We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.

In this note, we provide a general result that explains the examples contained in [1], [3], [4], and [5]. We also observe with interest that this problem seems to have been proposed anew at nearly regular intervals of ten to fifteen years. The article [2] also contains a discussion of this problem. Using the notation in [3], suppose that f is a real-valued function defined on the interval [0, 1...

The intelligent vehicle is a complicated nonlinear system, and the design of a path tracking controller is one of the key technologies in intelligent vehicle research. This paper mainly designs a lateral control dynamic model of the intelligent vehicle, which is used for lateral tracking control. Firstly, the vehicle dynamics model (i.e., transfer function) is established according to the vehic...

The modelling, numerical simulation and intelligent control of an expert HVAC (heating, ventilating and air-conditioning) system having two different zones with variable flow-rate were performed by considering the ambient temperature in this study. The sub-models of the system were obtained by deriving heat transfer equations of heat loss of two zones by conduction and convection, cooling unit ...

Seul Jung and Richard C. Dorf Department of Electrical and Computer Engineering University of California; Davis Davis, CA 95616 e-mail:[email protected], [email protected] Abstract : In this paper a new design technique for a proportional, integral, derivative (PID) and a proportional, integral, derivative and acceleration(PIDA) controller to satisfy speci cations for transient and steady...

This paper presents the implementation of Fractional Order PID controller as a supplementary controller to improve the dynamics of Load Frequency Control in an interconnected Power System. FOPID is a PID controller whose integral and derivative orders are of non-integer rather than integer. The extension of integration and derivative order from integer to fractional order provides more flexibil...

Feedback control is a control mechanism that uses information from measurements. In a feedback control system, the output is sensed. There are two main types of feedback control systems: 1) positive feedback 2) negative feedback. The positive feedback is used to increase the size of the input but in a negative feedback, the feedback is used to decrease the size of the input. The negative system...

This application note describes how to quickly implement and optimize floating-point Proportional-Integral-Derivative (PID) control algorithms specified in C/C++ code into an RTL design using Vivado HLS. You can use System Generator for DSP to easily analyze and verifiy the design. This enables floating-point algorithm designers to take advantage of high-performance, low cost, and power efficie...

Understanding the concepts of fractional and variable order differential calculus requires a willingness to depart from the traditional physical interpretations through which calculus is generally understood. Fractional calculus involves the computation of a derivative or integral of any real order, rather than just an integer. Several definitions for calculating a real order derivative or inte...