An FO–[PI] controller for inverted decoupled two-input two-output coupled tank system

In this paper, a new structured fractional order-[proportional integral] ( $ {\rm FO-}{{\left [ {\rm PI} \right ]}^{\lambda }} $ FO−[PI]λ) controller design method is demonstrated. The designed controller is implemented in decoupled Two-Input Two-Output (TITO) Coupled Tank System (CTS) for liquid level control. An inverted decoupling technique is used to decouple the TITO process into two independent SISO (single-input single-output) processes. The designed $ {\rm FO-}{{\left [ {\rm PI} \right ]}^{\lambda }} $ FO−[PI]λ controller is implemented for each SISO process. A frequency domain approach is used to tune the parameters of the controller. While designing, to approximate the fractional integral terms of the controller, Oustaloup's Recursive Approximation (ORA) method is used in the stable frequency bands. To validate the proposed approach, the performance of the controller is compared with the existing controllers designed based on the same specifications. From the simulation and experimental studies, it is shown that proposed $ {\rm FO-}{{\left [ {\rm PI} \right ]}^{\lambda }} $ FO−[PI]λ gives better performance than $ {\rm FO-P}{{{\rm I}}^{\lambda }} $ FO−PIλ, PI and PID controllers.