The Swirling Pendulum: Conceptualization, Modeling, Equilibria and Control Synthesis

This paper introduces the swirling pendulum, a two-link, two degree-of-freedom mechanism which is under-actuated and has an unusual non-planar coupling with axis of rotation of the two links being perpendicular to each other. The swirling pendulum mechanism, while being simple to mathematically represent and easy to physically construct, exhibits several properties like loss of inertial coupling, loss of relative degree, multiple stable and unstable equilibrium points. These properties are unique as well as interesting from dynamics and controls point of view which make the swirling pendulum an excellent test-bed for testing various ideas in control and demonstrating several notions associated with systems and control theory. In this paper, we discuss the modeling of the swirling pendulum mechanism based on Lagrange’s equation along with an analysis related to equilibrium points and their stability. We also present simulation results for regulatory as well as tracking control tasks through simulations on a non-linear model using control methods like LQR, lead compensator and system inversion-based control to demonstrate the utility of the proposed mechanism in the area of systems, control and dynamics. Furthermore, we also discuss experimental results for controls applied on a real-time hardware setup.

Mass-conserving coupling of total column CO₂ (XCO₂) from global to mesoscale models: Case study with CMS-Flux inversion system and WRF-Chem (v3.6.1)

Quantifying the uncertainty of inversion-derived fluxes and attributing the uncertainty to errors in either flux or transport continue to be challenges in the characterization of surface sources and sinks of carbon dioxide (CO2). It is also not clear if fluxes inferred in a coarse-resolution global system will remain optimal in a higher-resolution modeling environment. Here we present an off-line coupling of the mesoscale Weather Research and Forecasting (WRF) model to optimized biogenic CO2 fluxes and mole fractions from the global Carbon Monitoring System inversion system (CMS-Flux). The coupling framework consists of methods to constrain the mass of CO2 introduced into WRF, effectively nesting our North American domain within the global model. We test the coupling by simulating Greenhouse gases Observing SATellite (GOSAT) column-averaged dry-air mole fractions (XCO2) over North American for 2010. We find mean model-model differences in summer of ~ 0.12 ppm. While 85 % of the XCO2 values are due to long-range transport from outside our North American domain, most of the model-model differences appear to be due to transport differences in the fraction of the troposphere below 850 hPa. The framework methods can be used to couple other global model inversion results to WRF for further study using different boundary layer and transport parameterizations.

Electromechanical Modeling and Adaptive Feedforward Control of a Self-Sensing Scanning Fiber Endoscope

Precise image capture using a mechanical scanning endoscope is framed as a resonant structural-deflection control problem in a novel application. A bipolar piezoelectric self-sensing circuit is introduced to retrofit the piezoelectric tube as a miniature sensor. A data-driven electromechanical modeling approach is presented using system identification and system inversion methods that together represent the first online-adaptive control strategy for the scanning fiber endoscope (SFE). Trajectory tracking experiments show marked improvements in scan accuracy over previous control methods and significantly, the ability of the new method to adapt to changing operating environments.

Determining Upconversion Parameters and Invertibility of Nonlinear Dynamical Systems

ABSTRACTDetermining upconversion parameters is of high interest in laser material development. For many materials these parameters cannot be directly measured by experimental methods. These upconversion coefficients appear as unknown parameters in the laser rate equations, which are a system of coupled nonlinear differential equations that are used to model the dynamics of population densities in different energy levels. In this paper we propose the well-established system theoretic tools pertaining to the system inversion to be applied in this case. The unknown parameters can be considered as the inputs and the fluorescence signals can be considered as the outputs of the dynamical system. Therefore the determination of the unknown upconversion rates in the system equations from the output data is a classical system inversion problem. In this paper we demonstrate how to compute the unknown coefficients in the rate equations from the experimental emission data utilizing this method.