A Novel Fractional-Order Predictive PI Controller Approach for the Systems With Noninteger Order Delay

Time delay (TD) is a common phenomenon in practical systems. Most studies have focused on the classical notion of integer-order TD. However, it should not be neglected that the delay can also be noninteger. The number of studies on such systems is quite limited due to the complexity of the mathematical analysis. Addressing this gap, this study introduces a novel fractional-order TD (FOTD) based fractional-order predictive proportional-integral (FOPPI) controller, specifically designed for noninteger order delayed systems. Two distinct systems, the first-order and integrator distributed parameter system (DPS) are considered in the study. The parameters of the proposed FOPPI controller are optimized using the jellyfish search optimization (JSO) algorithm to minimize the time-weighted integral of absolute error (ITAE) criteria. The performance of the FOPPI controller is compared with optimized PI, fractional-order PI (FOPI), and integer-order predictive PI (PPI) controllers. In the study, performance tests such as time domain analysis, limited control signal performance, disturbance rejection at the input and output of the plant under noise, system parameter uncertainty, and frequency response analysis are used to comprehensively investigate the functionality of the controllers. The obtained results show that the time and frequency domain performance of the FOPPI controller is superior to FOPI, PPI, and PI controllers. The findings demonstrate that enhancements in the objective function of up to 62% for the first-order and up to 80% for the integrator DPS models are attained through the comparative controllers. The FOPPI controller exhibits remarkable robustness and control effort, providing a highly effective choice for uncertain control applications with systems having FOTD.