By Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska
This e-book offers the new advances and advancements up to the mark, automation, robotics and measuring concepts. It offers contributions of best specialists within the fields, enthusiastic about either idea and commercial perform. the actual chapters current a deep research of a selected technical challenge that is normally by way of a numerical research and simulation and result of an implementation for the answer of a true global challenge. The publication offers the result of the foreign convention AUTOMATION 2014 held 26 - 28 March, 2014 in Warsaw, Poland on Automation – options and destiny Prospectives The offered theoretical effects, useful ideas and directions could be beneficial for either researchers operating within the sector of engineering sciences and for practitioners fixing commercial problems.
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Extra info for Recent Advances in Automation, Robotics and Measuring Techniques
Banaszak, and P. Pawlewski means the th state of local processes: , , , , ,…, th – allocation of local processes In the ,…, ∆ ; – allocation meaning that the resource state, ∆ – means that the resource is occupied by the process , and unoccupied. e. which has an access to the resource is the next to access the resource . means that process – sequence of semaphore indexes of the th , ,…, ,…, – index determining the position of the semaphore value in state, the dispatching rule , , . For example, = 2 , means that the process is the second element of the and .
Let V (t ) = E T (t ) PE (t ), (23) where P is a positive definite symmetric constant matrix, be the Lyapunov function for the system (22). The derivative of (23) along solution of (22) is as follows V (t ) = E T (t ) PE (t ) + E T (t ) PE (t ) = E T (t )[ Ac T P + PAc ]E (t ), where Ac = A − K + M x . (24) 40 M. Busłowicz and A. Makarewicz The equation (24) can be written in the form V (t ) = E T (t )QE (t ), (25) Q = Ac T P + PAc = ( AT − K T + M x T ) P + P( A − K + M x ). (26) where According to the Lyapunov stability theory, the system (22) is asymptotically stable if and only if V (t ) < 0 for t ≥ 0, or equivalently, the symmetric matrix Q defined by (26) is negative definite (all eigenvalues have negative real parts).
From simulations we obtain that synchronization holds for k1 = 71, k 2 = 200 , k3 = 150 and also for values of these coefficients essentially smaller, for example, for k1 = 12 and k 2 = k3 = 10 . Results of simulations are shown in Fig. 5 . 6 second for k1 = 12 and k 2 = k3 = 10 . 8 time Fig. 4. Synchronization error: a) for k1=71, k2=200, k3=150; b) for k1=12, k2=k3=10 5 Concluding Remarks Chaotic behavior of the modified Van der Pol-Duffing oscillator of fractional order has been analyzed and the problem of synchronization of two such systems with linear coupling has been considered.
Recent Advances in Automation, Robotics and Measuring Techniques by Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska