Robust Decentralized Voltage Tracker of Islanded Multi-DG AC Microgrids Using Invariant Ellipsoids

2022 ◽  
pp. 1-35
Author(s):  
Ehab Hassan Eid Bayoumi ◽  
Hisham Soliman ◽  
Farag El-Sheikhi
Keyword(s):  
Decentralized Control ◽  
Time Domain ◽  
Invariant Sets ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Parameter Uncertainties ◽  
Local Loads ◽  
Disturbance Rejection Control ◽  
Parameter Variations ◽  
Local Measurements

This chapter develops a robust decentralized voltage tracker for islanded MGs. The proposed controller is robust against the plug and play operation of the MG, loads, and line parameter uncertainties. The problem is solved in the framework of linear matrix inequality (LMI). The proposed robust control represents the load changes and the parameter variations of lines connecting the DGs as a norm-bounded uncertainty. The proposed controller utilizes local measurements from DGs (i.e., it is totally decentralized). Control decentralization is accomplished by decomposing the global system into subsystems. The effect of the rest of the system on a specific subsystem is considered as a disturbance to minimize (disturbance rejection control). The controller is designed by the invariant-sets (approximated by the invariant ellipsoids). Different time-domain simulations are carried out as connecting and disconnected one or more DGs, connecting and disconnecting local loads DGs and transmission line parameters variation.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

scholarly journals Decentralized Control Strategies of Adjacent Building Structures Vibration under Earthquake Excitation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xiaofang Kang ◽  
Peipei Zhang ◽  
Yiwei Zhang ◽  
Dawei Man ◽  
Qinghu Xu ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
Decentralized Control ◽  
Control Algorithm ◽  
Control Method ◽  
Computational Cost ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Adjacent Buildings ◽  
Control Scheme

A decentralized control scheme can effectively solve the control problem of civil engineering structure vibration under earthquake. This paper takes a research into the decentralized control scheme of adjacent buildings when the earthquake happens. It combines overlapping decentralized control method and linear matrix inequality (LMI) with H ∞ control algorithm and puts forward the overlapping decentralized H ∞ control method. A simplified dynamical model of structural vibration control has been established considering the topology structural features of adjacent buildings. The H ∞ control algorithm is applied into each dynamically different subsystems and can be also served as the decentralized H ∞ controllers. Therefore, by contracting decentralized H ∞ controllers to original state space, overlapping decentralized H ∞ controllers are obtained. In this manner, the adjacent buildings’ structure model is analyzed in terms of simulation and calculation which provides a comprehensive insight into vibration control. The results show that the centralized control, the decentralized control, and the overlapping decentralized control, based on linear matrix inequality, can be nearly effective in cases above satisfactorily. Besides, it can also reduce the computational cost as well as increase the flexibility of controller design.

Decentralized Control of Rigid Robots Driven by Current-Fed Induction Motors

2002 ◽  
Vol 124 (4) ◽  
pp. 549-553 ◽  
Author(s):  
Gerardo Guerrero-Ramı´rez ◽  
Yu Tang
Keyword(s):  
Induction Motor ◽  
Decentralized Control ◽  
Closed Loop ◽  
Induction Motors ◽  
Control Technique ◽  
Parameter Uncertainties ◽  
Flux Observer ◽  
Current Controller ◽  
Local Measurements ◽  
Rotor Flux

The problem of controlling a rigid manipulator driven by induction motors to follow a desired trajectory using the decentralized control technique is considered in this paper. Parameter uncertainties of the rigid robot are considered. First, a PI controller is used to force an induction motor to work in the current-command mode, then based on a fourth-order reduced model of induction motors, a current controller is proposed using only local measurements of each link (link position, velocity and stator currents of the induction motor). The rotor flux is estimated through a closed-loop observer. Provided that the flux observer is properly initialized, this controller is singularity-free and guarantees the uniform ultimate stability of the closed-loop system. Simulations are presented to illustrate the performance of this controller.

scholarly journals Robust DistributedH∞Filtering for Nonlinear Systems with Sensor Saturations and Fractional Uncertainties with Digital Simulation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dong Liu ◽  
Guangfu Tang ◽  
Zhiyuan He ◽  
Yan Zhao ◽  
Hui Pang
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Digital Simulation ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Parameter Uncertainties ◽  
Error System ◽  
Filtering Problem ◽  
Fractional Parameter

This paper is concerned with the robust distributedH∞filtering problem for nonlinear systems subject to sensor saturations and fractional parameter uncertainties. A sufficient condition is derived for the filtering error system to reach the requiredH∞performance in terms of recursive linear matrix inequality method. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method.

Absolute stability analysis of nonlinear active disturbance rejection control for electromagnetic valve actuator system via linear matrix inequality method

2018 ◽  
Vol 232 (9) ◽  
pp. 1134-1145
Author(s):  
Da Shao ◽  
Sichuan Xu ◽  
Aimin Du
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequality ◽  
Disturbance Rejection ◽  
Absolute Stability ◽  
Linear Matrix ◽  
Active Disturbance Rejection Control ◽  
Matrix Inequality ◽  
Single Input Single Output ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

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