By Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska
This booklet offers the new advances and advancements on top of things, automation, robotics and measuring options. It provides contributions of most sensible specialists within the fields, occupied with either idea and business perform. the actual chapters current a deep research of a particular technical challenge that is mostly by way of a numerical research and simulation and result of an implementation for the answer of a true international challenge. The booklet offers the result of the foreign convention AUTOMATION 2014 held 26 - 28 March, 2014 in Warsaw, Poland on Automation – thoughts and destiny Prospectives The provided theoretical effects, useful strategies and guidance can be valuable for either researchers operating within the region of engineering sciences and for practitioners fixing commercial problems.
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Lemma 5. If all finite roots λ i of the characteristic equation (24) (finite eigenvalues ~ ~ of pair ( E , A) ) have negative real parts, then the fractional descriptor two-term regular system (1) is stable for all α ∈ (0, 1]. Stability Analysis of Descriptor Continuous-Time Two-Term Linear Systems 51 ~ ~ The method of Theorem 1 requires computation of eigenvalues of pair ( E , A) . Size of these matrices may be very high. 01 , k 2 = 97 and k1 = 70. In this case size of the matrices (10) is 97n × 97n .
001 mm/s for the servo drive with and without the BDKE block and various initial slide positions x. Owing to the use of the BDKE block the highest and the lowest values of the slide position error have decreased over fivefold for a short lead-screw and twofold for a long lead-screw. 00003 Fig. 18. 001 mm/s for the initial slide position X=10 mm – classic servo drive 30 B. 000004 Fig. 19. 000025 t [ms] 100 150 200 250 300 350 400 Fig. 20. 000015 Fig. 21. 001 mm/s for the initial slide position X=100 mm – modified servo drive Using Fuzzy Logic for Improving the Control Performance 31 All simulations have been carried out with controllers settings (RX, RV and RI) chosen to control the motion of a servo drive motor developing high velocities at no-load.
Keywords: linear system, descriptor, continuous-time, fractional, stability. 1 Introduction In the last decades, the problem of analysis and synthesis of dynamic systems described by fractional order differential or difference equations has been considered in many books (see [9, 15, 18, 20, 21], for example, and references therein). The problem of stability of linear fractional order systems has been investigated in monographs mentioned above and in the papers [1, 3, 4, 14, 19, 22, 23] for continuous-time systems and in [2, 5, 7, 8, 12] for discrete-time systems.
