Dynamic stabilization of an Euler–Bernoulli beam under boundary control and non-collocated observation

Guo, Bao‐Zhu; Wang, Junmin; Yang, Kun-Yi

doi:10.1016/j.sysconle.2008.02.004

Cited by 57 publications

(38 citation statements)

References 18 publications

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“…Therefore, the design of the feedback controller must contain the non‐collocated information. In addition, the non‐collocated feedback controllers are more feasible in engineering; in recent years some authors have used them to stabilize the system 10–13.…”

Section: Introductionmentioning

confidence: 99%

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Exponential stability of string system with variable coefficients under non‐collocated feedback controls

Chen

Han

et al. 2011

Asian Journal of Control

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In this paper, we describe a linear boundary non-collocated feedback controller to stabilize a string system with variable coefficients and investigate the exponential stability of the closed-loop system. We show that the system associates with a C 0 semigroup. Through the asymptotic analysis technique, we get the asymptotic values of all eigenvalues of the system operator A. Furthermore, we prove that there is a sequence of generalized eigenvectors of A that forms a Riesz basis with parentheses for the energy state space. Hence, the system satisfies the spectrum determined growth assumption. Finally, we show that the system is exponentially stable with suitable choice of the feedback gains.

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Section: Introductionmentioning

confidence: 99%

“…Observe that direct non‐collocated feedback does not ensure that the energy of the closed loop system decays. In order to get the dissipation of the energy of the closed loop system, the authors of 12 and 13 designed complementary systems. Complementary systems, however, are more complex than the original ones.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of string system with variable coefficients under non‐collocated feedback controls

Chen

Han

et al. 2011

Asian Journal of Control

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“…Indeed, a balance has to be found between the infinite dimensional representation of such model and the possibilities to implement a finite dimensional controller (in order to be technically feasible). Usually, theoretical studies keeping the initial infinite dimensional PDE model are focusing on the existence and unicity of the model solution and also on the solution of a control problem based on this model (Guo et al, 2008;Zong, 2008). Here, since we are interested in the real time control of a non-linear PDE model based process, we are focusing on finite dimensional approaches.…”

Section: Control Of Pde Systemsmentioning

confidence: 99%

Experimental predictive control of the infrared cure of a powder coating: A non-linear distributed parameter model based approach

Bombard¹,

Silva²,

Praly³

2010

Chemical Engineering Science

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This paper deals with the experimental model based predictive control of the infrared cure cycle of a powder coating. It is based on a dynamic infinite dimensional model of the cure in one spatial domain, which aims to represent the evolution of the temperature and the degree of cure during the cure under infrared flow. The sensitivity of this model with respect to the main radiative property is experimentally highlighted under open loop conditions. This partial differential equation model is then approximated in finite dimension in order to be used by the predictive controller. Since the sampling time is small (one second), a special model predictive control formulation is used here, which aims to decrease the on-line computational time required by the control algorithm. Experimental evaluation of this controller that is based on the MPC@CB software is then presented. For black and white paintings, the robustness of this control algorithm is shown during an experimental temperature constrained trajectory tracking, even under a strong modeling uncertainty. The conclusion of this study is that this controller may be used for advanced control of powder coating cure.

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“…Recently, inspired by the works of [7,19], we solved successfully the stabilization of one dimensional wave and beam equations with boundary control and non-collocated observation [12,14]. The generalization to multidimensional systems is also available [11].…”

Section: Introductionmentioning

confidence: 99%

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Guo

Hammouri

2010

ESAIM: COCV

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Abstract.The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.Mathematics Subject Classification. 35B37, 93B52, 93C05, 93C20, 93D15.

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Dynamic stabilization of an Euler–Bernoulli beam under boundary control and non-collocated observation

Cited by 57 publications

References 18 publications

Exponential stability of string system with variable coefficients under non‐collocated feedback controls

Exponential stability of string system with variable coefficients under non‐collocated feedback controls

Experimental predictive control of the infrared cure of a powder coating: A non-linear distributed parameter model based approach

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

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