What are the key stability challenges in high-bandwidth, non-minimum phase systems with time-varying, and non-smooth delays?

The analysis and control of stability in high-bandwidth systems characterized by non-minimum phase delays represent a formidable challenge within the realm of control theory and engineering. This research aims to address the pivotal question of whether it is feasible to enhance the stability of such intricate systems. These systems inherently possess uncertain and swiftly changing delay characteristics, rendering them exceptionally demanding to control effectively. In the course of this investigation, we embark on a comprehensive exploration of the theoretical underpinnings of the stability of high-bandwidth, non-minimum phase delay systems. This encompassing inquiry encompasses a meticulous consideration of both derivative-delay and piecewise continuous delay components. To underpin our analysis, we judiciously incorporate feedback mechanisms, drawing upon mathematical tools such as the Jensen inequality and Lyapunov-based methodologies to rigorously establish stability conditions. Furthermore, our exploration extends to encompass the concept of input-output stability and complements it with the notion of asymptotic stability, thereby ensuring that the systems in question exhibit uniform stability across diverse temporal domains. The outcomes of our investigation furnish compelling evidence that by harnessing the power of discrete-time Lyapunov-Krasovskii functionals, it becomes conceivable to circumscribe the maximum delay within predefined thresholds. This achievement holds the promise of enhancing stability in non-minimum phase delay systems characterized by high bandwidth. These findings have far-reaching implications, profoundly influencing the design and control paradigms across a spectrum of engineering applications. Notably, this impact extends to areas such as communication networks, real-time control systems, and robotics, where the mitigation of instability due to non-minimum phase delays has been an enduring challenge.

Design of infinite horizon LQR controller for discrete delay systems in satellite orbit control: A predictive controller and reduction method approach.

In the realm of satellite orbit control, powerful controller design plays a pivotal role in minimizing fuel consumption and ensuring orbit stability. This article introduces an advanced approach to the design of a Linear Quadratic Regulator (LQR) controller with an infinite horizon, tailored for discrete delay systems. The proposed methodology integrates predictive control with a reduction method, aiming for optimality while addressing performance and system constraints. Formulating the control problem as a quadratic program, the predictive control method generates a sequence of control inputs using a reducing horizon strategy. Stability analysis, employing Lyapunov-Krasovsky functions and linear matrix inequalities, yields delay-independent conditions for exponential convergence. A numerical example showcases the controller's effectiveness in maintaining orbit and reducing fuel consumption, underlining its capacity to achieve control objectives despite uncertainties and time delays. This research contributes to robust control strategies in satellite orbit systems, enhancing control performance and operational efficiency.

Low-voltage ride-through capability in a DFIG using FO-PID and RCO techniques under symmetrical and asymmetrical faults.

The power grid faults study is crucial for maintaining grid reliability and stability. Understanding these faults enables rapid detection, prevention, and mitigation, ensuring uninterrupted electricity supply, safeguarding equipment, and preventing potential cascading failures, ultimately supporting the efficient functioning of modern society. This paper delves into the intricate challenge of ensuring the robust operation of wind turbines (WTs) in the face of fault conditions, a matter of substantial concern for power system experts. To navigate this challenge effectively, the implementation of symmetrical fault ride-through (SFRT) and asymmetrical fault ride-through (AFRT) control techniques becomes imperative, as these techniques play a pivotal role in upholding the stability and dependability of the power system during adverse scenarios. This study addresses this formidable challenge by introducing an innovative SFRT-AFRT control methodology based on rotor components optimization called RCO tailored for the rotor side converter (RSC) within a doubly-fed induction generator (DFIG) utilized in wind turbine systems. The proposed control strategy encompasses a two-fold approach: firstly, the attenuation of both positive and negative components is achieved through the strategic application of boundary constraints and the establishment of reference values. Subsequently, the optimization of the control characteristic '[Formula: see text]' is accomplished through the utilization of a particle swarm optimization (PSO) algorithm integrated within an optimization loop. This intricate interplay of mechanisms aims to optimize the performance of the RSC under fault conditions. To measure the efficacy of the proposed control technique, a comparative analysis is conducted. Fractional-order (FO) proportional-integral-derivative (PID) controllers are employed as an additional method to complement the novel approach. By systematically juxtaposing the performance of the proposed SFRT-AFRT control technique with the FO-PID controllers, a comprehensive evaluation of the proposed approach's effectiveness is attained. This comparative assessment lends valuable insights into the potential advantages and limitations of the novel control technique, thereby contributing to the advancement of fault mitigation strategies in WT systems. Finally, the paper highlights the economic viability of the proposed control method, suggesting its suitability for addressing broader power network issues, such as power quality, in future wind farm research.