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Interconnected power systems receive power through tie lines. Sudden perturbation in load causes uneven power distribution issues resulting in sudden changes in the voltage and frequency in the given system (tie-line power exchange error). The Load Frequency Controller (LFC) has an ability to stabilize the system for the above mentioned disturbances. In this paper, a novel load frequency controller based on Type-2 Fuzzy Quasi-Decentralized Functional Observer (T2FQFO) is proposed. In the proposed methodology the observer gains are obtained mathematically which guarantees, the stability of the system. The efficacy of the proposed technique has been tested on an IEEE standard testing systems. The results shows the proposed T2FQFO has higher performance when compared with Fuzzy Quasi-Decentralized Functional observer, Quasi- Decentralized Functional observer and classical state observer. And the results say that the peak over shoot and settling time have been improved by 25% (Approx.) by Type-2 Quasi Decentralized Functional Observer ((T2FQFO) than other observers.

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Functional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H ∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach.

Safe driving requires a comprehension of critical instances and dangers, achievable only through accurate estimation of dynamic vehicle behavior and road characteristics. This study proposes a Takagi-Sugeno (T-S) fuzzy functional observer capable of real-time estimation of unmeasured states (side-slip angle, yaw rate, angular displacement) and unknown inputs such as road curvature, using Lyapunov-Krasovskii stability theory and Linear Matrix Inequalities (LMIs) for parameter design. The objective is to provide a computationally efficient and robust solution that overcomes the restrictive assumptions of Proportional-Multiple Integral Observers (PMIO) and the complexity of Fuzzy Unknown Input Observers (FUIO) while ensuring real-time feasibility for embedded automotive systems. Comparative simulations and Processor-in-the-Loop (PIL) validation demonstrated that the proposed observer achieved superior accuracy, faster convergence, and lower computational cost than Full-Order Observer (FO), PMIO, and FUIO, confirming its novelty and practical potential for integration into advanced driver assistance systems to enhance safety and reduce accident risks.

This technique note proposes two classes of functional and disturbance observers for positive systems with structural and non-structural disturbances, respectively. A positive functional observer is first proposed for positive systems by introducing the estimation of disturbance to the observer. By developing the disturbance observer technique, a positive disturbance observer is designed to supply the estimation of disturbance in the functional observer. Then, a new unknown input observer is constructed for positive systems. A matrix decomposition method is employed to design the observer gains. All conditions are described in terms of linear programming. The corresponding algorithms are addressed for computing the presented conditions. Finally, two examples are provided to verify the effectiveness of the theoretical findings.

This paper is concerned with the fuzzy functional observer‐based sliding mode control for T‐S fuzzy cyber‐physical systems subject to disturbances and deception attacks. First, the deception attack is modeled by an exogenous system with state dependent nonlinearity. Second, a fuzzy learning functional observer with fuzzy logic systems learning unknown nonlinear function, whose parameters can be directly found, is designed to estimate the partly unavailable states, deception attacks and lumped disturbances simultaneously. Then, a fuzzy sliding mode control is designed to compensate the effect of deception attack and reject the disturbances. Furthermore, some sufficient conditions are given to guarantee that the closed‐loop fuzzy system is exponential convergent. Finally, a numerical example is given to illustrate the validity of the proposed method. Fuzzy functional observer‐based sliding mode control for T‐S fuzzy cyber‐physical systems

This paper deals with the problem of functional observer design for systems with non-commensurate time varying delays. The main procedure of three types of functional observers are presented in this article, more precisely, observers with delays dependent, observers without internal delays and delay-free functional observers. A necessary condition for the existence of these observers is given as rank equality. The design conditions for functional observers are presented in terms of linear matrix inequalities (LMIs). The solution of these LMIs is used to determine the observers parameters. Finally, some numerical examples are given at the end of the paper to show the feasibility of the proposed approach.

In this paper, a nonlinear functional observer (NFO) is first proposed for the control design of robot manipulators under model uncertainties, external disturbances, and a lack of joint velocity information. In principle, the proposed NFO can estimate not only lumped disturbances and uncertainties but also unmeasurable joint velocities, which are then fed back into the main controller. Compared to the well-known ESO design, the proposed NFO has a simpler structure, more accurate estimations, and less computational effort, and consequently, it is easier for practical implementation. Moreover, unnecessary observations of joint displacements are avoided when compared to the well-known extended state observer (ESO). Based on the Lyapunov theory, globally uniformly ultimately bounded estimation performance is guaranteed by the proposed NFO. Consequently, it is theoretically proven that the estimation performances of the NFO are better than those of the ESO. Simulations with a two-degree-of-freedom (2-DOF) robot manipulator are conducted to verify the effectiveness of the proposed algorithm in terms of not only the estimation performance but also the closed-loop control performance.

To address the problem of control performance degradation caused by flexible attachment vibrations and external disturbances during attitude maneuvering of flexible spacecraft, this paper proposes a parametric method for improving flexible spacecraft attitude maneuver control (AMC) based on a functional observer. The objective was to enhance the control accuracy and disturbance rejection. First, state expansion was carried out for flexible spacecraft systems affected by disturbances. A functional observer was designed for the system, and sufficient conditions for the existence of the observer were obtained. Furthermore, a controller was designed by using the state information of the observer, which included state feedback and feed-forward compensation. Based on the parametric solution of a class of generalized Sylvester equations (GSEs), the parametric expressions of the controller and observer were established. Finally, a numerical example of a flexible spacecraft proved the effectiveness of the design method. The method can effectively suppress flexible vibrations and external disturbances while also meeting the high-precision control requirements of the flexible spacecraft.

This paper investigates the design of reduced-order functional observer for linear time-invariant systems (LTI) with time-varying delay. Firstly, the sufficient condition for the existence of reduced-order delay-free functional observers is obtained. Secondly, by solving generalized Sylvester matrix equations (GSEs), completely parameterized formulas of the coefficient matrices of reduced-order function observer are established. The free parameter matrices in the formulas provide the design degrees of the freedom and improve the convergence rate of the error system. Finally, two numerical and a practical examples are provided to illustrate the effectiveness of the proposed approach.