Design and Analysis of Fractional-Order PID Controller and its variants for Nonlinear Process using Kalman Filter

Abstract

Nonlinear control study has evolved owing to the complexity of systems in multi-faceted disciplines. The most effective method of dealing with nonlinear systems is through linearization. Another revolution in the field of control is identifying the system with the help of fractional-order differential equations. Later, the fractional-order transfer function is calculated and controlled with the help of fractional-order controllers. This paper is a comprehensive work on a nonlinear system by taking a spherical tank case study. The work models the latter into multi-model integer order transfer functions (IOTF) then converts them into fractional-order transfer functions (FOTFs) via the frequency-domain method. It uses the Kalman filter algorithm to estimate the outputs of the various models of the multi-model bank. It then designs controllers, namely Proportional-Integral-Derivative (PID), Fractional-Order Proportional Integral Derivative (FOPID), and Multi-term Fractional-Order PID (MFOPIDs), using genetic algorithm. Subsequently, the paper thoroughly compares servo, regulatory, and robust responses of the PID controller and its variants.