New flat phase margin fractional order PID design: Perturbed UAV roll control study

Abstract Fractional order PID is a regulator of choice in dealing with system uncertainties. In a typical FOPID design, a simple approximate model of the linearized system is derived and by making, the derivative of the open loop phase versus frequency at crossover frequency zero, flat phase margin is obtained. The method tolerates system gain uncertainty and involves two set of nonlinear computations: model approximation and five-parameter FOPID calculations. The method shows flaws where severe uncertainty occurs in the form of gain and poles–zeros locations. In this respect, a modified design method is suggested to prevent performance degradation. Using Monte Carlo simulation, the plot of distribution of open loop system phase margins versus crossover frequencies is drawn. Instead of approximate modeling, several frequencies at the crossover band are marked and their average phase margins from the distribution plot are picked to represent the real uncertain system. Calculations of the FOPID parameters are carried out using nonlinear optimization method to make phase plot flat around the crossover frequency. The design sequence is detailed by applying to the roll control of a small Unmanned Aerial Vehicles (UAV) where often rough approximates of its aerodynamic parameters are available. It is shown that the proposed design outperforms the conventionally designed FOPID and definitely PID in leading the roll, yaw and pitch motion in a very coherent manner. This is confirmed in this case by extensive simulations.