A Mixed H2/H∞ Based LMI Algorithm for Damping Inter-Area Oscillations

2011 ◽  
Vol 354-355 ◽  
pp. 974-977 ◽  
Author(s):  
Jing Ma ◽  
Rui Guo ◽  
Tong Wang
Keyword(s):  
Steady State ◽  
Power System ◽  
Linear Matrix Inequalities ◽  
System Parameter ◽  
Operating Conditions ◽  
Feedback Controller ◽  
Pole Placement ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Placement Technique

An algorithm of mixed H2/H∞ based LMI algorithm for damping inter-area oscillations is investigated. A feedback controller is designed for such problem, which takes the uncertainty of power system parameter into account. In order to gain desired dynamic and steady state qualities, a pole-placement technique based on Linear Matrix Inequalities is used. At last, simulation of 4-machine 2-area system using this method is carried out, which proves the validity and robust of the designed controller. Different operating conditions are considered to validate the adaptability of this algorithm.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

Disturbance Attenuation with Minimization of Ellipsoids Restricting Phase Trajectories in Transition and Steady State

2020 ◽  
Vol 21 (4) ◽  
pp. 195-199
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Steady State ◽  
Linear Matrix Inequalities ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequalities ◽  
Integral Control ◽  
Linear Dynamical Systems ◽  
Transition Mode ◽  
Phase Trajectories

Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state. 

scholarly journals Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

2020 ◽  
Vol 10 (16) ◽  
pp. 5494 ◽  
Author(s):  
Roberto Belotti ◽  
Dario Richiedei ◽  
Iacopo Tamellin ◽  
Alberto Trevisani
Keyword(s):  
Linear Matrix Inequalities ◽  
Complex Plane ◽  
Degrees Of Freedom ◽  
Active Vibration Control ◽  
Pole Placement ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Rank One ◽  
Uniqueness Of The Solution ◽  
Vibrating Systems

This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the dominant poles, while the remaining ones are free to assume arbitrary positions within a pre-specified region in the complex plane. Therefore, the method can be referred to as “regional pole placement”. A two-stage approach is proposed to accomplish both the tasks. In the first stage, the subset of dominant poles is assigned to exact locations by exploiting the receptance method, formulated for either symmetric or asymmetric systems. Then, in the second stage, a first-order model formulated with a reduced state, together with the theory of Linear Matrix Inequalities, are exploited to cluster the subset of the unassigned poles into some stable regions of the complex plane while keeping unchanged the poles assigned in the first stage. The additional degrees of freedom in the choice of the gains, i.e., the non-uniqueness of the solution, is exploited through a semidefinite programming problem to reduce the control gains. The method is validated by means of four meaningful and challenging test-cases, also borrowed from the literature. The results are also compared with those of classic partial pole placement, to show the benefits and the effectiveness of the proposed approach.

Robust H∞ Control for Uncertain Nonlinear Stochastic Systems with Delayed State and Control

2011 ◽  
Vol 58-60 ◽  
pp. 685-690
Author(s):  
Cheng Wang ◽  
Yun Xu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Stochastic Systems ◽  
Stochastically Stable ◽  
Nonlinear Uncertain Systems ◽  
And Control

This paper considers the issue of robust H∞ control for a class of nonlinear uncertain systems with delayed states and control, and the feedback controller is designed. By constructing proper Lyapunov-krasovskii function, the resulting closed-loop system is stochastically stable for all admissible uncertainties, time-delays and nonlinearities, and satisfies a prescribed H∞ performance. Sufficient conditions for the system to be robustly stochastically asymptotically stable are derived, by using linear matrix inequalities and Lyapunov-krasovskii stability theory. The feedback controller is obtained by solving the linear matrix inequalities. Numerical example is provided to show the validity of the proposed approaches.

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