Download Application of Dimensional Analysis in Systems Modeling and by Pedro Balaguer PDF

By Pedro Balaguer

ISBN-10: 1849196214

ISBN-13: 9781849196215

Dimensional research is an engineering device that's extensively utilized to various engineering difficulties, yet has just recently been utilized to manage thought. software of Dimensional research in structures Modeling and keep watch over layout goals to resolve regulate difficulties comparable to identity and version aid, strong keep watch over, adaptive keep watch over and PID control.

This new ebook introduces the basics of dimensional research to either regulate engineers and theorists with examples of sensible applicability to business keep watch over difficulties. via adopting keep watch over concept study, the writer describes the right way to make the most the advantages that dimensional research can supply to regulate theoretic and functional difficulties.

Topics include:
• dimensional research and dimensional similarity
• dynamical platforms dimensionless representation
• dimensionless structures id and version order reduction
• homogeneity of PID tuning rules
• dimensionless PID tuning ideas comparison
• dimensional research regulate fundamentals
• keep an eye on of dimensionally related systems
• strong control
• adaptive keep watch over within the presence of enter saturation
• time scales keep an eye on.

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Extra info for Application of Dimensional Analysis in Systems Modeling and Control Design

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Cm , l. The relative system order is n + l − m ≥ 0. K is the gain dimension and T the time dimension. The dimensions of the transfer function parameters are [k] = K/(Tl ), [τpi ] = [τcj ] = T for i = 1, . . , n and j = 1, . . , m, [h] = T, and [l] = 1, where 1 stands for dimensionless quantity. Proof. First we show that ni=1 (τpi s + 1) is dimensionless, thus [ ni=1 (τpi s + 1)] = 1. The dimension of τpi for i = 1, . . , n is time dimension [τpi ] = T. On the other hand, the dimension of the s operator is [s] = T−1 , as can be seen either in the time domain, where the s operator is transformed to operator d/dt, or in the frequency domain, where s is transformed to jω.

3) Note that, by P matrix being the identity, there is one dimensionless number for each one of the transfer function parameters with dependent dimensions {G, τp2 , . . , τpn , τc1 , . . , τcm , h, s, l}. As a result, for a generic transfer function with integrators and time delay, the quantity of dimensionless numbers is equal to Nv − Nd = n + m + 4, where n is the number of poles and m the number of zeroes. The reduction of transfer function dimensional parameters Nd is limited to Nd = 2. The dimensionless transfer function parameters can be interpreted as follows: ● ● ● ● ● The dimensionless number 1 = G(s) l kτp1 is the dimensionless transfer function.

The development of system identification and model reduction algorithms faces two difficulties. First the relations between transfer function parameters and time domain data are complex, and it is not straightforward to obtain model parameters from data, especially when the parameters number increases. For instance, approaches for the identification of integral second order systems showing inverse response have been based on the solution of a set of nonlinear equations [6] or the numerical evaluation of an integral [11].

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