Optimal sensor and actuator placement for feedback control of vortex shedding

TL;DR

This paper investigates optimal placement of a single sensor and actuator for feedback control of vortex shedding in low Reynolds number flow, using resolvent modes to design H2 controllers and analyzing performance trade-offs.

Contribution

It introduces a systematic approach to determine optimal sensor and actuator locations for single-input single-output feedback control in fluid flows.

Findings

Optimal placements depend on control objectives and Reynolds number.

Trade-offs exist between estimation accuracy and control effectiveness.

Performance limitations are identified for single sensor-actuator configurations.

Abstract

We consider linear feedback control of the two-dimensional flow past a cylinder at low Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a single actuator. To accommodate the high dimensionality of the flow we compute its leading resolvent forcing and response modes to enable the design of H2-optimal estimators and controllers. We then investigate three control problems: i) optimal estimation (OE) in which we measure the flow at a single location and estimate the entire flow; ii) full-state information control (FIC) in which we measure the entire flow but actuate at only one location; and iii) the overall feedback control problem in which a single sensor is available for measurement and a single actuator is available for control. We characterize the performance of these control arrangements over a range of sensor and actuator placements and discuss implications for effective feedback control when using a single sensor and a single actuator. The optimal sensor and actuator placements found for the OE and FIC problems are also compared to those found for the overall feedback control problem over a range of Reynolds numbers. This comparison reveals the key factors and conflicting trade-offs that limit feedback control performance.