By Pedro Balaguer
Dimensional research is an engineering instrument that's extensively utilized to varied engineering difficulties, yet has only in the near past been utilized to manage thought. software of Dimensional research in platforms Modeling and keep watch over layout goals to resolve regulate difficulties similar to id and version relief, strong keep an eye on, adaptive regulate and PID control.
This new e-book introduces the basics of dimensional research to either regulate engineers and theorists with examples of sensible applicability to commercial keep watch over difficulties. via adopting keep watch over idea examine, the writer describes the right way to take advantage of the advantages that dimensional research can supply to regulate theoretic and functional difficulties.
• dimensional research and dimensional similarity
• dynamical structures dimensionless representation
• dimensionless structures id and version order reduction
• homogeneity of PID tuning rules
• dimensionless PID tuning ideas comparison
• dimensional research regulate fundamentals
• keep watch over of dimensionally related systems
• strong control
• adaptive regulate within the presence of enter saturation
• time scales keep watch over.
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Additional resources for Application of Dimensional Analysis in Systems Modeling and Control Design
Furthermore, even the theoretical results obtained in dimensionless systems can be easily extrapolated to dimensionally similar models . In this chapter we present the conditions for establishing dimensional similarity between systems represented in transfer function form and in state space form. It is easier to establish dimensional similarity between transfer functions than between state space systems representation. The transfer function framework only requires two scaling factors between model and prototype, the gain scaling factor and the time scaling factor.
On the contrary, the state space dimensionless representation is obtained from physical parameters such as capacitance and electrical resistance. The physical parameters of state space representation are dumped into transfer function parameters. In this way the dimensionless representation of transfer function loses physical insight. However, the obtention of dimensionless representation of transfer functions is straightforward and of great generality. In fact, the procedure for dimensionless representation of transfer functions is not dependent on the physical problem at hand.
Dimensional Analysis. Gordon and Breach Science Publishers, 1987 T. Szirtes and P. Rózsa. Applied Dimensional Analysis and Modeling. 1 Introduction The dimensionless representation minimizes the number of parameters necessary for the system description, and may provide further knowledge of the parameters influence on the dynamical response. Furthermore, as proposed in Reference 7, the number of dimensionless numbers is a measure of the complexity of the problem at hand. Henceforth, the dimensionless representation may provide a system complexity characterization that is different from mere system order.