Oscillation Analysis for Longitudinal Dynamics of a Fixed-Wing UAV Using PID Control Design

Abstract

A longitudinally disturbed motion of a UAV after an arbitrary initial disturbance consists normally of two oscillatory modes: the short-period oscillation and the phugoid oscillation.The typical longitudinal model of a UAV in state-space can be separated into short-period mode and phugoid period mode equations of motion. In this study, we choose to investigate the dynamic characteristics of the longitudinal dynamic equation of a mini-UAV and its reduced forms popularly known as short-period and phugoid period modes. This is necessary to establish a basis for plant selection during PID autopilot design. The short and phugoid period oscillations modes are sieved from the longitudinal dynamic equation and carry the same eigenvalues of the longitudinal model, but they still differ. Firstly, the three systems have different step response trajectories due to their different DC gain values. Secondly, the variables that constitute the short-period and phugoid mode dynamic equations can be identified by their settling time after designing PID controllers. State-space model of the longitudinal dynamics, phugoid mode and short period dynamics of a UAV can be transformed into equivalent transfer functions. These transfer functions are then used in the design of Proportional, Integral and Derivative (PID) controllers. Hence, the phugoid mode variables are the system variables in the longitudinal dynamic model with the longest settling time. The short period mode variables are the longitudinal system variables with the shortest settling time. Synthesis and simulation were done in MATLAB/Simulink. Also, from simulation results, plant for autopilot design could be selected based on the system with smallest rise time.