ODE state is driven by the uncontrolled boundary of the wave PDE. A backstepping compensator is designed such that the closed-loop system is globally asymptotically stable. The controller design and stability analysis are based on coordinate and backstepping transformations. Changes of coordinate recast the original system into a coupled 2 × 2 first-order hyperbolic system with spatially-varying coefficients cascading into an ODE. Backstepping transformations are exploited to design a compensator for the resulting coupled system. The validity of the proposed design is illustrated by controlling a bit of the oil well drilling system to operate at a constant uniform rotary speed.