AGTM Optimization Technique for Multi-Model Fractional-Order Controls of Spherical Tanks

Spherical tanks are widely utilized in process industries due to their substantial storage capacity. These industries’ inherent challenges necessitate using highly efficient controllers to manage various process parameters, especially given their nonlinear behavior. This paper proposes the Approximate Generalized Time Moments (AGTM) optimization technique for designing the parameters of multi-model fractional-order controllers for regulating the output (liquid level) of a real-time nonlinear spherical tank. System identification for different regions of the nonlinear process is here innovatively conducted using a black-box model, which is determined to be nonlinear and approximated as a First Order Plus Dead Time (FOPDT) system over each region. Both model identification and controller design are performed in simulation and real-time using a National Instruments NI DAQmx 6211 Data Acquisition (DAQ) card (NI SYSTEMS INDIA PVT. LTD., Bangalore Karnataka, India) and MATLAB/SIMULINK software (MATLAB R2021a). The performance of the overall algorithm is evaluated through simulation and experimental testing, with several setpoints and load changes, and is compared to the performance of other algorithms tuned within the same framework. While traditional approaches, such as integer-order controllers or linear approximations, often struggle to provide consistent performance across the operating range of spherical tanks, it is originally shown how the combination of multi-model fractional-order controller design—AGTM optimization method—GA for expansion point selection and index minimization has benefits in specifically controlling a (difficult to be controlled) nonlinear process.