The objective of this study is to develop a method of controlling vortex shedding
behind a bluff body using control theory. A suboptimal feedback control procedure
for local sensing and local actuation is developed and applied to the flow behind
a circular cylinder. The location of sensors for feedback is limited to the cylinder
surface and the control input from actuators is the blowing and suction on the cylinder
surface. Three different cost functionals to be minimized
(J1 and J2) or maximized
(J3) are investigated: J1 is proportional
to the pressure drag of the cylinder, J2 is the
square of the difference between the target pressure (inviscid flow pressure) and real
flow pressure on the cylinder surface, and J3 is the square of the pressure gradient on
the cylinder surface, respectively. Given the cost functionals, the flow variable to be
measured by the sensors and the control input from the actuators are determined from
the suboptimal feedback control procedure. Several cases for each cost functional have
been numerically simulated at Re = 100 and 160 to investigate the performance of the
control algorithm. For all actuations, vortex shedding becomes weak or disappears,
and the mean drag and drag/lift fluctuations significantly decrease. For a given
magnitude of the blowing/suction, reducing J2 provides the largest drag reduction
among the three cost functionals.