Title :
Two approaches to the stabilization of Euler-Bernoulli beam equation with control matched disturbance
Author :
Bao-Zhu Guo ; Feng-Fei Jin
Author_Institution :
Acad. Sinica, Beijing, China
Abstract :
The boundary feedback stabilization of a one-dimensional Euler-Bernoulli beam equation with the external disturbance flowing to the control end by the active disturbance rejection control (ADRC) and sliding mode control (SMC) are concerned. By the ADRC approach, the disturbance is estimated and canceled in real time. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented. The numerical simulations validate the effectiveness of both methods.
Keywords :
beams (structures); closed loop systems; feedback; numerical analysis; partial differential equations; stability; variable structure systems; ADRC approach; Euler-Bernoulli beam equation stabilization; SMC approach; active disturbance rejection control; boundary feedback stabilization; closed-loop solution existence; closed-loop solution uniqueness; closed-loop system; control end; control matched disturbance; disturbance derivative; disturbance rejection; external disturbance; external disturbance flowing; numerical simulations; one-dimensional Euler-Bernoulli beam equation; real time disturbance cancellation; real time disturbance estimation; sliding mode control; Closed loop systems; Educational institutions; Equations; Mathematical model; Sliding mode control; Uncertainty;
Conference_Titel :
American Control Conference (ACC), 2013
Conference_Location :
Washington, DC
Print_ISBN :
978-1-4799-0177-7
DOI :
10.1109/ACC.2013.6580015