Linear matrix inequality based controller design with feedback linearisation: application to power systems

2003 ◽  
Vol 150 (5) ◽  
pp. 551-556 ◽  
Author(s):  
R.A. Ramos ◽  
L.F.C. Alberto ◽  
N.G. Bretas
Keyword(s):  
Power Systems ◽  
Linear Matrix Inequality ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequality

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 3 (1) ◽  
pp. 38
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power Systems ◽  
Power System ◽  
Controller Design ◽  
Damping Ratio ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</p>

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.

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