Design and implementation of Predictive Fractional-Order PID controller for the minimum phase of a multivariable system

In single-input single-output (SISO) process control applications, the PID family of controllers remains popular due to its simple structure, ease of tuning, and effective performance. However, many real-world processes are inherently multivariable, non-linear, and dynamically interacting, where conventional PID controllers have degraded performance. To address these challenges, this paper proposes a Predictive Fractional-Order PID (FOPPID) controller for multivariable process control. The proposed controller integrates the predictive control technique with a fractional-order PID structure, enabling it to anticipate future process behaviour and improve closed-loop tracking and disturbance rejection. The proposed FOPPID controller has been designed and experimentally validated for a minimum-phase in the Quadruple Tank System (QTS). This controller utilizes its fractional-order characteristics to enhance robustness in shaping the closed-loop response and incorporates a predictive mechanism designed to minimize control error over a defined prediction horizon. Experimental results show that the proposed controller exhibits significant improvements in transient response characteristics compared to conventional methods. Especially, the proposed controller achieves a rise time that is 67.43% faster and an average settling time that is 14.99% quicker than traditional controllers. Furthermore, the peak overshoot has been reduced by 47.93% compared to the average overshoot of conventional controllers. The controller also realizes substantial decreases in performance metrics, achieving an average reduction in Integral Absolute Error (IAE) of 90.96%, Integral Squared Error (ISE) of 94.75%, Integral Time Absolute Error (ITAE) of 96.65%, and Integral Time Squared Error (ITSE) of 99.78%.