Application of Dimensional Analysis in Systems Modeling and by Pedro Balaguer

By Pedro Balaguer

Dimensional research is an engineering software that's generally utilized to varied engineering difficulties, yet has just recently been utilized to manage idea. program of Dimensional research in platforms Modeling and keep an eye on layout goals to unravel keep an eye on difficulties similar to id and version aid, powerful keep an eye on, adaptive regulate and PID control.

This new e-book introduces the basics of dimensional research to either keep an eye on engineers and theorists with examples of sensible applicability to business keep watch over difficulties. by way of adopting keep watch over concept study, the writer describes find out how to make the most the advantages that dimensional research can provide to regulate theoretic and useful difficulties.

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

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

Example text

4). 24) The transformations to obtain a dimensionless model can be interpreted in terms of a coordinate transformation, a signal scaling, and a time scaling. The state space vector x of a state space model can be transformed by a nonsingular matrix T , giving a new state space representation xT , that is x = TxT [3]. This transformation is also known as similar transformation. However, to avoid confusion with dimensional analysis similarity concepts, we will refer it as coordinate transformation.

Alfaro and O. 1 Introduction The identification of models from experimental data is the first step in model-based control design. Furthermore, when the model is of high order, it is normal to reduce the model order for a simpler controller design. Low order identified models are the fundamental elements for the design of practical control systems. Although there are well-established techniques of general application for model identification and model order reduction, such as minimum squares and balanced model reduction, they are based on numerical calculations and give no parameter value insight.

For example consider the plasma confinement problem. In this case all the hydrodynamic, electromagnetic, and nuclear dimensionless numbers are relevant in the plasma confinement, making the dynamical behavior very complex [7]. Another property of the dimensionless representation is that it is the fingerprint of dimensional similarity. In this way two dimensionally similar systems have the same dimensionless representation. Consequently, the analysis and design results over dimensionless models are applicable not only to one dynamical model, but also to the infinite family of all dimensionally similar models.

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