Abstract This work proposes a fractional-order internal model controller (FOIMC), for the height control of a conical tank nonlinear system. The proposed controller has a fractional filter cascaded with an integer-order PID controller. The FOIMC combines the advantages of IMC such as few tuning parameters, and a stable controller with the advantages of fractional control such as robustness, flexibility in tuning parameters, and a wide stability margin. Linearising the nonlinear system includes the Lagrange remainder term to compensate for the higher-order derivatives. The PSO algorithm and WOA are used to optimise the FOIMC controller parameters. The servo and regulatory responses of the proposed controller are compared with those of state-of-the-art technique showing a 35% improvement in the rise time and 100% improvement in the peak overshoot of the step response. The proposed controller shows better robustness to gain variations and consumes less control energy than the other controller. The proposed controller rejects disturbances faster than the other controller.

中文翻译：

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使用分数阶控制器控制锥形罐的液位

摘要 这项工作提出了一种分数阶内模控制器（FOIMC），用于锥形储罐非线性系统的高度控制。所提出的控制器具有与整数阶 PID 控制器级联的分数滤波器。FOIMC 结合了 IMC 的优点，例如调整参数少，稳定控制器与分数控制的优点，例如鲁棒性、调整参数的灵活性和宽的稳定性裕度。线性化非线性系统包括拉格朗日余项以补偿高阶导数。PSO 算法和 WOA 用于优化 FOIMC 控制器参数。将所提出的控制器的伺服和调节响应与最先进的技术进行比较，显示上升时间提高了 35%，阶跃响应的峰值过冲提高了 100%。与其他控制器相比，所提出的控制器对增益变化表现出更好的鲁棒性并消耗更少的控制能量。所提出的控制器比其他控制器更快地拒绝干扰。