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Compressor maps are one of the main elements describing the behaviour of centrifugal compressors. Although the compressor map is often provided by the manufacturer, there may be changes during the lifetime of the compressor due to refurbishments or wear. Since the compressor maps are often used in real-time optimization problems, there is a need for simple approximation methods. This paper focuses...
Stability analysis in non-integer order systems is a complex issue and requires detailed analysis. This paper aims to show the stability region for fourth order system with noninteger PDÄ controller. Such system was analysed with use of Ddecomposition method. Moreover, we presented stability analysis for implementation in optimization procedure based on system in of form of fractional differential...
Non-integer order systems take an increasing part in science and engineering. Unfortunately for practical applications they posses infinite memory. In order to realize such system one needs to use approximations. In this paper a novel method of approximation of non-integer order integrator 1/sα is considered. This method is based on approximating the so called diffusive realization of integrator with...
Tuning non-integer order controllers is one of the problems in modern control theory. One of the questions which need addressing is how to calculate performance indicator without finding the solution of the non-integer order system. This paper shows how to calculate the indicators using Laguerre Impulse Response Approximation method along with optimization algorithm. We show theoretical analysis of...
Typical approach to non-integer order filtering consists of analogue design and implementation. Digital realization of non-integer order systems is susceptible to problems such as infinite memory requirement and sensitivity to numerical errors. The aim of this paper is to present two efficient methods for digital realization of non-integer order filters: discrete time-domain Oustaloup approximation...
Control of active magnetic bearings is an important area of research. In this paper authors present the methodology of design, discretization and implementation PIλD controller for magnetic levitation system. Implementation on the laboratory system was performed to validate the presented methodology. The presented methodology is promising and can be successfully used in other control systems.
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.
In this paper the method for optimisation of PDα controllers for linear systems was investigated. A new method for approximation of performance index with infinite horizon was presented and used. Optimisation was undertaken on approximated performance index with satisfactory results for multiple test systems. Results are promising, convergence of approximant and performance index was observed and...
Non-integer order filters allow much greater flexibility in shaping of frequency responses than classical methods. In this paper authors present the methodology of digital filter design using non-integer order filter as a prototype. Implementation on the embedded testbed was performed to validate the presented method. Experiments with measuring of frequency response show consistency of implementation...
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...
In this paper, the authors wanted to analyse the behaviour of fractional order system under relay control. There is a brief introduction to finding a solution for non-integer order systems both with zero and non-zero initial conditions. Then, the numerical approach is presented with some examples.
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.
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...
In this paper a special case of non-integer filters — namely bi-fractional filters (BFF) — are considered. Those filters are characterised by three parameters and offer rich possibilities of frequency response shaping. This paper is a continuation of an earlier research and focuses on stable filters with eigenvalues in right complex half plane. Conditions on stability of such filters are presented,...
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