Control of a small helicopter with linear matrix inequality-based design assuring stability and performance

Abstract

This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local ${\mathcal{H}}_{\infty }$ controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based ${\mathcal{H}}_{\infty }$ controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local ${\mathcal{H}}_{\infty }$ controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.