OPTIMAL BOUNDARY CONTROL OF A TIMOSHENKO BEAM VIA MAXIMUM PRINCIPLE

摘要

Boundary control to damp the undesirable vibrations in arnTimoshenko beam is considered. For this purpose, controllabilityrnand wellposedness of the system are examined.rnPerformance index is defined with regards to the dynamicrnresponse of the beam that is defined as a weighted quadraticrnfunctional of the displacement and the velocity at terminalrntime and expenditure of the control energy added as arnpenalty term. In order to obtain the optimal control function,rnan adjoint variable satisfying the adjoint equation correspondingrnto state equation is introduced. The maximumrnprinciple is formulated and optimal control function is obtained.rnAlso, by using maximum principle, control problemrnis transformed into solving a system of partial differentialrnequations including state and adjoint variables with initial,rnboundary and terminal conditions. MATLAB is used to obtainrnthe solution of the system. Numerical results are givenrnin tables and graphical forms.