Abstract: This paper presents an innovative approach on classical distributions theory, insisting on very practical applications in digital control engineering. The distributions theory was years ago only an interesting mathematical instrument, rarely used in engineering applications. As it is well known, many times when we have to solve complex control problems, we encounter difficulties in writing the mathematical models for the analyzed process. The real world phenomena cannot be always represented as mathematical closed formula. This is because the practical phenomena have discontinuities, severe nonlinearities and non-derivation points. In order to solve these problems using classical mathematics these regions are represented by partitioning method, eliminating this way the discontinuities and the use of derivation operator. The main disadvantages of this approach are: the mathematical model is complicated, the working points of the system that appear as discontinuities are eliminated, difficult to represent the equations for digital and/or nonlinear systems, cannot be used the differential equations etc. The distributions theory with its remarkable properties represents a link between the continuous systems with their vast experience and the digital systems with the above constraints. First, the paper presents the definition of elementary pulse and step distributions and their properties, which are validated by modeling and simulation. Then, starting from the elementary distributions, new distributions, theorems and properties are demonstrated, modeled and simulated with digital application examples. The final of the paper presents complex control engineering applications, like: Pulse Width Modulation (PWM) and Pulse Amplitude Modulation (PAM) digital controllers for power electronics, adaptive closed loop DC servo controller and water drain process nonlinear controller. All of these controllers based on distributions theory can be easily coded in any programming language. Moreover there can be used even a Hardware Description Language (HDL) as an ASIC embedded solution.
 
 

Brief Biography of the Speaker:
Emil Pop: graduated with BSc(Hons) in Electrical Engineering in 1967 and gained a PhD in System Control in 1975, based upon the research developed at the University La Sapienza, Rome, Italy and at the University of Petrosani. He joined in 1967 the University of Petrosani. In 1990 became Professor of System Control Engineering, Ph.D advisor and was for many years the Head of System Control and Applied Informatics Engineering Department. In 1993 he was for 4 years General Director in the Romanian Ministry of Education and Research and from 2008 he is the Rector of the University of Petrosani. In 2001 he was Visiting Professor at the University of Clausthal, Germany. In 2007 he was made Academician of the Technical Academy of Russia. His general research interests are in system control engineering, nonlinear systems, VLSI system design, robot control, modelling and simulation and applied informatics.

Monica Leba: received a BSc(Hons) in System Control and Applied Informatics Engineering in 1998, a MSc in Information Systems and Technologies in 2007 and gained a PhD in System Control in 2002. She joined in 1999 the University of Petrosani. In 2008 became Associated Professor of System Control Engineering. She is Director of European Program Centre of the University of Petrosani from 2008. In 2001 she achieved a research project at the University of Clausthal, Germany and in 2006 at the University of Florence, Italy. Her general research interests are in applied informatics, system control engineering, robot control, modelling and simulation and computer engineering.