17,006 research outputs found
Nonlinear Analysis of an Improved Swing Equation
In this paper, we investigate the properties of an improved swing equation
model for synchronous generators. This model is derived by omitting the main
simplifying assumption of the conventional swing equation, and requires a novel
analysis for the stability and frequency regulation. We consider two scenarios.
First we study the case that a synchronous generator is connected to a constant
load. Second, we inspect the case of the single machine connected to an
infinite bus. Simulations verify the results
Dynamics of heavy and buoyant underwater pendulums
The humble pendulum is often invoked as the archetype of a simple, gravity
driven, oscillator. Under ideal circumstances, the oscillation frequency of the
pendulum is independent of its mass and swing amplitude. However, in most
real-world situations, the dynamics of pendulums is not quite so simple,
particularly with additional interactions between the pendulum and a
surrounding fluid. Here we extend the realm of pendulum studies to include
large amplitude oscillations of heavy and buoyant pendulums in a fluid. We
performed experiments with massive and hollow cylindrical pendulums in water,
and constructed a simple model that takes the buoyancy, added mass, fluid
(nonlinear) drag, and bearing friction into account. To first order, the model
predicts the oscillation frequencies, peak decelerations and damping rate well.
An interesting effect of the nonlinear drag captured well by the model is that
for heavy pendulums, the damping time shows a non-monotonic dependence on
pendulum mass, reaching a minimum when the pendulum mass density is nearly
twice that of the fluid. Small deviations from the model's predictions are
seen, particularly in the second and subsequent maxima of oscillations. Using
Time- Resolved Particle Image Velocimetry (TR-PIV), we reveal that these
deviations likely arise due to the disturbed flow created by the pendulum at
earlier times. The mean wake velocity obtained from PIV is used to model an
extra drag term due to incoming wake flow. The revised model significantly
improves the predictions for the second and subsequent oscillations.Comment: 15 pages, 8 figures, J. Fluid Mech. (in press
Model-Based Control Using Koopman Operators
This paper explores the application of Koopman operator theory to the control
of robotic systems. The operator is introduced as a method to generate
data-driven models that have utility for model-based control methods. We then
motivate the use of the Koopman operator towards augmenting model-based
control. Specifically, we illustrate how the operator can be used to obtain a
linearizable data-driven model for an unknown dynamical process that is useful
for model-based control synthesis. Simulated results show that with increasing
complexity in the choice of the basis functions, a closed-loop controller is
able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore,
the specification of the basis function are shown to be of importance when
generating a Koopman operator for specific robotic systems. Experimental
results with the Sphero SPRK robot explore the utility of the Koopman operator
in a reduced state representation setting where increased complexity in the
basis function improve open- and closed-loop controller performance in various
terrains, including sand.Comment: 8 page
- …