Fractional-order VRFT Reference Model and Controller Synthesis for Uniformity Temperature Control Applications

Data-driven controller synthesis methods allow finding controller parameters based only on the system input-output response. Among these methods, Virtual Reference Feedback Tuning (VRFT) is accepted thanks to its reference-model based direct parameters synthesis, including robustness and noise rejection considerations for integer and fractional-order controller design. However, for fractional-order VRFT controller synthesis, a direct solution is harder to reach involving a complex optimization problem to solve. This paper presents a recursive VRFT method for synthesizing arbitrary degree fractional-order controllers with feedforward based on a integer or fractional-order reference model. This methodology leverages existing optimization tools for fractional-order systems identification to obtain integer and fractional-order controller gains when integer and fractional-order reference models are used for the virtual error computation. The proposed method synthesizes a set of feedforward VRFT controllers implemented to control a uniform temperature control system. The results show that combining a fractional-order model or compensator improves the energy consumption of the controller and the transient temperature response in tracking and regulation tasks.