Level control of a conical tank using the fractional order controller

•A fractional-order internal model controller for the height control of a conical tank nonlinear system is proposed.•A first-order transfer function model of the conical tank system is obtained using the Taylor series expansion, including the Lagrange remainder term.•The controller parameters are optimised using particle swarm optimisation algorithm and the whale optimisation algorithms.•Servo and disturbance responses of the controllers obtained using the particle swarm optimisation algorithm, and the whale optimisation algorithms are compared.•Robustness of the proposed controller is verified. 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. [Display omitted]