Back to Search
Start Over
Differential-Geometric-Control Formulation of Unconventional Flight Dynamics
Differential-Geometric-Control Formulation of Unconventional Flight Dynamics
- Publication Year :
- 2018
-
Abstract
- Differential-geometric control theory exploits \textit{differential geometry} in the analysis of dynamical control systems. Differential geometry is a mathematical discipline that is concerned with studying calculus on curved (non-Euclidean) spaces. The main focus of this Dissertation is to formulate modern aeronautical engineering applications in a differential-geometric control framework. Nonlinear controllability analysis is one of the most important aspects of differential-geometric control theory. Its importance emanates from the fact that linear controllability conditions for linearized systems are not necessary. That is, there exists a class of nonlinear systems that are linearly uncontrollable but nonlinearly controllable. In particular, it allows for identification of the ability to generate motions along unactuated (nonintuitive) directions through specific interactions between the system dynamics and control inputs. In this Dissertation, differential-geometric control theory is utilized to analyze the nonlinear controllability of airplane flight dynamics. This study lead to several discoveries. First, it is found that an airplane in an upset situation where all control surfaces are blocked (inoperative) and linear controllability is lost, nonlinear controllability can be recovered using engine control only. More importantly, the study reveals unconventional mechanisms to generate motion along different directions in the state space. In particular, a novel roll mechanism that relies on nonlinear interactions between the elevator and aileron control surfaces is discovered. This novel roll mechanism is found to be superior in comparison to the conventional one (using ailerons only) near stall. Using differential-geometric control tools (e.g., non-holonomic motion planning and Fliess functional expansion), it is shown that the discovered roll mechanism can provide four times rolling motion near stall in comparison to the conventional roll control using ailero
Details
- Database :
- OAIster
- Notes :
- application/pdf, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1287453005
- Document Type :
- Electronic Resource