Stable adaptive NSOF domain FOPID controller for a class of non‐linear systems

The present study proposes a new approach for designing stable adaptive fractional‐order proportional–integral–derivative (FOPID) controllers, which employs non‐sinusoidal orthogonal function (NSOF) domain‐based design approach. The objective is to design a self‐adaptive FOPID controller such that the designed controller can guarantee desired stability and simultaneously it can provide satisfactory transient performance. The proposed design methodology simplifies and eliminates the complexity of solving fractional‐order system dynamics by converting it into the algebraic vector–matrix equation with the help of NSOF. The conventional FOPID, NSOF‐based FOPID and NSOF‐based adaptive FOPID controllers are implemented for benchmark simulation case studies and real‐life experimentation and their results demonstrate the usefulness of the proposed approach.