Dual approaches to strictly positive real controller synthesis with a H2 performance using linear matrix inequalities

2012 ◽  
Vol 23 (8) ◽  
pp. 903-918 ◽  
Author(s):  
James Richard Forbes
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Positive Real ◽  
Strictly Positive Real ◽  
H2 Performance ◽  
Dual Approaches

Robust controller synthesis via non-linear matrix inequalities

1999 ◽  
Vol 72 (11) ◽  
pp. 971-980 ◽  
Author(s):  
Emmanuel G. Collins ◽  
Debashis Sadhukhan ◽  
Layne T. Watson
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Non Linear

H∞ Optimal Controller Design With Closed-Loop Positive Real Constraints

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
L. Hewing ◽  
S. Leonhardt ◽  
P. Apkarian ◽  
B. J. E. Misgeld
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Controller Synthesis ◽  
Optimal Controller ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Positive Real ◽  
Promising Tool ◽  
Control Framework ◽  
Real Constraint

Positive real constraints on the closed-loop of linear systems guarantee stable interaction with arbitrary passive environments. Two such methods of H∞ optimal controller synthesis subject to a positive real constraint are presented and demonstrated on numerical examples. The first approach is based on an established multi-objective optimal control framework using linear matrix inequalities and is shown to be overly restrictive and ultimately infeasible. The second method employs a sector transformation to substitute the positive real constraint with an equivalent H∞ constraint. In two examples, this method is shown to be more reliable and displays little change in the achieved H∞ norm compared to the unconstrained design, making it a promising tool for passivity-based controller design.

scholarly journals Linear Matrix Inequalities in multivariable ship’s steering

2012 ◽  
Vol 19 (Special) ◽  
pp. 37-44 ◽  
Author(s):  
Monika Rybczak
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Pid Controllers ◽  
Linear Matrix ◽  
Programming Environment ◽  
Matrix Inequalities ◽  
Matlab Simulink ◽  
Ship Model ◽  
Ship Control

ABSTRACT This paper explains the basics of the Linear Matrix Inequalities (LMI), with examples of simulations and calculations created in Matlab/Simulink programming environment where the controlled plant is the “Blue Lady” ship model. First chapter of this paper gives a short overview of publications describing the use of Linear Matrix Inequalities method. Second chapter contains basic definitions and equations for the LMI method. Chapter three presents the use of LMI method for ship control by describing controller synthesis for the “Blue Lady”. Chapter four compares the operation of two controllers, the first one consisting of three independent proper adjusted PID controllers and the second one being a multivariable LMI controller. Finally conclusions from the above comparison are drawn.

Multivariable anti-windup controller synthesis using linear matrix inequalities

Automatica ◽  
2001 ◽  
Vol 37 (9) ◽  
pp. 1407-1416 ◽  
Author(s):  
Eric F. Mulder ◽  
Mayuresh V. Kothare ◽  
Manfred Morari
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Matrix Inequalities

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
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