Striking developments have taken place in feedback control theory after the evolution of the fractional-order (FO) control concept. However, for large-scale (high-order) systems, these well-established FO techniques become rigorous and lead to an infeasible solution. To overcome this issue, this paper proposes a three-fold control policy. The first step finds the optimal reduced-order (low-order) model using Big-Bang, Big-Crunch (BB–BC) optimisation algorithm. Based on the obtained reduced model, the control structure is formulated in the internal model control (IMC) framework. The controller acquires a PID form followed by an additional term and FO integrator. Unlike the FO-PID controller which demands five tuning parameters, the proposed controller requires only two tuning parameters whose evaluation is done on the basis of user specified gain crossover frequency and phase margin. To substantiate the design approach, a detailed simulation study has been carried out, in which the problems of tracking control, disturbance rejection, and time-delay compensation are illustrated.

在分数阶 (FO) 控制概念演变之后，反馈控制理论发生了惊人的发展。然而，对于大规模（高阶）系统，这些成熟的 FO 技术变得严格并导致不可行的解决方案。为了克服这个问题，本文提出了三重控制策略。第一步是使用 Big-Bang, Big-Crunch (BB–BC) 优化算法找到最优的降阶（低阶）模型。基于获得的简化模型，在内部模型控制（IMC）框架中制定控制结构。控制器获取一个 PID 形式，后跟一个附加项和 FO 积分器。与需要五个调整参数的 FO-PID 控制器不同，建议的控制器只需要两个调谐参数，其评估是根据用户指定的增益交叉频率和相位裕度完成的。为了证实设计方法，进行了详细的仿真研究，其中说明了跟踪控制、干扰抑制和时延补偿问题。