The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

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With the growing importance of environmental issues in our society, extremely low-permeability geotechnical materials are being studied increasingly for their long-term stability and effectiveness in retarding the transport of hazardous wastes. Relatively rapid measurements of the permeability and specific storage of the materials, using relatively low hydraulic gradients, can be obtained with a constant flow pump and the corresponding theoretical analysis proposed by Morin and Olsen (1987). However, the accuracy of this method is limited because their theoretical analysis does not take into account the storage capacity of the experimental system. This paper presents a more general theoretical analysis and shows how it can be used to determine not only the permeability and specific storage of a test specimen, but also the storage capacity of the experimental system. Experimental data are presented that illustrate the accuracy and efficiency of the general theoretical analysis.

The purpose of this study is to develop a model for the gas exchange process in a rebreathing homogeneous charge compression ignition (HCCI) engine. HCCI engines are attracting significant attention due to their low emissions and high efficiency. To design the control system of an HCCI engine, it is necessary to develop a control-oriented engine model. The developed model lowers its computational load by combining two types of models. The model consists of a discrete model for the exhaust process (the first half of the gas exchange process) and a continuous model with a variable calculation step size for the rebreathing process (the latter half of the gas exchange process). Also, the constructed model maintained its prediction accuracy, as the pressure pulsation in the exhaust port was modeled, and an unsteady flow equation was used. It was confirmed that the model developed for the gas exchange process calculated in about half time of one cycle and reproduced the results of 1D engine simulation software with a maximum error of about 10% in the in-cylinder pressure, temperature, and trapped mass.