scholarly journals Robust Decentralized Tracking Voltage Control for Islanded Microgrids by Invariant Ellipsoids

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5756
Author(s):  
Hisham M. Soliman ◽  
Ehab Bayoumi ◽  
Amer Al-Hinai ◽  
Mostafa Soliman
Keyword(s):  
Linear Time ◽  
Robustness Analysis ◽  
Voltage Control ◽  
Invariant Sets ◽  
Linear Matrix ◽  
Integral Control ◽  
Linear Time Invariant ◽  
Decentralized Controllers ◽  
Voltage Sourced Converter ◽  
Time Invariant

This manuscript presents a robust tracking (servomechanism) controller for linear time-invariant (LTI) islanded (autonomous, isolated) microgrid voltage control. The studied microgrid (MG) consists of many distributed energy resources (DERs) units, each using a voltage-sourced converter (VSC) for the interface. The optimal tracker design uses the ellipsoidal approximation to the invariant sets. The MG system is decomposed into different subsystems (DERs). Each subsystem is affected by the rest of the system that is considered as a disturbance to be rejected by the controller. The proposed tracker (state feedback integral control) rejects bounded external disturbances by minimizing the invariant ellipsoids of the MG dynamics. A condition to design decentralized controllers is derived in the form of linear matrix inequalities. The proposed controller is characterized by rapid transient response, and zero error in the steady state. A robustness analysis of the control strategy (against load changes, load unbalances, etc.) is carried out. A MATLAB/SimPowerSystems (R2017b, MathWorks, Natick, MA, USA) simulation of the case study confirm the robustness of the proposed controller.

A Static Anti-Windup Compensator Design Technique for Robust Regional Pole Placement

2006 ◽  
Author(s):  
Brandon Hencey ◽  
Andrew Alleyne
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Linear Matrix ◽  
Test Bed ◽  
Hydraulic Test ◽  
Linear Time Invariant ◽  
Loop Dynamics ◽  
Performance Deterioration ◽  
Time Invariant

This paper develops a new method of designing anti-windup compensators using the concept of robust pole placement using linear matrix inequality (LMI) regions. The anti-windup problem seeks to minimize the closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time-invariant plant and controller. Existing LMI-based anti-windup synthesis techniques do not explicitly provide a method to account for robust pole placement. This paper suggests a LMI-based method that not only attempts to minimize performance deterioration, but also explicitly restricts the anti-windup closed loop dynamics to an admissible set. Finally, the techniques discussed in this paper are demonstrated on a hydraulic test bed.

scholarly journals A multi-model approach to Saint-Venant equations: A stability study by LMIs

2012 ◽  
Vol 22 (3) ◽  
pp. 539-550 ◽  
Author(s):  
Valérie Dos Santos Martins ◽  
Mickael Rodrigues ◽  
Mamadou Diagne
Keyword(s):  
Linear Time ◽  
Dimensional Space ◽  
Stability Study ◽  
Linear Matrix ◽  
Model Concept ◽  
Infinite Dimensional ◽  
Linear Time Invariant ◽  
Saint Venant Equations ◽  
The Stability ◽  
Time Invariant

Abstract This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

scholarly journals Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Xie
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Admissible Solution ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lpv Control ◽  
Lpv System ◽  
Time Invariant ◽  
Iterative Linear Matrix Inequality

A linear time-invariant (LTI) output feedback controller is designed for a linear parameter-varying (LPV) control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI) formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

2006 ◽  
Vol 10 (4) ◽  
pp. 486-493 ◽  
Author(s):  
Péter Baranyi ◽  
◽  
Zoltán Petres ◽  
Péter L. Várkonyi ◽  
Péter Korondi ◽  
...  
Keyword(s):  
Model Transformation ◽  
Linear Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Wing Section ◽  
Parameter Varying ◽  
Time Invariant

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

scholarly journals PID Control Design for SISO Strictly Metzlerian Linear Systems

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1979
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Pid Control ◽  
Linear Time ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Control Law ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Parameter Constraints ◽  
Structural Influence

For linear time-invariant Metzlerian systems, this paper proposes an original approach reflecting specific structural system constraints and positiveness in solving the problem of PID control. Refining parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with the control law representation and is formulated as a linear matrix inequality feasibility problem. Taking into account structural restriction of Metzlerian positive systems, a characterization of PID control law parameters is permitted, to highlight dynamical properties of the closed-loop system solutions and the significant structural influence of derivative gain value of the control law parameters in design.

Fault Estimation for Linear Systems with Multi Time-Delay

2012 ◽  
Vol 263-266 ◽  
pp. 578-583 ◽  
Author(s):  
Zhi Dan Li ◽  
Quan Chao Dong ◽  
Jian Xiao ◽  
Chang Chun Hua
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Linear Time ◽  
Estimation Error ◽  
Design Procedure ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Linear Time Invariant ◽  
Bounded Real Lemma ◽  
Time Invariant

This paper deals with the problem of observer-based fault estimation for a class of linear systems with multi time-delay. The key of this paper is the introduction of a generalized coordinate transform, such that in the new coordinates, all the time-delay terms are injected by the system’s input and output. Based on the new obtained system expression, the design of fault estimator is formulated in the framework of H∞ filtering by incorporating the prior knowledge of fault into the design procedure, and the dynamics of the estimation error is converted into a general linear time invariant form with generalized unknown input time-delay terms. Based on the bounded real lemma, the observer gain matrix is obtained in terms of linear matrix inequality. A numerical example is given to illustrate the effectiveness of the proposed approach.

scholarly journals Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems

2014 ◽  
Vol 62 (3) ◽  
pp. 495-503 ◽  
Author(s):  
S. Balochian
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Variable Structure ◽  
Switched System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Linear Time Invariant ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Derivative Order

Abstract In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.

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