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This paper presents a robust model order reduction technique with guaranteed stability, minimum phase, and matched steady-state response for linear time-invariant single-input-single-output systems. The proposed approach is generalized, allowing the designer to select any desired order of the reduced-order model (ROM). In contrast to the published literature, which primarily uses the time-domain behavior, the proposed technique utilizes the frequency-domain information of the full-order system. The suggested strategy allows the determination of the optimal ROM in a single step, simpler than the various recently reported mixed methods. The robustness is demonstrated using convergence studies and statistical measures about the final solution quality and model coefficients. The superiority over the recent literature is illustrated through four numerical examples using various time-domain and frequency response performance metrics.

The interest in fractional-order (FO) control can be traced back to the late nineteenth century. The growing tendency towards using fractional-order proportional-integral-derivative (FOPID) control has been fueled mainly by the fact that these controllers have additional 'tuning knobs' that allow coherent adjustment of the dynamics of control systems. For instance, in certain cases, the capacity for additional frequency response shaping gives rise to the generation of control laws that lead to superior performance of control loops. These fractional-order control laws may allow fulfilling intricate control performance requirements that are otherwise not in the span of conventional integer-order control systems. However, there are underpinning points that are rarely addressed in the literature: (1) What are the particular advantages (in concrete figures) of FOPID controllers versus conventional, integer-order (IO) PID controllers in light of the complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are indeed equivalent to high-order linear controllers. What, then, is the benefit of using FOPID controllers? Finally, (3) What advantages are to be had from having a near-ideal fractional-order behavior in control practice? In the present paper, we attempt to address these issues by reviewing a large portion of relevant publications in the fast-growing FO control literature, outline the milestones and drawbacks, and present future perspectives for industrialization of fractional-order control. Furthermore, we comment on FOPID controller tuning methods from the perspective of seeking globally optimal tuning parameter sets and how this approach can benefit designers of industrial FOPID control. We also review some CACSD (computer-aided control system design) software toolboxes used for the design and implementation of FOPID controllers. Finally, we draw conclusions and formulate sugge, Mechatronic Systems Design