A simple approach to mathematical modelling of integer order and fractional order fuzzy PID controllers using one-dimensional input space and their experimental realization

Abstract Though over the years, mathematical modelling of fuzzy PID controllers is carried out extensively with two-dimensional and three-dimensional input spaces, the modelling is rarely attempted using one-dimensional input space. In this paper, this gap is reduced by proposing a simple approach where each of the fuzzy P, fuzzy I, and fuzzy D components is modelled using one-dimensional input space and merged to provide the complete PID action. Another speciality of the proposed approach is that it does not require any AND or OR operator for obtaining the mathematical models of individual PID components. To the best of author’s knowledge, such a modelling approach is completely new. This newly introduced idea of modelling is further extended to fractional order fuzzy PID controllers. Applicability of the proposed fuzzy controllers is delineated with four simulation examples and one real-time experimentation case study. To understand the usefulness of the proposed control schemes, performances of the newly obtained controllers are compared with the results available in literature. As the proposed controllers are model-free controllers, they can easily be implemented for other control applications also.