弹性飞机的混合H_2/H_∞最优PID控制器设计

Exploring a Better Design of Mixed H_2/H_∞ Optimal PID Controller for Flexible Aircraft

针对弹性飞机强鲁棒性、低阶次、低增益鲁棒控制器的设计问题,以某弹性飞机12阶模型为研究对象,研究了基于弹性飞机降阶模型的混合H2/H∞最优PID控制器的设计。首先基于平衡截断法得到了6阶降阶模型。然后,根据全阶模型和降阶模型的频域降阶误差选取了合适的鲁棒加权函数。之后,给出了系统跟踪误差的H2范数的一种简化计算方法用于计算H2范数优化设计指标。最后使用粒子群优化算法进行了混合H2/H∞最优PID控制器参数的优化得到了最优PID控制器。仿真结果表明,与H∞混合灵敏度控制器相比,混合H2/H∞最优PID控制器阶次更低,并能同时镇定参数和非参数两种不确定性具有更强的鲁棒性;对弹性形变有较好的抑制作用,对刚性模态也取得了很好的控制效果。

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.