International Conference on Mathematical Advances and Applications, İstanbul, Türkiye, 3 - 05 Mayıs 2019, ss.101
The control of vibrations in beam-string
complex system is considered by applying piezoelectric patch actuators. An
optimization problem is to find the control voltage applied to the actuators
with least control effort. The objective functional is given as a weighted
quadratic functional of the displacement and velocity and a penalty term which
includes expenditure of the actuators. The equation of the motion is
transformed to a number of coupled ordinary differential equations by using
eigenfunction expansion and optimal control law is derived by using the
variational theory. The effectiveness of the method is demonstrated by a
numerical example.