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The coupled tank system (comprising two tanks) is used in the chemical industries, water treatment plants etc. Level control of the coupled tank system is a common problem in the process control industry. This work proposes a fractional order internal model controller (FOIMC) with a higher order fractional filter for the level control of the coupled tank system. A first order plus delay time (FOPDT) model of the system is used in the controller design. FOIMC has advantages like robustness to changes in the system gain and extended stability margins. The proposed higher order fractional filter makes the controller physically realisable, and quickly roll off the magnitude Bode plot, neglecting the high frequency noise. The PSO algorithm is a swarm intelligence based algorithm used for the optimisation problems. The parameters of the FOIMC are optimised with the particle swarm optimisation (PSO) algorithm, by minimising an objective function constructed using time domain specifications. The novel objective function includes weighted peak overshoot, settling time, and integral square error. A MATLAB based tool, fractional order modelling and control (FOMCON) is used to simulate the fractional order controller. Performance of the proposed FOIMC is compared with two state of the art. Robustness to change in the operating point (tank height) is verified. The proposed FOIMC and the state of the art controllers are implemented on the laboratory setup, and the experimental results are compared.

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<div data-canvas-width="397.2227827050999">This paper proposes a fractional order controller (FOC) for the level control problem of the coupled tank system, using the desired time domain specifications. The coupled tank system is used in the chemical industries for the storage and mixing of liquids. The FOC is designed analytically using the direct synthesis method. In the direct synthesis method, the Bode's ideal loop transfer function is chosen as the desired transfer function. Bode's loop transfer function has the advantages like robustness to system gain variations, constant phase and very high gain margin. Performance of the proposed controller is compared with the state of the art literature. Simulation results showed that the proposed controller has the least peak overshoot. The robust performance of the proposed controller is also the best. Robust stability of the system with the proposed controller is verified, and the system is found to be robustly stable.</div>