Direct Model Reference Adaptive Control for Linear Fractional System of Commensurate Order with Time Delay Using Smith Predictor

This project designs and simulates a direct model‑reference adaptive control (MRAC) scheme for linear fractional‑order systems that have a common (commensurate) order and large time delays. Because transport delays can make fractional‑order dynamics unstable and hurt performance, the design includes a modified Smith predictor. Instead of the usual integer‑order model, the predictor uses a fractional‑order inner model that matches the plant’s dynamics. The controller parameters are updated online with a gradient‑based MIT rule that has been adapted for fractional‑order representations. Simulations are set up to test whether the control system can follow a reference model while cancelling the dead time. The project also gives step‑by‑step instructions for * building commensurate

fractional‑order transfer functions, * implementing the modified Smith predictor, and * deriving the sensitivity functions needed for the MIT‑rule adaptation loop. The resulting framework provides a solid reference for studying both transient and steady‑state behavior of adaptive controllers that operate under delayed fractional‑order dynamics. It offers a practical method for process‑control applications where fractional‑order behavior and transport delays occur together.

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