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In this brief the design and analysis of an optimal robust minimax linear quadratic Gaussian (LQG) control of vibration of a flexible beam is studied. The analysis is performed by transforming the minimax LQG control design problem to its equivalent mixed sensitivity design problem. The first six modes of the beam in the frequency range of 0–700 Hz are selected for control purpose. Among these modes, three modes in the frequency range of 100–400 Hz are used for control, while the other three modes are left as the uncertainty of modeling. Both the model and the uncertainty are measured based on experimental data. The nominal model is identified from frequency response data and the uncertainty is presented by frequency weighted multiplicative modeling method. For the augmented plant consisting of the nominal model and its accompanied uncertainty, a minimax LQG controller is designed. Analysis and tradeoff between robust stability and robust performance is shown by selecting two different choices of uncertainty modeling. Simulation results used to show how the uncertainty weights can be tuned so that the proposed robust controller increase the damping of the system in its resonance frequencies and maintain the robust stability of the feedback system at the same time. [ABSTRACT FROM PUBLISHER]

The article presents a reprint of the article "Modal Analysis for Global Control of Broadband Noise in a Rectangular Enclosure," by Allahyar Montazeri, Javad Poshtan and Mohammad Hossein Kahaei, which appeared in an issue of "Journal of Low Frequency Noise, Vibration and Active Control." Modal analysis for examination of the possibility of the global reduction of broadband noise in a rectangular enclosure has been studied in this paper. By developing a modal model of the acoustic environment of the enclosure the shape modes and their frequencies are obtained and on suitable bandwidth for the controller design is calculated. In order to simplify the analysis the noise sources are assumed localized and internal in one corner of the kiosk. The analysis results show that due to the existence of some degenerate modes in this application, the control action is complicated. Simulation results demonstrate how positions and number of loudspeakers and microphones will change the performance of the controller and its corresponding control effort. Based on these results and analysis a reasonable size for the controller and proper locations for sensors and actuators are proposed. Simulation results also confirm the effectiveness of the proposed system in reduction of the acoustic potential energy in the kiosk. [ABSTRACT FROM AUTHOR]

One of the main important aspects in designing an active control system is the optimization of position and number of sensors and actuators. In this paper this problem is addressed for the implementation of a multi-channel active noise control (ANC) system with the aim of global reduction of broadband noise in a telephone kiosk. This includes optimizing the locations for loudspeakers and microphones, finding proper size of the control system, i.e. the number of loudspeakers and microphones, and optimization of the control signals. The mean of acoustic potential energy in the enclosure in a frequency range of 50 Hz to 300 Hz is selected as the performance index for optimization purpose. Several genetic algorithms are proposed and compared to find the global minimum of this performance index. In order to have a better performance in reaching the global minimum, the parameters of these genetic algorithms are tuned, and the best genetic algorithm is selected among them. The main difference between the proposed algorithms is the used coding scheme. Numerical simulations of the acoustical potential energy and also sound pressure at the height where the head of a person may be located, confirms the optimality of the locations proposed by the genetic algorithm. [ABSTRACT FROM AUTHOR]