Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
The paper presents results of studies on linear synchronous motors controlled in CNC feed axes through an intelligent digital servodrive. The research includes a conceptual design of an open servodrive control system and identification of dynamic models of a test stand with an open CNC system. Advantages of robust control over the classic one are discussed. A hybrid predictive approach to robust control of milling machine X-Y table velocity is proposed and results of simulation tests are presented. Was prepared during the work for the Ministry of Science and Higher Education grant number N N502 336936, (acronym for this project is M.A.R.I.N.E. multivariable hybryd ModulAR motIon coNtrollEr), while its main purpose is the development of new rob ust position/velocity model-based control system, as well as to introduce the measurement of the actual state into the switching algorithm between the locally synthesized controllers. Such switching increases the overall robustness of the machine tool feed-drive module. The paper is the extended version of material proposed in .
Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonparametric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the fundamental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks - recognition of outliers, clustering and classification - solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated