Paweł Piątek

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.

Observer-based feedback for the 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 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.

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.

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.

Fractional Band-Pass Filters: Design, Implementation and Application to EEG Signal Processing

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.

Adaptive Non-Integer Controller for Water Tank System

In this article, the authors consider a new method of designing adaptive controller for non-integer order systems. The theoretical approach was verified with computer simulation of three-tank system. Further research will include implementation in a real system.

Lyapunov Direct Method for Non-integer Order Systems

In this paper an extension of Lyapunov direct method for non-integer order systems is presented. It allows to analyse a special case of classic stability theory - the Mittag-Leffler stability. However, there are some differences that are worth considering. Some of them are analysed in presented examples.

Application of kernel density estimators for analysis of EEG signals

Nowadays analysis of EEG signals is a very popular area of biomedical engineering and science for both civil and military markets. In this paper a novel analysis of EEG signal with the implementation of kernel density estimators in order to construct densitograms of the examined EEG signals was presented. This approach allows obtaining the statistically filtered signals, which enables to conduct the analysis in easier and quicker way. It is also important to mention that analysed signals were obtained from an inexpensive, easily available on the open market headset --- Emotiv EPOC. This paper also contains illustration of signal processing and justification of the chosen approach by spectral analysis.

Non-integer Order Filtration of Electromyographic Signals

Electromyography (EMG) is recently of growing interest of doctors and scientists as it provides a tool for muscle performance verification. In this paper a new approach to EMG signal processing is considered. This approach is non-integer order filtering. Bi-fractional filter is designed and filtering occurs through exact computation.

Hybrid Newton Observer in Analysis of Glucose Regulation System for ICU Patients

Glucose regulation system is one of the most important problems in ICUs. Nowadays either frequent testing and insulin shots or automatic insulin pumps are used to avoid hyperglycemia even for patients without history of diabetes. As it is impossible to directly measure the glucose level, there is a need for estimation tools ensuring appropriate quality of measurements.