Marta Zagórowska

Impulse response approximation method for bi-fractional filter

In this paper method of impulse response approximation with orthogonal Laguerre functions is used for the approximation of bi-fractional filter (BFF). This filter is a new development in the field of non-integer order signal processing. Filter with three parameters allows advanced shaping of frequency response, especially the phase characteristic. Method of impulse response approximation is a very promising one because of its great conditioning and sound theoretical basis.

Robust non-integer order controller for air heater

Robust non-integer control is an emerging field in control theory. Multiple works are focused on designing controllers with flatphase and robust stability margins. In this paper design of non-integer order with robust properties is considered. This controller is designed for the model of air heating process trainer system belonging to the Department of Automatics and Biomedical Engineering of AGH University and Science and Technology and verified experimentally with that system.

Impulse Response Approximation Method for “Fractional Order Lag”

”Fractional order lag” is a system that is popular in multiple applications. In this paper, authors consider a new method for approximation of this system based on its impulse response. Certain assumptions of the approximation method are verified and algorithm is presented. Also certain problems with this system analysis are discussed, especially its realisation in the form of non-integer order differential equations.

Time-domain Oustaloup approximation

Paper presents a new method for implementing Oustaloup approximation of non-integer order systems in digital environment. Classical method and its limitations are presented and discussed. Method of realization is formulated and schemes for discretization are presented. Operation of method is illustrated with two examples. Work is ended with discussion of method limitations and conclusions.

Comparison of Performance Indices for Tuning of PIλDμ Controller for Magnetic Levitation System

Control of active magnetic bearings is an important area of research. The laboratory magnetic levitation system can be interpreted as a model of a single axis of bearings and is a useful testbed for control algorithms. The mathematical model of this system is highly nonlinear and requires careful analysis and identification. In this paper authors compare performance indices for tuning of PI λ D μ controller for this system. It is a part of an ongoing research on non integer controller tuning rules.

Bi-fractional filters, part 2: Right half-plane case

In this paper new non-integer order filter is proposed. Considered filter is given by a transfer function \(\cfrac{c}{s^{2\alpha}+ b s^{\alpha}+c}\), with parameters b and c chosen in a way, that locates the eigenvalues of the system in left open complex half plane. Dependence of frequency characteristic of the system on parameters α, b and c is investigated. Also method for realisation in the form of non-integer order differential equations is analysed.

Robust Non-integer Order Controller for Air Heating Process Trainer

Robust non-integer control is an emerging field in control theory. Multiple works are focused on designing controllers with flatphase and robust stability margins. In this paper design of non-integer order with robust properties is considered. This controller is designed and analysed for the model of air heating process trainer system belonging to the Department of Automatics and Biomedical Engineering of AGH University and Science and Technology.

Parametric Optimization of Non-Integer Order PD\(^\mu \) Controller for Delayed System

In this paper, we analysed a new tuning method for \({ {PD}}^{\alpha }\) controller using approximation with Laguerre functions. The optimization was performed for various sets of parameters. We also analysed the convergence of chosen optimization parameters. The results were tested for a first-order system with delay.

Discretisation of different non-integer order system approximations

The goal of this paper is to compare popular methods of approximation on non-integer order systems and propose strategies of increasing their robustness to numerical errors of their coefficients. It is shown, that popular methods during discretisation lead to instability.

Stability Properties of Discrete Time-Domain Oustaloup Approximation

The paper presents an analysis of discrete time domain realization of Oustaloup approximation. The scheme for realization is presented along with method of implementation of discretization formulas. Discussion for need for such realization is also presented. Finally the stability analysis is given, considering influences of sampling frequency, order and bandwidth. Analysis is illustrated with behavior of spectral radius of the discretized system.