Comparative Design for Improved LQG Control of Longitudinal Flight Dynamics of a Fixed-Wing UAV

Abstract

This paper explores the design, simulation and analysis of three novel Linear Quadratic Gaussian (LQG) control system for a Longitudinal dynamic of a fixed wing mini Unmanned Aerial Vehicle (UAV). Modelling results for the small UAV using Aircraft DIGITAL DATCOM® are presented. The novelty of the design is from the stand point of the Kalman Filter, with Kalman gain obtained from the solution to a Differential Riccati Equation (DRE) rather than the popular Algebraic Riccati Equation (ARE). The formulated DRE to the Kalman filter design is solved as an Initial Value Problem (IVP) in the MATLAB/Simulink® using explicit algorithm ode45. The algorithm converges to a solution of interest with 6671steps. Each step has a covariance matrix hence a different Kalman gain value as the solution tries to converge, after 10 seconds of simulation. Three of 6671 step values are selected based on the observed trajectory of the Kalman gain matrix and the time for the set-point tracking control of the pitch angle to reach a steady-state value. Three of these Kalman gains obtained were used in the design of the linear Kalman filter, which serves as the observer for the Linear Quadratic Regulator (LQR), hence the improved LQG controllers. Comparison is made between the three improved LQG controllers and the LQG controller on the bases of step response characteristics and robustness. Using the robustness properties of the Kalman filter as a benchmark, simulation result shows that all the three improved LQG controllers outperform the LQG.