This paper is concerned with the quantized identification of rational systems, where the systems’ output is quantized by a logarithmic quantizer. Under the assumption that the systems’ input is periodic, the identification procedure is categorized into two steps. The first step is to identify the noise-free output of systems based on the quantized data. The second is to identify the unknown parameter based on the input and the estimation of the noise-free output. The identification algorithm is also summarized. Asymptotic convergence of the estimators is analyzed in detail, which shows that the estimators are convergent almost everywhere. A numerical example is given to illustrate the results obtained in this paper.
The article is devoted to the calculated regulation of the stress deformation state (SDS) of combined steel trusses, which allows to reduce the efforts in some sections of the structure by increasing the efforts in other and design evenly stressed structures as the most rational systems. It is shown that the calculated method of SDS regulation makes it possible to reduce steel consumption by up to 34%. Four methods of calculated SDS regulation are proposed. The advantages of combined structures are given: the concentration of materials and the possibility of designing them as low-element. As shown in the example, for the quantitative criterion of quality it is possible to use rationally the maximum potential energy of deformation. Dependences for calculation of the maximum potential energy of compressed stretched, and compressed-bent elements of rod-bearing steel structures are given.
This work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the contribution of this research, four different non-rational reference systems have been considered. The method proposed here contributes first to a simpler and graphical modeling of these complex systems, and second to provide an effective tool to face the unsolved control problem of these systems.
The main goal of this paper is to investigate the global asymptotic behavior of the difference system xn+1=γ1yn/A1+xn, yn+1=β2xn/B2+yn, n=0,1,2,…. with γ1,β2,A1,B2∈(0,∞) and the initial condition (x0,y0)∈[0,∞)×[0,∞). We obtain some global attractivity results of this system for different values of the parameters, which answer the open problem proposed in “Rational systems in the plane, J. Difference Equ. Appl. 15 (2009), 303-323”.
Identification of Rational Systems with Logarithmic Quantized Data
