Title :
Observer Based Boundary Control of an Unstable Wave Equation
Author :
Krstic, Miroslav ; Guo, Bao-Zhu ; Balogh, Andras ; Smyshlyaev, Andrey
Author_Institution :
Univ. of California, La Jolla
Abstract :
We consider the problem of stabilization of a one- dimensional wave equation that contains instability at its free end and control on the opposite end. In contrast to classical collocated "boundary damper" feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition, the controllers and the associated observers designed in the paper are more complex due to the open- loop instability of the plant. The controller and observer gains are designed using the method of "backstepping," which results in explicit formulae for the gain functions. We prove exponential stability and the existence and uniqueness of classical solutions for the closed-loop system. We illustrate the applicability of our designs using simulation results.
Keywords :
asymptotic stability; feedback; observers; open loop systems; vibration control; wave equations; 1D wave equation; backstepping; boundary control; boundary damper feedbacks; exponential stability; observer; open-loop instability; stabilization; unstable wave equation; Actuators; Backstepping; Books; Boundary conditions; Control systems; Damping; Mathematics; Output feedback; PD control; Partial differential equations;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4282422