Quadratically constrained linear-quadratic optimization of linear output feedback: a linear matrix inequalities approach

2002 ◽  
Author(s):  
A. Cygankov ◽  
A. Megretski
Keyword(s):  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Quadratic Optimization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Quadratic ◽  
Quadratically Constrained

scholarly journals Multivariable Static Output Feedback Control of a Binary Distillation Column using Linear Matrix Inequalities and Genetic Algorithm

2017 ◽  
Author(s):  
Kalpana R. ◽  
Harikumar Kandath ◽  
Senthilkumar J. ◽  
Balasubramanian G. ◽  
Abhay S. Gour
Keyword(s):  
Genetic Algorithm ◽  
Linear Matrix Inequalities ◽  
Simulation Study ◽  
Output Feedback ◽  
Distillation Column ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Static Output

The current work addresses the control of two-input two-output (TITO) Wood and Berry model of a binary distillation column. The controller design problem is formulated in terms of multivariable H∞ control synthesis. The controller structure takes the form of simplest static output feedback (SOF) control. The controller synthesis is performed using a hybrid approach of blending linear matrix inequalities (LMI) and genetic algorithm (GA). The performance of the static output feedback controller is compared with three other controllers designed for Wood and Berry model available in the literature. The first simulation study is performed for the case of tracking a unit step command in the presence of a step change in output disturbance. A second simulation study is performed for rejecting a change in sinusoidal output disturbance.

scholarly journals Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3285
Author(s):  
Andreas Rauh ◽  
Swantje Romig
Keyword(s):  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Iterative Solution ◽  
Simultaneous Optimization ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Optimization Task ◽  
State Observers

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

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