Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non‐collocated control

Int. J. Robust. Nonlinear Control

Liu

2013

Self Cite

121

In this paper, we are concerned with the boundary stabilization of a one-dimensional antistable Schrödinger equation subject to boundary control matched disturbance. We use both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the "reaching condition" is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control, but also giving an online estimation of the disturbance. It is shown that the resulting closed-loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero.

Section: Introductionmentioning

confidence: 99%

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

Int. J. Robust. Nonlinear Control

Liu

2013

Self Cite

121

“…A recent progress is made in [8] where an adaptive observer and controller is designed for a one-dimensional wave equation with output disturbances and non-collocated control.…”

Section: Introductionmentioning

confidence: 95%

Parameter estimation and stabilization for an unstable one-dimensional wave equation with boundary input harmonic disturbances

2012 American Control Conference (ACC)

2012

This paper is concerned with the parameter estimation and stabilization of a one-dimensional wave equation with instability suffered at one end and uncertainty of harmonic disturbances at the controlled end. An adaptive observer is designed in terms of measured position at one end and velocity at the other end. The backstepping method for infinite-dimensional system is adopted in the design of the feedback law. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity.

“…In the last three decades, the boundary control, due to its easy physical implementation in engineering, is applied widely as a major control strategy for the systems governed by partial differential equations (PDEs), see for instance, Cheng, Radisavljevic, and Su (2011), Guo, Guo, and Shao (2011), Krstic (2010), Krstic, Guo, Balogh, and Smyshlyaev (2008), , Luo, Guo, and Morgul (1999), Smyshlyaev and Krstic (2009), Susto and Krstic (2010) and the references therein. In many situations, the control is used not only to guarantee the system to be normally operated in an ideal environment but also to be normally operated in the environment with uncertainties coming from either the internal or the external disturbance.…”

Section: Introductionmentioning

confidence: 99%

“…There are many works contributed to this aspect. In Guo et al (2011) and Guo and Guo (2013), the stabilisations of one-dimensional wave equation with harmonic uncertainty suffered from input and output are considered. Based on semigroup theory, the sliding mode control method is used to deal with a class of abstract infinite-dimensional systems in Orlov and Utkin (1987), where the control operator and disturbance operator are all assumed to be bounded, which represents mainly the distributed control strategy.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov approach to the boundary stabilisation of a beam equation with boundary disturbance

International Journal of Control

Kang

2013

Self Cite

In this paper, we are concerned with the boundary output feedback stabilisation of an Euler-Bernoulli beam equation with one free boundary end and control/disturbance on the other end. A variable structure output feedback stabilising control law is designed by the Lyapunov functional approach. It is shown that the resulting closed-loop system without disturbance is associated with a nonlinear semigroup and asymptotically stable except the zero dynamics. In addition, we show that this control law is robust to the external disturbance in the sense that the vibrating energy of the closed-loop system outside of the zero dynamics converges to zero as time goes to infinity in spite of the presence of finite sum of harmonic disturbance on the control end. The existence of the Filippov solution with disturbance is developed by the Galerkin approximation scheme.