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- All Subjects: Advection Diffusion
- Member of: ASU Electronic Theses and Dissertations
Description
Traditional approaches to modeling microgrids include the behavior of each inverter operating in a particular network configuration and at a particular operating point. Such models quickly become computationally intensive for large systems. Similarly, traditional approaches to control do not use advanced methodologies and suffer from poor performance and limited operating range. In this document a linear model is derived for an inverter connected to the Thevenin equivalent of a microgrid. This model is then compared to a nonlinear simulation model and analyzed using the open and closed loop systems in both the time and frequency domains. The modeling error is quantified with emphasis on its use for controller design purposes. Control design examples are given using a Glover McFarlane controller, gain sched- uled Glover McFarlane controller, and bumpless transfer controller which are compared to the standard droop control approach. These examples serve as a guide to illustrate the use of multi-variable modeling techniques in the context of robust controller design and show that gain scheduled MIMO control techniques can extend the operating range of a microgrid. A hardware implementation is used to compare constant gain droop controllers with Glover McFarlane controllers and shows a clear advantage of the Glover McFarlane approach.
ContributorsSteenis, Joel (Author) / Ayyanar, Raja (Thesis advisor) / Mittelmann, Hans (Committee member) / Tsakalis, Konstantinos (Committee member) / Tylavsky, Daniel (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis considers two problems in the control of robotic swarms. Firstly, it addresses a trajectory planning and task allocation problem for a swarm of resource-constrained robots that cannot localize or communicate with each other and that exhibit stochasticity in their motion and task switching policies. We model the population dynamics of the robotic swarm as a set of advection-diffusion- reaction (ADR) partial differential equations (PDEs).
Specifically, we consider a linear parabolic PDE model that is bilinear in the robots' velocity and task-switching rates. These parameters constitute a set of time-dependent control variables that can be optimized and transmitted to the robots prior to their deployment or broadcasted in real time. The planning and allocation problem can then be formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. Simulations of a commercial pollination scenario validate the ability of our control approach to drive a robotic swarm to achieve predefined spatial distributions of activity over a closed domain, which may contain obstacles. Secondly, we consider a mapping problem wherein a robotic swarm is deployed over a closed domain and it is necessary to reconstruct the unknown spatial distribution of a feature of interest. The ADR-based primitives result in a coefficient identification problem for the corresponding system of PDEs. To deal with the inherent ill-posedness of the problem, we frame it as an optimization problem. We validate our approach through simulations and show that reconstruction of the spatially-dependent coefficient can be achieved with considerable accuracy using temporal information alone.
Specifically, we consider a linear parabolic PDE model that is bilinear in the robots' velocity and task-switching rates. These parameters constitute a set of time-dependent control variables that can be optimized and transmitted to the robots prior to their deployment or broadcasted in real time. The planning and allocation problem can then be formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. Simulations of a commercial pollination scenario validate the ability of our control approach to drive a robotic swarm to achieve predefined spatial distributions of activity over a closed domain, which may contain obstacles. Secondly, we consider a mapping problem wherein a robotic swarm is deployed over a closed domain and it is necessary to reconstruct the unknown spatial distribution of a feature of interest. The ADR-based primitives result in a coefficient identification problem for the corresponding system of PDEs. To deal with the inherent ill-posedness of the problem, we frame it as an optimization problem. We validate our approach through simulations and show that reconstruction of the spatially-dependent coefficient can be achieved with considerable accuracy using temporal information alone.
ContributorsElamvazhuthi, Karthik (Author) / Berman, Spring Melody (Thesis advisor) / Peet, Matthew Monnig (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2014