The small independent induction generator can build up voltage under its remanent magnetizing and excitation capacitance, but it is prone to voltage sag and harmonic increment when running with load. Therefore, the controller for constant voltage is designed based on the natural coordinate system to adjust the static synchronous compensator (STATCOM), which provides two-way dynamic reactive power compensation for power generation system to achieve voltage stability and harmonic suppression. The control strategy is verified on Matlab/Sinmulik, and the results show that the STATCOM under the controller can effectively improve the load capacity and reliability of asynchronous generator.
This paper studies the problem of vehicle state estimation. In view of the longitudinal lateral coupling dynamics and the existence of unknown inputs, a new fuzzy observer design method is proposed based on Takagi-Sugeno (TS) fuzzy control technology to realize the effective estimation of vehicle state. Aiming at the difficulty of observer synthesis of TS fuzzy system with unmeasurable antecedent variables, this paper proposes an N-TS fuzzy modeling method which can effectively avoid unmeasurable antecedent variables by using nonlinear partition method, and explores a new method of fuzzy observer synthesis of nonlinear vehicle system based on this model. This fuzzy modeling not only effectively avoids the appearance of unmeasurable antecedent variables, but also significantly reduces the real-time calculation workload of estimating vehicle variables.
This paper is concerned with fuzzy model-based blood glucose control problem for diabetes patients. The glucose metabolism model used in this paper is expressed in the Takagi-Sugeno (T-S) form obtained by sector nonlinearity approach. Two different rates of basal exogenous insulin are considered to analysis and design T-S fuzzy controllers. It is shown that conditions for the solvability of the blood glucose controller design given here are written in the form of linear matrix inequality (LMI) which can be efficiently solved by convex optimization techniques. One simulation example is given to demonstrate the validity of the proposed approach.
This paper investigates the steering fault detection problem for autonomous ground vehicles (AGVs). Using an observer-based approach, a new fuzzy fault detector for steering actuator is designed for safety concern. To this end, a two degrees-of-freedom (2-DOF) nonlinear vehicle model is adopted to represent the nonlinear dynamics of AGVs. Since it is not easy to measure the lateral velocity in practice, this model is then represented in a specific Takagi-Sugeno (TS) fuzzy form with nonlinear consequents. In contrast to the conventional TS fuzzy modeling, it allows separating the unmeasured premise variables in the local nonlinear consequent, which enables a more effective way to deal with the challenging issue of unmeasured premise variables. Moreover, to minimize the effect of disturbances on system performance and maximize that of actuator faults on the generated residual, both H∞ disturbance attenuation index and H_fault sensitivity index are taken into account in a finite-frequency domain. The conditions to design fault detection TS fuzzy observer are derived using Lyapunov stability method. The design procedure can be reformulated as an optimization problem under linear matrix inequalities, efficiently solved by standard numerical solvers. Simulation results are given to verify the fault detection performance of the proposed method.
This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno (T-S) fuzzy systems. New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model, the information of the membership functions can be brought into the stabilization design of the fuzzy systems, thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems. Unlike some previous fuzzy Lyapunov function approaches reported in the literature, the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. A simulation example is given to demonstrate the validity of the proposed approach.
This article develops a unified framework to design fuzzy-model-based observers of general nonlinear systems for both discrete-time and continuous-time cases. This observer problem is known as a challenging task due to the mismatch caused by the unmeasurable premise variables. To deal with this major challenge, we propose to rewrite the nonlinear system as a specific fuzzy model with two types of local nonlinearities: measurable and unmeasurable. Then, a differential mean value theorem for vector-valued functions is applied to local unmeasurable nonlinearities. This allows to represent the estimation error dynamics in a special polytopic form involving measurable membership functions and unknown but bounded time-varying parameters. Using Lyapunov-based arguments, design conditions in terms of linear matrix inequalities are derived to guarantee the asymptotic convergence of the estimation error. Three illustrative examples are given to demonstrate the interests of the new fuzzy observer framework in reducing: 1) the design conservatism and 2) the numerical complexity of the fuzzy observer structure for real-world applications.
Abstract This article presents a new observer design framework for a class of nonlinear descriptor systems with unknown but bounded inputs. In the presence of unmeasured nonlinearities, that is, premise variables, designing nonlinear observers is known as particularly challenging. To solve this problem, we rewrite the nonlinear descriptor system in the form of a Takagi–Sugeno (TS) fuzzy model with nonlinear consequents. This model reformulation enables an effective use of the differential mean value theorem to deal with the mismatching terms involved in the estimation error dynamics. These nonlinear terms, issued from the unmeasured nonlinearities of the descriptor system, cause a major technical difficulty for TS fuzzy‐model‐based observer design. The descriptor form is treated through a singular redundancy representation. For observer design, we introduce into the Luenberger‐like observer structure a virtual variable aiming at estimating the one‐step ahead state. This variable introduction allows for free‐structure decision variables involved in the observer design to further reduce the conservatism. Using Lyapunov‐based arguments, the observer design is reformulated as an optimization problem under linear matrix inequalities with a single line search parameter. The estimation error bounds of both the state and the unknown input can be minimized by means of a guaranteed ℓ ∞ ‐gain performance level. The interests of the new ℓ ∞ TS fuzzy observer design are clearly illustrated with two physically motivated examples.
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