Exploring a better design of mixed H₂/H_∞ optimal PID controller for flexible aircraft

Aim. The introduction of the full paper reviews a number of papers and then, in its last paragraph, proposes the exploration of a better design; the exploration results are explained in sections 1 and 2. Section 1 employs the balanced truncation reduction method to obtain the model of a flexible aircraft, which is reduced from 12 orders to six orders, and then selects a suitable robust-weighting function. Section 2 proposes a simplified method for computing the H₂ norm of system tracking error so as to obtain the H₂ performance index of our optimal design; it also optimizes the parameters of the mixed H₂/H_∞ optimal PID controller with the particle swarm optimization algorithm. Section 3 simulates the full-order model of the flexible aircraft controlled by using the mixed H₂/H_∞ optimal PID controller designed by us and the H_∞ mixed sensitivity controller respectively. The simulation results, given in Figs. 5 through 8, and their analysis indicate preliminarily that: (1) our mixed H₂/H_∞ optimal PID controller has lower order than the H_∞ mixed sensitivity controller and can stabilize the parameter uncertainty and non-parameter uncertainty simultaneously; (2) it can suppress the elastic structural deformation of the flexible aircraft and control its rigid modal effectively.