Experimental Validation of Linear Matrix Inequality Based H2 Full State Feedback Controllers on a 3-DoF 4-Pole Hybrid Electromagnetic Vibration Isolation Stage

2019 ◽  
Author(s):  
Baris Can Yalcin ◽  
Ahmet Fevzi Bozkurt ◽  
Kadir Erkan
Keyword(s):  
Linear Matrix Inequality ◽  
State Feedback ◽  
Experimental Validation ◽  
Vibration Isolation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Feedback Controllers ◽  
Electromagnetic Vibration ◽  
Full State ◽  
Full State Feedback

scholarly journals A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

2020 ◽  
Vol 10 (17) ◽  
pp. 5859
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
State Feedback ◽  
Optimization Problems ◽  
Seismic Protection ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Static State ◽  
Fluid Viscous Dampers ◽  
Iterative Linear Matrix Inequality

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

scholarly journals Observer-based H2 controller design for a vibration isolation stage having hybrid electromagnets

2018 ◽  
Vol 37 (4) ◽  
pp. 1134-1150 ◽  
Author(s):  
Barış Can Yalçın ◽  
Mert Sever ◽  
Kadir Erkan
Keyword(s):  
Linear Matrix Inequality ◽  
Permanent Magnet ◽  
Vibration Isolation ◽  
Permanent Magnets ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Compact Structure ◽  
Highly Nonlinear

Vibration isolation systems based on hybrid electromagnets, consisting of electromagnet and permanent magnet, have a potential usage in many industrial areas, such as clean room design, transportation, semiconductor manufacturing, suspension systems, and robotic surgery due to providing mechanical contact free vibration isolation. Using permanent magnets in the electromagnet structure has some crucial advantages, such as a minimized volume and a more compact structure. Furthermore, the essential force for levitation of vibration isolation stage can be generated by only the permanent magnet(s), which means, by using hybrid electromagnets, magnetic levitation can be achieved with considerably low energy consumption against possible vibrations. This property is called zero-power behavior. However, the main problems of magnetic levitation process are as follows: it has highly nonlinear nature even if it can be linearized; it has unstable pole(s), which makes the system vulnerable in terms of stability. In recent years, linear matrix inequality-based design of controllers has received considerable attention and become very popular due to their ability to satisfy multiobjective design requirements. However, an observer-based H2 controller design for a vibration isolation system having hybrid electromagnets has not been considered yet. Therefore, the linear matrix inequality-based controller is employed to minimize the effect of disturbances on the following objectives, such as vibration isolation, zero-power property, and protection of the levitation gap. The effectiveness of the proposed method is shown with the numerical simulation studies and compared with classical Linear Quadratic Regulator (LQR) approach.

scholarly journals Robust H∞ control of an uncertain bilateral teleoperation system using dilated LMIs

2021 ◽  
pp. 014233122110490
Author(s):  
Bilal Gormus ◽  
Hakan Yazici ◽  
İbrahim Beklan Küçükdemiral
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
State Feedback ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Slave System ◽  
Bilateral Teleoperation ◽  
Reference Tracking ◽  
Teleoperation System ◽  
Force Reflection

A robust state-feedback [Formula: see text] controller is proposed for an uncertain bilateral teleoperation system having norm-bounded parametric uncertainties on mass and damping coefficients of the considered master/slave system. The proposed method ensures robust stability and successful reference tracking and force reflection performance. While Lyapunov stability is used to ensures asymptotic stability, the [Formula: see text] norm from exogenous input to the controlled output is utilized in satisfying the reference tracking and force reflection. As two performance objectives and robust stability requirement are conflicting with each other, the proposed controller reduces the associated conservatism with dilated linear matrix inequalities. Standard and dilated linear matrix inequality-based robust [Formula: see text] state-feedback controllers are performed with a one degree of freedom uncertain master/slave system under reference signal and environmental-induced exogenous force. Numerical simulation results show that the dilated linear matrix inequality-based [Formula: see text] control satisfies lower [Formula: see text] norm than a standard [Formula: see text] control. Moreover, the proposed controller demonstrates a very successful performance in achieving performance objectives despite the stringent norm-bounded parameter uncertainties.

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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