Analysis of the Band-Pass and Notch Filter with Dynamic Damping of Fractional Order Including Discrete Models

The paper presents analysis of the second order band-pass and notch filter with a dynamic damping factor βd of fractional order. Factor βd is given in the form of fractional differentiator of order a, i.e. βd=β/sa, where β and a are adjustable parameters. The aim of the paper is to exploit an extra degree of freedom of presented filters to achieve the desired filter specifications and obtain a desired response in the frequency and time domain. Shaping of the frequency response enables achieving a better phase response compared to the integer-order counterparts which is of great concern in many applications. For the implementation purpose, the paper presents a comparison of four discretization techniques: the Osutaloup’s Recursive Algorithm (ORA+Tustin), Continued Fractional Expansion (CFE+Tustin), Interpolation of Frequency Characteristic (IFC+Tustin) and recently proposed AutoRegressive with eXogenous input (ARX)-based direct discretization method

Model of Three-Limb Three-Phase Transformer Based on Nonlinear Open Circuit Characteristic with Experimental Verification

This paper describes the realization of a three-phase transformer model based on a non-linear open-circuit characteristic. The proposed model is based on the fact that in case of a star connection with a neutral wire on the primary windings for all three phases, the applied voltage presents phase voltage and line (phase) currents are magnetization currents. These variables are available for measuring and it is easy to obtain three non-linear open circuit characteristics. The results of simulations and a comparison with references and experimental results verified this approach

D-decomposition technique for stabilization of Furuta pendulum: fractional approach

In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out

D-decomposition technique for stabilization of Furuta pendulum: fractional approach

In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out