By Aleksei Tepljakov

ISBN-10: 3319529498

ISBN-13: 9783319529493

ISBN-10: 3319529501

ISBN-13: 9783319529509

This booklet stories on a very good learn dedicated to modeling and regulate of dynamic platforms utilizing fractional-order calculus. It describes the advance of model-based keep an eye on layout tools for platforms defined through fractional dynamic types. greater than three hundred years had handed considering Newton and Leibniz constructed a suite of mathematical instruments we now be aware of as calculus. Ever considering then the assumption of non-integer derivatives and integrals, universally known as fractional calculus, has been of curiosity to many researchers. notwithstanding, because of numerous concerns, using fractional-order types in real-life purposes used to be constrained. Advances in glossy machine technology made it attainable to use effective numerical easy methods to the computation of fractional derivatives and integrals. This publication describes novel tools constructed through the writer for fractional modeling and keep an eye on, including their winning software in real-world method keep an eye on situations.

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Additional info for Fractional-order Modeling and Control of Dynamic Systems

Sample text

Order the n + 1 vertices, so that F(x1 ) satisfied. Apply tie-breaking rules when necessary. 2. Reflect. 44) i=1 is the centroid of the n best vertices. Evaluate Fr = F(xr ). If F1 xn+1 = xr and terminate the iteration. 3. Expand. 45) and evaluate Fe = F(xe ). If Fe < Fr , set xn+1 = xe and terminate the iteration. Otherwise, set xn+1 = xr and terminate the iteration. Fn , perform a contraction between x¯ and the better of xn+1 4. Contract. If Fr and xr : (a) Contract outside. 46) Fr , set xn+1 = xc and terminate the and evaluate Fc = F(xc ).

Fundamentals of Algorithms. (Society for Industrial and Applied Mathematics, 2003) 9. C. A. H. E. Wright, Convergence properties of the NelderMead simplex method in low dimensions. SIAM J. Optim. 9(1), 112–147 (1998) 10. Y. Luo, Y. Chen, Fractional-order [proportional derivative] controller for robust motion control: Tuning procedure and validation, in Proceedings ACC ’09, American Control Conference, (2009), pp. 1412–1417 11. H. Malek, Y. Q. Chen, Tuning fractional order proportional integral controllers for time delayed systems with a fractional pole, in Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol.

C. Yu, Autotuning of PID Controllers: A Relay Feedback Approach (Springer, 2006) 17. W. Zhang, An extended ADALINE neural network trained by Levenberg-Marquardt method for system identification of linear systems, in Control and Decision Conference (CCDC), 2013 25th Chinese (2013), pp. 2453–2458 Chapter 4 Fractional-Order PID Controller Design In this chapter, the problem of FOPID controller design is investigated. The treated problems include controller design for nonlinear and unstable systems.

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Fractional-order Modeling and Control of Dynamic Systems by Aleksei Tepljakov

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