HIL co-simulation of an optimal hybrid fractional-order type-2 fuzzy PID regulator based on dSPACE for quadruple tank system

Accurate regulation of the liquid level in a quadruple tank system (QTS) is not easy and imposes higher requirements on control strategies, so the design of controllers in these systems is challenging due to the difficulty of dynamic analysis of its nonlinear characteristics and parametric uncertainties. To overcome these problems in liquid level regulation and increase the robustness to the pump coefficients, this article proposes and investigates the use of an optimal hybrid fractional-order type-2 fuzzy-PID (OH-FO-T2F-PID) regulator using a combination of two bio-inspired evolutionary optimizers, namely augmented grey wolf optimizer and cuckoo search optimizer, which gives rise to the new hybrid A-GWOCS algorithm. This control mechanism was chosen to facilitate the convergence of the water liquids in the two tanks as quickly as possible to the corresponding required values. In addition, a collaborative optimization technique with several objectives is used to adjust the regulator parameters. The capability and efficiency of the suggested regulator is first investigated through computer simulation results and then confirmed by real-time control experimental results on the QTS based on dSPACE 1104 computation engine. The findings showed that the suggested OH-FO-T2F-PID regulator significantly outperformed both the optimized ADRC and the OH-FO-T1F-PID regulators. Specifically, it reduced the rising time by 17.02% and 95.21%, respectively, and the settling time by 25.13% and 74.28%. Additionally, the designed OH-FO-T2F-PID regulator successfully eliminated the steady-state error and overshoot, enabling precise regulation of the QTS, and maintenance the liquid level at the desired set point under a wide range of working situations. The robustness of the recommended regulator is also studied by considering - 50% disturbance in the QTS parameters, and the findings showed that the OH-FO-T2F-PID regulator is less susceptible to variations in parameters.