An algorithm for computerized automatic tuning of power system stabilizers

The main objective of this paper is to relieve the power system engineers from the burden of the complex and time-consuming process of power system stabilizer (PSS) tuning. To achieve this goal, the paper proposes an automatic process for computerized tuning of PSSs, which is based on an iterative process that uses a linear matrix inequality (LMI) solver to find the PSS parameters. It is shown in the paper that PSS tuning can be written as a search problem over a non-convex feasible set. The proposed algorithm solves this feasibility problem using an iterative LMI approach and a suitable initial condition, corresponding to a PSS designed for nominal operating conditions only (which is a quite simple task, since the required phase compensation is uniquely defined). Some knowledge about the PSS tuning is also incorporated in the algorithm through the specification of bounds defining the allowable PSS parameters. The application of the proposed algorithm to a benchmark test system and the nonlinear simulation of the resulting closed-loop models demonstrate the efficiency of this algorithm. (C) 2009 Elsevier Ltd. All rights reserved.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness.

Controle ótimo H2 e H¥ com modificação de zeros para o problema de rastreamento usando LMI

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Experimental Active Vibration Control in Truss Structures Considering Uncertainties in System Parameters

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Global optimization approach for the H2-norm model reduction problem

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem for continuous-time linear systems, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through Linear Matrix Inequalities formulations. Examples illustrate the results.

Otimização global para os problemas de redução H2 de modelos e redução H2 da ordem do controlador

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem and the H2-norm controller reduction problem, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through linear matrix inequalities formulations. Examples illustrate the results.

A comparative study between two relaxed LMI-based fuzzy control designs

A comparative study, with theoretical analysis and digital simulations, of two conditions based on LMI for the quadratic stability of nonlinear continuous-time dynamic systems, described by Takagi-Sugeno fuzzy models, are presented. This paper shows that the methods proposed by Teixeira et. al. in 2003 provide better or at least the same results of a recent method presented in the literature. © 2005 IEEE.

Robust control applications for smart truss structure

A finite element modeling of an intelligent truss structure with piezoelectric stack actuators for the purpose of active damping and structural vibration attenuation is presented. This paper concerns with the following issues aspects: the design of intelligent truss structure considering electro-mechanical coupling between the host structure and piezoelectric stack actuators; the H 2 norm approach to search for optimal placement of actuators and sensors; and finally some aspects in robust control techniques. The electro-mechanical behavior of piezoelectric elements is directly related to the successful application of the actuators in truss structures. In order to achieve the desired damping in the interested bandwidth frequency it is used the H ∞ output feedback solved by convex optimization. The constraints to be reached are written by linear matrix inequalities (LMI). The paper concludes with a numerical example, using Matlab and Simulink, in a cantilevered, 2-bay space truss structure. The results demonstrated the approach applicability.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Comparative study of LMI-based output feedback spr synthesis for plants with different numbers of inputs and outputs

New Linear Matrix Inequalities (LMI) conditions are proposed for the following problem, called Strictly Positive Real (SPR) synthesis: given a linear time-invariant plant, find a constant output feedback matrix Ko and a constant output tandem matrix F for the controlled system to be SPR. It is assumed that the plant has the number of outputs greater than the number of inputs. Some sufficient conditions for the solution of the problem are presented and compared. These results can be directly applied in the LMI-based design of Variable Structure Control (VSC) of uncertain plants. ©2008 IEEE.

Structural real time control using fluid magnetorheologic damper

In the last decades there was a great development in the study of control systems to attenuate the harmful effect of natural events in great structures, as buildings and bridges. Magnetorheological fluid (MR), that is an intelligent material, has been considered in many proposals of project for these controllers. This work presents the controller design using feedback of states through LMI (Linear Matrix Inequalities) approach. The experimental test were carried out in a structure with two degrees of freedom with a connected shock absorber MR. Experimental tests were realized in order to specify the features of this semi-active controller. In this case, there exist states that are not measurable, so the feedback of the states involves the project of an estimator. The coupling of the MR damper causes a variation in dynamics properties, so an identification methods, based on experimental input/output signal was used to compare with the numerical application. The identification method of Prediction Error Methods - (PEM) was used to find the physical characteristics of the system through realization in modal space of states. This proposal allows the project of a semi-active control, where the main characteristic is the possibility of the variation of the damping coefficient.

Design of a state observer using decay rate LMI constraints for fault detection in mechanical systems

Nowadays, one of the most important concerns for many companies is to maintain the operation of their systems without sudden equipment break down. Because of this, new techniques for fault detection and location in mechanical systems subject to dynamic loads have been developed. This paper studies of the influence of the decay rate in the design of state observers using LMI for fault detection in mechanical systems. This influence is analyzed by the performance index proposed by Huh and Stein for the condition of a state observer. An example is presented to illustrate the methodology discussed.

Robust control applied to power flow control in single-phase inverter with LCL filter, using droop control and D-stability

This paper proposes a new methodology to control the power flow between a distributed generator (DG) and the electrical power distribution grid. It is used the droop voltage control to manage the active and reactive power. Through this control a sinusoidal voltage reference is generated to be tracked by voltage loop and this loop generates the current reference for the current loop. The proposed control introduces feed-forward states improving the control performance in order to obtain high quality for the current injected to the grid. The controllers were obtained through the linear matrix inequalities (LMI) using the D-stability analysis to allocate the closed-loop controller poles. Therefore, the results show quick transient response with low oscillations. Thus, this paper presents the proposed control technique, the main simulation results and a prototype with 1000VA was developed in the laboratory in order to demonstrate the feasibility of the proposed control. © 2012 IEEE.

Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.