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 noninteger order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation. Properties of both methods are investigated with use of non-integer low-pass filter. Filters realized with presented methods are then used for filtering of EEG signal. Paper concludes with discussion of merits and flaws of both methods.Keywords Non-integer order filter · Fractional filter · Oustaloup method · discretization · Laguerre impulse response approximation Work realized in the scope of project titled "Design and application of non-integer order subsystems in control systems". Project was financed by National Science Centre on the base of decision no.
Fractional band-pass filters are a promising area in the signal processing. They are especially attractive as a method for processing of biomedical signals, such as EEG, where large signal distortion is undesired. We present two structures of fractional band-pass filters: one as an analog of classical second-order filter, and one arising from parallel connection of two fractional low-pass filters. We discuss a method for filter implementation — Laguerre Impulse Response Approximation (LIRA) — along with sufficient conditions for when the filter can be realized with it. We then discuss methods of filter tuning, in particular we present some analytical results along with optimization algorithm for numerical tuning. Filters are implemented and tested with EEG signals. We discuss the results highlighting the possible limitations and potential for development.
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 non-linear and requires careful analysis and identification. The system is observable from position measurements as long as the electromagnet is powered as shown during the research. Practically measurable signals are the position and the coil current. The velocity that is necessary for any stabilizing control usually is obtained by numerical differentiation of the position. A more sophisticated approach is to estimate the velocity with an observer. Efficient observer types for this system are high-gain and non-linear reduced observers. The velocity estimated by an observer can be effectively used instead of a derivative in PID control of the position. Such an approach substantially improves control quality and extends the range of system’s stable operation. Even greater improvement is introduced by the addition of the non-linear feedforward to the control structure. The best results, provided the model parameters are correctly identified, are obtained with a control system consisting of the PID controller, the high-gain observer and the non-linear feedforward.
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