Plenary lecture 4: some interesting aspects of elementary distributions with applications in control algorithms design

This paper presents interesting aspects of classical distributions theory and the elementary distributions, insisting on practical applications in software control of power electronics and digital control engineering. The practical real world phenomena have discontinuities, severe nonlinearities and non-derivation points and therefore cannot be represented as mathematical closed formula. In order to solve this problem using classical mathematics the discontinuous or nonlinear regions are represented using partitioning method in order to eliminate the discontinuities. But this way we eliminate also the use of derivation operator and this is a great disadvantage, because the discontinuity points represent the points where the system is actually working. The distributions theory was years ago only a mathematical theory, never used in practical applications, but the distributions theory with its remarkable properties represents a link between the continuous systems with their vast experience and the digital systems. The development of information technology and control engineering demands the use of distributions theory in order to elaborate the mathematical model. First, the paper presents the definition of elementary distributions and their properties, validated by modeling and simulation. Then, based on the elementary distributions, new properties are introduced, modeled and simulated with digital application examples. The final part of the paper presents complex control engineering applications, like: software oriented digital controllers for power electronics and industrial elevator software controller. All of these controllers algorithms based on distributions theory can be easily coded in any programming language, like microcontrollers, microprocessors or ASIC - HDL embedded solution.