Takagi-Sugeno Model for Quadrotor Modelling and Control using Nonlinear State Feedback Controller

Abstract

In this paper we present a Takagi-Sugeno (T-S) model for Quadrotor modelling. This model is developed using multiple model approach, composed of three locally accurate models valid in different region of the operating space. It enables us to model the global nonlinear system with some degree of accuracy. Once the T-S model has been defined it is claimed to be relatively straightforward to design a controller with the same strategy of T-S model. A nonlinear state feedback controller based on Linear Matrix Inequality (LMI), and PDC technique with pole placement constraint is synthesized. The requirements of stability and poleplacement in LMI region are formulated based on the Lyapunov direct method. By recasting these constraints into LMIs, we formulate an LMI feasibility problem for the design of the nonlinear state feedback controller. This controller is applied to a nonlinear Quadrotor system, which is one of the most complex flying systems that exist. A comparative study between controller with stability constraints and controller with pole placement constrains is made. Simulation results show that the controller with pole placement constrains yields good tracking performance. The designed T-S model is validated using Matlab Simulink.