Fractional-Order Feedforward Enhanced Delay-Aware Self-Optimizing Control for First-Order Plus Delay-Time Systems

First-order plus delay time systems are commonly used to approximate thermal or temperature process control systems, covering approximately 80% of all industrial controls. These systems are characterized by a “relative time delay,” which represents the delay (L) about the time constant (τ). However, this relative time delay can fluctuate in real-time control scenarios, potentially compromising system stability. To address this issue, control experts have introduced a supervisory layer called self-optimizing control (SOC) on top of the control layer. SOC aims to determine optimal feedback control (PID) parameters considering the varying relative time delay. Despite efforts to optimize parameters, it has been observed that the best results often lead to longer rise time and convergence time. This paper explores using fractional-order and integer-order reference models as feedforward compensation alongside the supervisory layer to enhance the SOC controller performance. The globalized constrained Nelder-Mead (GCNM) algorithm finds optimal parameters for the feedforward and feedback controllers. Performance indices, including root mean square (RMS), root mean square error (RMSE), integral square error (ISE), integral absolute error (IAE), SOC convergence time, settling time, and overshoot, are computed to evaluate the overall controller performance. The results indicate that the fractional-order feedforward setup slightly outperforms the integer-order feedforward setup with variable relative time delays.