参数不确定统一混沌系统的鲁棒分数阶比例-微分控制

针对含参数不确定的整数阶统一混沌系统, 提出一种鲁棒分数阶比例-微分(PD^μ)控制. 通过变换将受控统一混沌系统转换成等效被控对象及其等效控制器. 针对等效被控对象, 基于一种改进Monje-Vinagre方法并考虑到求解性能约束方程组的复杂度, 设计了鲁棒PD^μ控制器. 通过基于最小相角边界传递函数和最大增益边界传递函数的设计约束来保证受控统一混沌系统对参数不确定性的鲁棒性能. 数值仿真验证了所提出方法的有效性.

Robust fractional-order proportional-derivative control of unified chaotic systems with parametric uncertainties

In this paper, a robust fractional-order proportional-derivative (PD^μ) control is designed for controling in integer-order unified chaotic systems with parametric uncertainties. Equivalent plant is obtained by transforming the controlled dynamic system, and then the PD^μ controller as an equivalent controller is applied to the equivalent plant. In the uncertain controlled unified chaotic systems, one equation is certain, and the other two equations are uncertain . The equivalent controller for the certain system is then designed based on a fractional-order proportional-derivative controller, in which three specifications for phase margin, gain crossover frequency, and robustness should be met. On the other hand, the robustness of uncertain systems is achieved by an improved Monje-Vinagre tuning method, however, the pre-specified frequency band should be replaced by the gain crossover frequency in order to reduce the complexity in determining the controllers for the uncertain systems. Specifications related to phase margin for the lower bound of the phase, gain crossover frequency for the upper bound of the gain, and robustness for the lower bound of the phase constraints are satisfied by the uncertain system. Parameters of the equivalent controller are determined based on a graphical method. Origins of the unstable equilibrium can be asymptotically stabilized by the proposed strategy for the integer-order unified chaotic systems with parametric uncertainties. Numerical simulation examples for Chen system, Lü system, and Lorenz system, are given to show the effectiveness of the proposed method.