Percorrer por autor "Kozlowski, K."
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- Adaptive Controller for Systems of Fractional Dynamics Based on Robust Fixed Point TransformationsPublication . Tar, J. K.; Rudas, I. J.; Bitó, J. F.; Tenreiro Machado, J. A.; Kozlowski, K.In this paper a discrete time approximation of Caputo’s fractional order derivatives is used for modeling the dynamic behavior of hypothetical fractional order systems the appropriate responses of which that can directly be manipulated by some physical agents are some fractional order time-derivatives of their state variables. A possible generalization of the concept of “initial conditions” of the integer order systems is proposed as “preceding history” for fractional order ones. It is shown that the number of the independent data characteristic to the “preceding history” can be made independent of the order of derivation. It is shown that the discrete time approximation proposed makes it possible to interpret the order of derivation in a higher range than in the case of the original integral form of Caputo’s definition. By providing a simple analysis of the so obtained time-sequences it is shown that by manipulating the order of differentiation in this model both dissipative and unstable behavior can be modeled. The dissipative casecorresponds to the presence of unmodeled internal degrees of freedom that are dynamically coupled to the directly controlled ones but cannot directly be controlled. The unstable case seems to be appropriate for modeling the behavior of systems coupled to some directly unmodeled exciting environment. For this purpose very simple mathematical estimations can be applied. The paradigm controlled is a fractional order Φ6 type Van der Pol oscillator that already obtained certain attention in the literature. It is shown that the simple fixed point transformations based adaptive control elaborated for integer order systems can be applied without any modification for fractional order ones.
- Adaptive VS/SM Controller based on Robust Fixed Point TransformationsPublication . Tar, J. K.; Rudas, I. J.; Bitó, J. F.; Tenreiro Machado, J. A.; Kozlowski, K.The great advantage of the Variable Structure Sliding Mode controllers is their simplicity, and that they can efficiently work in the possession of a very rough model of the system to be controlled. Instead investing any effort into identifying the precise analytical model of this system they apply well timed bang-bang type control signals in order to drive the “error metrics” near zero during finite time. The effects of modeling errors and unknown external perturbations are compensated by the application of great amplitude for this fluctuation often induce chattering that can be obviated by smoothing these signals normally at the cost of degraded precision of trajectory tracking. The recently proposed adaptive control based on robust fixed point transformations drives the system nearby the kinematically arbitrarily prescribed trajectories by the use local basins of attraction in an iterative learning control also abandoning the identification of the precise model of the system. By the combination of these different approaches efficient adaptive VS/SM controller can be developed that more precisely can trace the desired trajectory kinematically prescribed by the usual relaxation of the error metrics. Chattering can be evaded by decreasing the amplitude of the fluctuating control signal without degrading the tracking precision. This statement is substantiated by simulation results obtained for a simple paradigm.