Design and implementation of the fractional-order controllers for a real-time nonlinear process using the AGTM optimization technique

Spherical tanks have been predominantly used in process industries due to their large storage capability. The fundamental challenges in process industries require a very efficient controller to control the various process parameters owing to their nonlinear behavior. The current research work in this paper aims to propose the Approximate Generalized Time Moments (AGTM) optimization technique for designing Fractional-Order PI (FOPI) and Fractional-Order PID (FOPID) controllers for the nonlinear Single Spherical Tank Liquid Level System (SSTLLS). This system features a large dead time, and its real-time modeling generally represents a Single Input Single Output (SISO) model. However, in practice, the derived SISO model is often a First Order Plus Dead Time (FOPDT) model, necessitating an effective controller to maintain the tank's steady-state level. In this research, the proposed AGTM method, based on the conventional Proportional Integral (PI) and Proportional Integral Derivative (PID) controllers, is compared with the FOPI and FOPID controllers for the nonlinear SSTLLS. The performance of these controllers is contrasted using metrics such as Integral Squared Error (ISE) and Integral Absolute Error (IAE), as well as time-domain characteristics containing Rise time, Peak time, Settling time, Peak overshoot, and Steady-state error. The implementation of the aforementioned controllers is done in simulation and real-time employing the MATLAB software environment and the Data Acquisition (DAQ) device National Instrument NI-DAQmx 6211. The simulation and experimental results demonstrate the exceptional performance of the designed Fractional-Order controllers based on the proposed method which offers an increased degree of freedom despite the more complex design process.