Industrial process control systems suffer from the overshoot problem. Designing the controller plant models by conventional Proportional Integral Derivative (PID) may increase the rise time, settling time and overshoot. Cascade control is a remedial measure undertaken to overcome these problems. In this paper, we present a new cascade model using fractional-order PIDs. The fractional-order cascade controller can be expressed by fractional-order differential equations. Different laws proposed in the field of fractional calculus form the theoretical part in evaluating the equations and designing the controllers. The new structure gives improved responses for the first-order and second-order systems with time delay. Better simulation results are obtained by introducing Smith predictor in primary and secondary loops. Detailed analyses have been done on the stability, performance criteria and disturbance rejection. The usefulness of this proposed cascade structure and its superiority over normal cascade are illustrated with examples.

工业过程控制系统存在过冲问题。通过常规比例积分微分（PID）设计控制器工厂模型可能会增加上升时间，建立时间和过冲。级联控制是为克服这些问题而采取的补救措施。在本文中，我们提出了一种使用分数阶PID的新级联模型。分数阶级联控制器可以由分数阶微分方程表示。分数微积分领域提出的不同定律构成了评估方程和设计控制器的理论部分。新的结构为具有时间延迟的一阶和二阶系统提供了改进的响应。通过在主回路和副回路中引入Smith预测器，可以获得更好的仿真结果。已经对稳定性，性能标准和干扰抑制进行了详细分析。举例说明了这种建议的级联结构的有用性及其相对于普通级联的优越性。