scholarly journals Robust pole placement stabilizer design using linear matrix inequalities

2000 ◽  
Vol 15 (1) ◽  
pp. 313-319 ◽  
Author(s):  
P.S. Rao ◽  
I. Sen
Keyword(s):  
Linear Matrix Inequalities ◽  
Pole Placement ◽  
Linear Matrix ◽  
Matrix Inequalities

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.

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

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

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