Application of Dimensional Analysis in Systems Modeling and by Pedro Balaguer

By Pedro Balaguer

Dimensional research is an engineering device that's largely utilized to various engineering difficulties, yet has only in the near past been utilized to regulate idea. software of Dimensional research in structures Modeling and keep an eye on layout goals to resolve keep watch over difficulties corresponding to id and version aid, strong keep watch over, adaptive regulate and PID control.

This new publication introduces the basics of dimensional research to either keep watch over engineers and theorists with examples of sensible applicability to commercial keep watch over difficulties. via adopting regulate thought study, the writer describes how one can take advantage of the advantages that dimensional research can provide to manage theoretic and sensible difficulties.

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

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

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Bd m ) Cd 1 , . . , Cd p ) Dd 1 , . . , Dd q ) where there are n + m + p + q dimensionless numbers related with governing variables. 38) In this case, there are as many scaling factors as governing variables, and they are also problem dependent. 4 Exercises 1. 41) a) Determine if they are dimensionally similar. b) Modify the model time delay in order to achieve complete similarity. Dynamical systems: dimensional similarity 49 c) Find the relationship between sampling times that preserve dimensional similarity.

M; and (ai )p = (ai )m , i = 1, . . , n. The parameters bj and ai are obtained by the discretization process , which can be, for instance, the zero order hold method or Tustin method. The discretization depends on the continuous time transfer function parameters and on the sampling time Ts , thus ai = (τp1 , . . , τpn , τc1 , . . 33) are equal for the prototype and the model, yielding (ai )m = (ai )p . The equality (bj )m = (bj )p is established by similar reasoning. The discrete time delay is related with the continuous time delay and the sampling time by q = h/Ts .

48) y(k) = −a1 y(k − 1) − · · · − an y(k − n) + k(b0 u(k − q) + · · · + bm u(k − m − q)) by dimensional homogeneity considerations [6], the dimensions of [ai y(k − i)] must be equal to [ y(k)], then [ai y(k − i)] = Y . It then follows that [ai ] = 1. In a similar way [kbj u(k − j − q)] = Y , being Y the output dimension. Note also that [u(k − j − q)] = U , being U the input dimension, then [kbj ] = YU −1 = K. As a result, a possible dimensional decomposition of the parameter kbj into a gain k and a parameter bj is [k] = K and [bj ] = 1.

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