A proportional–integral–differential control of flow over a circular cylinder

Abstract

In the present study, we apply proportional (P), proportional-integral (PI) and proportional-differential (PD) feedback controls to flow over a circular cylinder at Re = 60 and 100 for suppression of vortex shedding in the wake. The transverse velocity at a centreline location in the wake is measured and used for the feedback control. The actuation (blowing/suction) is provided to the flow at the upper and lower slots on the cylinder surface near the separation point based on the P, PI or PD control. The sensing location is varied from 1d to 4d from the centre of the cylinder. Given each sensing location, the optimal proportional gain in the sense of minimizing the sensing velocity fluctuations is obtained for the P control. The addition of I and D controls to the P control certainly increases the control performance and broadens the effective sensing location. The P, PI and PD controls successfully reduce the velocity fluctuations at sensing locations and attenuate vortex shedding in the wake, resulting in reductions in the mean drag and lift fluctuations. Finally, P controls with phase shift are constructed from successful PI controls. These phase-shifted P controls also reduce the strength of vortex shedding, but their results are not as good as those from the corresponding PI controls.

Stabilization of absolute instability in spanwise wavy two-dimensional wakes

“…Many of these efforts have often focused on developing control methods within two-dimensional framework: the control input is homogeneous in the spanwise direction (we shall refer to this approach as 'two-dimensional' control). The well-known examples include end plate (Nishioka & Sato 1974;Stansby 1974), base bleed (Wood 1967;Bearman 1967), splitter plate (Roshko 1955;Bearman 1965;Kwon & Choi 1996), secondary small cylinder (Strykowski & Sreenivasan 1990), and active blowing/suction based with flow sensing (Min & Choi 1999;Son et al 2011). On the contrary, a number of relatively recent studies have proposed a conceptually different approach where the control input varies along the spanwise direction (we shall refer to this approach as 'three-dimensional' control).…”

Vortex shedding suppression and wake control: A review

“…It should be noted that the controller is a combination of a simple gain (P control), an integrator (I control), a differentiator (D control) or some weighted combination of these possibilities, see e.g. Son et al (2011). Extremum is another feedback control method used to supress the vortex shedding by seeking control.…”

Prediction of Near-Wake Velocity in Laminar Flow over a Circular Cylinder Using Neural Networks with Instantaneous Wall Pressure Input

“…In this study, we aim to predict the near-wake transverse velocity in laminar flow over a circular cylinder by using a neural network with instantaneous wall pressures on the cylinder surface as the input variables. The transverse velocity in the wake of a circular cylinder has been considered a good indicator for the state of Kármán vortex shedding [27][28][29][30][31]. In this regard, one of the motivations for constructing neural networks to predict the transverse velocity is to further integrate them, in future studies, with active feedback control methods such as proportional-integral-derivative (PID) control [27,29], whose control purpose is to mitigate the strength of the Kármán vortex shedding.…”