A design approach of fractional model error compensator for fractional dynamical systems with polytopic uncertainty and disturbance

We present a novel design methodology for a fractional model error compensator (FMEC) that addresses the challenge of model errors in fractional dynamical systems with polytopic uncertainty and disturbances. The FMEC can effectively compensate for model errors, thereby enhancing the performance of control systems. This approach leverages a combination of \(\mathcal{H}_\infty \) ${\mathcal{H}}_{\infty }$ -norm criteria and the Particle Swarm Optimization (PSO) algorithm to optimize the compensator design. The methodology integrates \(\mathcal{H}_\infty \) ${\mathcal{H}}_{\infty }$ -norm criteria for robust performance evaluation and PSO for optimization. The proposed FMEC design is validated through numerical simulations conducted on a fractional dynamical system. These simulations demonstrate that the design successfully compensates for model errors and improves the overall performance of the control system. This study offers a practical solution for designing robust FMECs applicable in various engineering fields, particularly for systems susceptible to polytopic uncertainty and disturbances.