Control Theory Commons^™

A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams, Md Rafi As Sadeq Ibn Emran

Masters Theses & Specialist Projects

The one-dimensional Partial Differential Equation (PDE) model of the wave equation, which describes wave dynamics of a wide-range of controlled mechanical systems, with a state feedback controller at its boundary is known to have exponentially stable solutions. Moreover, it is also reported that the several model reductions of the wave equation by the standard Finite Differences and Finite Elements approximations suffer from the lack of exponential stability (and exact observability without a state feedback controller) uniformly as the discretization parameter tends to zero. This is due to the loss of a uniform gap among the high-frequency eigenvalues as the discretization …

Analysis Of Boundary Observability Of Strongly Coupled One-Dimensional Wave Equations With Mixed Boundary Conditions, Wilson Dennis Horner

Masters Theses & Specialist Projects

*see note below

In control theory, the time it takes to receive a signal after it is sent is referred to as the observation time. For certain types of materials, the observation time to receive a wave signal differs depending on a variety of factors, such as material density, flexibility, speed of the wave propagation, etc. Suppose we have a strongly coupled system of two wave equations describing the longitudinal vibrations on a piezoelectric beam of length L. These two wave equations have non-identical wave propagation speeds c1 and c2. First, we prove the exact observability inequality with the optimal …

Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen

Masters Theses & Specialist Projects

This thesis aims to investigate the controllability and observability of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally …