scholarly journals Construction of Lyapunov Function for Power System based on Solving Linear Matrix Inequality

2005 ◽  
Vol 125 (5) ◽  
pp. 461-468
Author(s):  
Atsushi Ishigame ◽  
Hiromu Sakaguchi ◽  
Jun Takashima ◽  
Shirou Suzaki
Keyword(s):  
Lyapunov Function ◽  
Power System ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality

Construction of Lyapunov function for power system based on solving linear matrix inequality

2007 ◽  
Vol 158 (4) ◽  
pp. 42-50 ◽  
Author(s):  
Atsushi Ishigame ◽  
Hiromu Sakaguchi ◽  
Jun Takashima ◽  
Shirou Suzaki
Keyword(s):  
Lyapunov Function ◽  
Power System ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality

Nonlinear Position Control of Digital Hydraulic Cylinder Despite Disturbance

2014 ◽  
Vol 998-999 ◽  
pp. 638-641
Author(s):  
Shi Jie Xu ◽  
J.F. Xing ◽  
Li Kun Peng
Keyword(s):  
Control System ◽  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Nonlinear Model ◽  
Position Control ◽  
Hydraulic Cylinder ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Nonlinear Controller ◽  
Position Control System

A nonlinear controller is presented for a digital hydraulic cylinder against disturbance. We first establish the nonlinear model of digital hydraulic cylinder position control system. Then a Lyapunov function and a nonlinear controller are presented. The controller designing problem is translated into the problem of solving a linear matrix inequality. The experiment results show that the controller proposed by this paper has much better performance than traditional one.

scholarly journals Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 6 (5) ◽  
pp. 1956
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript  proposes two  designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  The approach provides a systematic way to design a robust output feedback PSS which  guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 6 (5) ◽  
pp. 1956
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript  proposes two  designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  The approach provides a systematic way to design a robust output feedback PSS which  guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

scholarly journals A Reconstruction Procedure Associated with Switching Lyapunov Function for Relaxing Stability Assurance of T-S Fuzzy Mode

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yau-Tarng Juang ◽  
Chih-Peng Huang ◽  
Chung-Lin Yan
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Fuzzy Model ◽  
Alternative Form ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Variables ◽  
Stability Criteria ◽  
Quadratic Lyapunov Function ◽  
Reconstruction Procedure

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method.

scholarly journals A Wide Range Robust PSS Design Based on Power System Pole-Placement Using Linear Matrix Inequality

2012 ◽  
Vol 63 (4) ◽  
pp. 233-241 ◽  
Author(s):  
Mohammad Ataei ◽  
Rahmat-Allah Hooshmand ◽  
Moein Parastegari
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Controller Design ◽  
Damping Ratio ◽  
Pole Placement ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequality ◽  
Gain Matrix ◽  
Wide Range

A Wide Range Robust PSS Design Based on Power System Pole-Placement Using Linear Matrix InequalityIn this paper, a new method for robust PSS design based on the power system pole placement is presented. In this stabilizer, a feedback gain matrix is used as a controller. The controller design is proposed by formulating the problem of robust stability in a Linear Matrix Inequality (LMI) form. Then, the feedback gain matrix is designed based on the desired region of the closed loop system poles. This stabilizer shifts the poles of the power system in different operational points into the desired regions ins-plane, such that the response of the power system will have proper damping ratio in all the operational points. The uncertainties of the power system parameters are also considered in this robust technique. Finally, in order to show the advantages of the proposed method in comparison with conventional PSS, some simulation results are provided for a power system case study in different operational points.

scholarly journals Output Strictly Passive Control of Uncertain Singular Neutral Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Jichun Wang ◽  
Qingling Zhang ◽  
Dong Xiao
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
State Feedback ◽  
Passive Control ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Neutral Systems ◽  
Previous Approach ◽  
State Feedback Controller

This paper concerns the problem of output strictly passive control for uncertain singular neutral systems. It introduces a new effective criterion to study the passivity of singular neutral systems. Compared with the previous approach, this criterion has no equality constraints. And the state feedback controller is designed so that the uncertain singular neutral systems are output strictly passive. In terms of a linear matrix inequality (LMI) and Lyapunov function, the strictly passive criterion is formulated. And the desired passive controller is given. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.

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