The research objective of the Marine Renewable Energy Lab (MRELab) is to design multi-cylinder VIVACE Converters and optimize their power output for a broad range of velocities. For a given geometric and mass configuration of a school of cylinders, each point on the power envelope, at a given flow-speed, is a function of the spring constant and damping. Conducting tests with real springs and dampers requires lengthy preparation for each set of experiments. A more efficient way to conduct experiments faster and accurately is developed based on a controller embedded virtual spring-damping system (Vck) that des not include the hydrodynamic force in the closed loop. Each oscillator consists of one Vck, one interchangeable cylinder moving on submerged roller blocks and driven by the fluid flow, and connected to the controller through belts and pulleys. It is designed to achieve the desired static/dynamic friction through the Vck. An Arduino embedded board controls a servomotor with an optical encoder, which enables real-time position/speed measurement. A system identification (SI) methodology is developed making possible to identify the damping model of any oscillator, which is typically much more complicated than the classical linear viscous model. Upon completion of the SI process for an oscillator, the actual nonlinear damping model is subtracted using the controller and leaving the system with zero damping. Then, a mathematically linear damping model is added, thus, resulting in a system with real linear viscous damping. This process enables changing the spring constant and harnessing damping through the controller instantly. Experiments are then conducted with both real spring dampers and Vck to validate the process. All FIM experiments are conducted in the Low Turbulence Free Surface Water Channel of the University of Michigan at 16,000<Re<140,000.
The main findings are: (a) The Vck system was developed keeping the hydrodynamic force out of the control loop and, thus, not biasing the FIM. (b) The agreement between real and virtual springs and dampers was excellent in FIM measurements over the entire range of spring constants and velocities tested. (c) The lag due to the controller was minimal and significantly reduced compared to the first generation of Vck built in the MRELab.
Bayesian Evidence for a Nonlinear Damping Model for Coronal Loop Oscillations
