the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

In the paper we present tuning rules for PI and PID controllers and the first order plus dead time (FOPDT) process model. The settings respect both performance and stability indices and provide a high degree of robustness for any value of the dead time parameter. As the performance index we are using the well known modulus optimum criterion, which requires that the amplitude of the closed-loop ...

Many analyses of software systems can be formalized as relational queries, for example the detection of design patterns, of patterns of problematic design, of code clones, of dead code, and of differences between the as-built and the as-designed architecture. This paper describes the concepts of CrocoPat, a tool for querying and manipulating relations. CrocoPat is easy to use, because of its si...

This paper presents a delay-type PID controller (shortened as dPID) or a PID controller which is implemented using two delay elements. The gains are analytically tuned; one of the delay is optimally tuned and the other one is chosen to be equal to the sampling time. The poles of the discrete version of the dPID controller lies inside the unit circle and far away from the point . Hence, it is st...

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.