Piecewise-affine control of a three DOF helicopter

This paper develops a piecewise-affine (PWA) controller for a nonlinear three degree of freedom (DOF) helicopter model. To design this controller a local linear controller is designed for a PWA approximation of the 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 semi-global extension of the linear controller. A piecewise-quadratic Lyapunov function is found which proves stability of the PWA closed-loop system in the whole domain of the nonlinearity. This research represents the first development of a PWA model and controller for a helicopter. The synthesis method presented in this paper enables the extension of a local linear controller designed for helicopter performance to a stabilizing semi-global PWA controller that still meets the helicopter performance requirements while the system operates close to the equilibrium point.