Download Challenges in Automation, Robotics and Measurement by Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska PDF

By Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska

This ebook offers the set of papers accredited for presentation on the foreign convention Automation, held in Warsaw, 2-4 March of 2016. It provides the examine effects awarded by way of most sensible specialists within the fields of commercial automation, keep watch over, robotics and size thoughts. each one bankruptcy offers an intensive research of a selected technical challenge that's frequently through numerical research, simulation, and outline of result of implementation of the answer of a true international challenge. The awarded theoretical effects, functional recommendations and instructions can be precious for either researchers operating within the region of engineering sciences and for practitioners fixing commercial difficulties.

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Additional info for Challenges in Automation, Robotics and Measurement Techniques: Proceedings of AUTOMATION-2016, March 2-4, 2016, Warsaw, Poland

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1 Training of Classical Neural Models Accuracy of models is assessed taking into account the SSE index (3). For model training the efficient Broyden-Fletcher-Goldfarb-Shanno (BFGS) nonlinear optimisation algorithm is used, training is carried out in the parallel (recurrent) configuration. e. ???? = 1, nA = nB = 2) as in [6, 8]. In order to find a neural model with good accuracy and generalisation abilities the networks with K = 1, … , 7 hidden nodes are trained and compared. For each structure training is repeated 10 times (because of possible shallow local minima), all weights are initialised randomly.

Drazin inverse method is given in Sect. 4. Section 5 reccals Weierstrass-Kronecker decomposition method. In Sect. 6 single numerical example, illustrating three methods is presented. Concluding remarks are given in Sect. 7. The following notation will be used: ℜ—the set of real numbers, ℜn × m —the set of n × m real matrices, Z + —the set of nonnegative integers, In —the n × n identity matrix. 2 Preliminaries Consider the descriptor fractional discrete-time linear system described by the state equation EΔα xi + 1 = Axi + Bui , i ∈ Z + = f0, 1, .

3b) i by i + 1 we obtain A2 xi + 1 = − B2 ui + 1 . ð3:4Þ The Eqs. 4) can be written in the form             A1 − c 1 E1 c2 E1 ci + 1 E1 B1 0 E1 xi − xi − 1 − ⋯ − x0 + u + x = u . 5) we obtain             A A21 A2, i B20 B21 E2 xi + 1 = 20 + + ⋯ + + + x x x u i i−1 i ̄ ̄ ̄ i 0 ̄ ̄ ui + 1 , 0 A20 A21 A2, B20 B21 ð3:7Þ Ł. Sajewski 40 where E2 ∈ ℜn2 × n is full row rank with n2 ≥ n1 and A2, j ∈ ℜn2 × n , Ā2, j ∈ ℜðn − n2 Þ × n , j = 0, 1, . . , i B2, k ∈ ℜn2 × m , B̄2, k ∈ ℜðn − n2 Þ × m , k = 0, 1.

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