Application of Dimensional Analysis in Systems Modeling and by Pedro Balaguer

By Pedro Balaguer

Dimensional research is an engineering software that's commonly utilized to various engineering difficulties, yet has only in the near past been utilized to manage conception. program of Dimensional research in structures Modeling and keep watch over layout goals to resolve regulate difficulties equivalent to id and version aid, powerful regulate, adaptive keep an eye on and PID control.

This new ebook introduces the basics of dimensional research to either keep watch over engineers and theorists with examples of useful applicability to commercial regulate difficulties. via adopting regulate concept learn, the writer describes find out how to make the most the advantages that dimensional research can supply to manage theoretic and sensible difficulties.

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

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28) m(Nv −Nd −1) then the prototype and model are dimensionally similar. Finally, we define the concept of partial similarity. 2. If in two systems (prototype and model) some dimensionless numbers related to the governing variables are not equal, then the systems are partially dimensionally similar. 3. 29) with = v0 /vi the governed variable dimensionless number and 1 = t/rc the governing variable dimensionless number. e. e. = v0 /vi ). In this case both assumptions are fulfilled and two systems with identical 1 dimensionless numbers are dimensionally similar, that is p1 = m1 with p1 = tp /rp cp and m1 = tm /rm cm .

M]. = ai i ∈ [1, . . , n]. 49) As a result, a discrete transfer function is made dimensionless by just dividing by k. 2 Discrete time state space model dimensionless representation Consider the following discrete time state space model. 51) In this case the dimensionless discrete state space model is given in a similar manner as in the continuous time case. However, in the discrete time case, despite its name, there is no time, just a sequence of samples. As a result, there is no time scaling factor as the dimensions of xk+1 are equal to the dimensions of xk because there is no time derivative, just a sequence index increase.

S. Bernstein, and R. Venugopal. Dimensional analysis of matrices state-space models and dimensionless units [lecture notes]. Control Systems Magazine, IEEE, 27(6):100–109, 2007 [5] S. Skogestad and I. Postlethwaite. Multivariable Feedback Control. Analysis and Design. Wiley, 1996 [6] T. Szirtes and P. Rózsa. Applied Dimensional Analysis and Modeling. Butterworth-Heinemann, 2007 [7] B. West. ‘The tyranny of many dimensionless constants: a constraint on knowability’. 1 Introduction The dimensionless representation of dynamical systems presented in the previous chapter is the fingerprint for establishing dimensional similarity among dynamical systems.

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