Abstract

The study of highly maneuverable aerobatic helicopters has received a growing amount of interest in the past few years. This thesis describes the development of an analytic dynamic model of an aerobatic helicopter with the least amount of complexity and with sufficient accuracy for control system development. The model is based on a rigid body dynamics formulation with applied external forces and moments including the effects of gravity and aerodynamics. The model is validated by comparing simulation results with flight test data available in the literature for a YAMAHA R-50 helicopter. The model is further simplified to obtain a three degree of freedom helicopter model and a piecewise-affine (PWA) approximate representation. The model is then used to develop a PWA controller for the system. To design this controller a local linear controller is designed for the PWA approximate model in the region where the desired closed-loop equilibrium point lies. An optimization problem subject to Bilinear Matrix Inequalities (BMIs) is then solved to find a PWA extension of the linear controller. A piecewise quadratic Lyapunov function is found which proves stability of the closed-loop system in the whole domain of the nonlinearity. This work develops a physics-based model for aerobatic helicopters representing a complete derivation that allows approximations to be made to yield a simplified representation for PWA control design and analysis. The model is also expressed in a linear parameterized form ideal for parameter estimation and adaptive control. Finally, this research represents the first development of a PWA model and controller for an aerobatic helicopter system.