scholarly journals Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles

2014 ◽  
Vol 141 (9) ◽  
pp. 094101 ◽  
Author(s):  
Gerhard Ritschel ◽  
Alexander Eisfeld
Keyword(s):  
Correlation Functions ◽  
Spectral Densities

scholarly journals Identification of signals as one of the stages of synthesis of the system of automatic stabilization of the height of the fluidized bed in the grain dryer

2021 ◽  
Vol 4 (135) ◽  
pp. 85-94
Author(s):  
Marianna Fedotova ◽  
Ivan Skrynnik ◽  
Serhiy Osadchy ◽  
Dmitry Trushakov
Keyword(s):  
Spectral Density ◽  
Fluidized Bed ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Energy Use ◽  
Object Identification ◽  
Spectral Densities ◽  
Initial State ◽  
Automatic Stabilization ◽  
Drying Efficiency

Drying is one of the most responsible and energy-intensive post-harvest grain pro-cessing operations. The constant rise in heat prices has led to the search for new designs of grain dryers, or improvements to existing ones. Studies of well-known scientists such as Romankov, Rezchikov, Rashkovskaya have proven the potential effectiveness of using a fluid-ized bed for drying grain.The degree to which this drying efficiency approaches the potential is determined by how much the change in the actual humidity of the material during drying approaches the theoretical drying curve at the same resource consumption and the same initial state of the material to be dried.The study of the designs of fluidized bed grain dryers showed that they show irregular fluctuations in the height of the fluidized bed, and, accordingly, the efficiency of energy use for drying. The reason for this phenomenon is related, on the one hand, to random fluctua-tions in the amount of grain in the fluidized bed, and on the other - to the shortcomings of the system of automatic stabilization of its height.Taking into account the provisions of the theory of optimal control indicates that max-imizing the accuracy of stabilization of a given value of the height of the fluidized bed should be achieved by developing an optimal multidimensional stabilization system of the specified height. The basis for solving the first of these is the study of the design of a fluidized bed grain dryer.The decomposition of the grain dryer allows to present it in the form of a set of multidimensional objects with pure delay. The size of this set is determined by the number of cascades, and the dynamic characteristics of its elements depend on the distance of the cascade to the gate.The degree of connections between input-output signals in the form of correlation and cross-correlation functions was studied, and the physical processes occurring in the grain dryer were analyzed. As a result of applying the Blackman-Tukey algorithm to the implemen-tations of the components of the control signal vectors and output signals, estimates of the corresponding correlation functions and spectral densities for all elements of the set of con-trol objects were obtained. The discrete Fourier transform of smoothed estimates of correla-tion and cross-correlation functions allowed us to calculate estimates of the spectral and mutual spectral densities of the respective signals. Approximation of spectral and mutual spectral density estimates by the method of generalized logarithmic frequency characteristics allowed to determine the mathematical description of these signals in the form of spectral density expressions, which will be the basis for the next stage of object identification.

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