Bifurcation-based fractional-order PI~λD~μ controller design approach for nonlinear chaotic systems

用于非线性混沌系统的基于分岔分数阶PID控制器设计方法（英文）

We propose a novel approach called the robust fractional-order proportional-integral-derivative（FOPID）controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system,we show that the fractional PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

提出一个新的鲁棒分数阶比例-积分-微分(FOPID)控制器,以其中一个不稳定的固定点来稳定一个扰动非线性混沌系统。基于使用分岔图的比例-积分-微分行为,分析非线性混沌系统的稳定性。提取控制器参数的初始集,其后续可通过二次准则优化。积分和微分分数阶也被二次准则识别。在两个非线性系统(陈氏多涡卷混沌系统和Genesio-Tesi混沌系统)中应用数值模拟,结果表明分数阶比例-积分-微分控制器在稳定非稳定固定点过程中,甚至在随机扰动情况下,能够提供最好的闭环系统性能。