scholarly journals Well-Posedness and Stability of Infinite-Dimensional Linear Port-Hamiltonian Systems with Nonlinear Boundary Feedback

2019 ◽  
Vol 57 (3) ◽  
pp. 1818-1844 ◽  
Author(s):  
Björn Augner
Keyword(s):  
Hamiltonian Systems ◽  
Nonlinear Boundary ◽  
Well Posedness ◽  
Infinite Dimensional ◽  
Boundary Feedback ◽  
Nonlinear Boundary Feedback

scholarly journals Tracking control of a flexible beam by nonlinear boundary feedback

1995 ◽  
Vol 8 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Bao-Zhu Guo ◽  
Qian Song
Keyword(s):  
Tracking Control ◽  
Horizontal Plane ◽  
Closed Loop ◽  
Nonlinear Boundary ◽  
Flexible Beam ◽  
Well Posedness ◽  
Boundary Feedback ◽  
Closed Loop Systems ◽  
The One ◽  
Nonlinear Boundary Feedback

This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.

Stabilization of an Axially Moving String by Nonlinear Boundary Feedback

1999 ◽  
Vol 121 (1) ◽  
pp. 117-121 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jinn-Wen Wu ◽  
Sheng-Luong Wu
Keyword(s):  
Nonlinear Boundary ◽  
Mechanical Energy ◽  
Control Laws ◽  
Axially Moving String ◽  
Boundary Feedback ◽  
Boundary Velocity ◽  
Total Mechanical Energy ◽  
Axially Moving ◽  
The Right ◽  
Nonlinear Boundary Feedback

In this paper, we consider the system modeled by an axially moving string and a mass-damper-spring (MDS) controller, applied at the right-hand side (RHS) boundary of the string. We are concerned with the nonlinear string and the effect of the control mechanism. We stabilize the system through a proposed boundary velocity feedback control law. Linear and nonlinear control laws through this controller are proposed. In this paper, we find that a linear boundary feedback caused the total mechanical energy of the system to decay an asymptotically, but it fails for an exponential decay. However, a nonlinear boundary feedback controller can stabilize the system exponentially. The asymptotic and exponential stability are verified.

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