This paper investigates the development of a novel analytic approach for computing Unity Magnitude (UM) shapers that deviates from established numerical methodologies. The experimental validation on a test bench confirms the practicality and benefits of the suggested UM shaper technique. The study extends the use of UM shapers to improve the control of wind conversion systems (WCSs), particularly those including hybrid excitation synchronous generators (HESGs), demonstrating their adaptability and versatility. Experimental validation guarantees real-world application, confirming the suggested UM shapers’ trustworthiness. Strict management is still required to assure the system’s efficiency and dependability. In reality, the dynamic equations of a turbine, as well as those of an HESG, are substantially nonlinear; most system parameters are very uncertain; and, finally, a WCS is always impacted by disturbance sources such as load variations, harmonics, and mechanical vibrations. Robust control measures must be used to overcome these issues. A CRONE controller (Robust Fractional Order Control) of the second generation is created. A comparative study performed on the Simulink platform reveals substantial gains brought about by UM shapers in real-world circumstances. The study demonstrates the effectiveness of UM-shaped inputs in mechanical stabilization and Maximum Power Point Tracking (MPPT), emphasizing both theoretical soundness and practical advantages. The analytic equations for UM shapers in undamped and damped systems, offered together with a real-time algorithm, contribute to the optimization of wind conversion systems.

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional integer-order derivative to the Hadamard fractional-order derivative, offering a more universally applicable method for system analysis. Furthermore, the traditional Lipschitz condition is adapted to a one-sided Lipschitz condition, broadening the range of systems amenable to analysis using these techniques. The efficacy of the proposed theoretical findings is illustrated through several numerical examples. For instance, in Example 1, we select an order of derivative r = 0.8; in Example 2, r is set to 0.9; and in Example 3, r = 0.95. This study enhances the comprehension and regulation of nonlinear Hadamard fractional-order systems, setting the stage for future explorations in this domain.

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS.

In this study, an unknown input observer is proposed for a class of nonlinear GPFOSs. For this class of systems, both full-order and reduced-order observers have been established. The investigated system satisfies the one-sided Lipschitz nonlinear condition, which is an improvement of the classic Lipschitz condition. Sufficient conditions have been proposed to ensure the error dynamics’ Mittag–Leffler stability. The value of this work lies in the fact that, to the best of the authors’ knowledge, this is the first research work that investigates the issue of Observer Design (OD) for GPFOSs. To exemplify the usefulness of the suggested observers, an illustrative numerical example is suggested.