Improved pilot training via bifurcation analysis and robust control for aircraft loss of control problems

Variable structure systems with sliding modes

Abstract: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.

Variable structure control: a survey

Abstract: A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >

MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs

Abstract: MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.

Bifurcation Analysis of Nonlinear Aircraft Dynamics

Abstract: A new approach is presented for analyzing nonlinear and high-a dynamic behavior and stability of aircraft. This approach involves the application of bifurcation analysis and catastrophe theory methodology to specific phenomena such as stall, departure, spin entry, flat and steep spin, nose slice, and wing rock. Quantitative results of a global nature are presented, using numerical techniques based on parametric continuation. It is shown how our methodology provides a complete representation of the aircraft equilibrium and bifurcation surfaces in the state-control space, using a rigid body model with aerodynamic controls. Also presented is a particularly useful extension of continuation methods to the detection and stability analysis of stable attracting orbits (limit cycles). The use of this methodology for understanding high-a phenomena, especially spin-related behavior, is discussed. RENDS in fighter aircraft design over the past few decades have resulted in configuration s noted for their high speed and performance capability. The cost of achieving this capability has been a drastic, often fatal loss of positive control of the aircraft as the pilot operates at or near the extremes of the flight envelope. This is especially true for aircraft motion at high angles of attack (a), where large deviations both in the state and control variables limits the application of the usual linearized analysis techniques. There is a conspicuous lack of techniques for analyzing global stability and large maneuver response of aircraft. While certain phenomena (e.g., roll coupling) have been analyzed in an isolated manner, there exists a clear need for a unified approach to analyze systematically global aircraft behavior at high a.

Application of bifurcation methods to nonlinear flight dynamics problems

Abstract: Applications of global stability and bifurcational analysis methods are presented for different nonlinear flight dynamics problems, such as roll-coupling, stall, spin, etc. Based on the results for different real aircraft, F-4, F-14, F-15, High Incidence Research Model, (HIRM), the general methods developed by many authors are presented. The outline of basic concepts and methods from dynamcal system theory are also introduced.