By Pedro Balaguer
Dimensional research is an engineering software that's largely utilized to varied 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 unravel keep watch over difficulties comparable to id and version relief, strong regulate, adaptive keep an eye on and PID control.
This new ebook introduces the basics of dimensional research to either keep an eye on engineers and theorists with examples of useful applicability to commercial keep an eye on difficulties. by means of adopting keep an eye on conception learn, the writer describes find out how to make the most the advantages that dimensional research can provide to regulate theoretic and useful difficulties.
• dimensional research and dimensional similarity
• dynamical structures dimensionless representation
• dimensionless platforms identity and version order reduction
• homogeneity of PID tuning rules
• dimensionless PID tuning ideas comparison
• dimensional research keep an eye on fundamentals
• keep an eye on of dimensionally comparable systems
• strong control
• adaptive keep watch over within the presence of enter saturation
• time scales regulate.
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Extra resources for Application of Dimensional Analysis in Systems Modeling and Control Design
The procedure is as follows: Dynamical systems: dimensionless representation (i) (ii) (iii) (iv) 27 Choose the transfer function dominant time constant τp1 . Divide each transfer function parameter with time dimension by τp1 . Perform the following variable substitution s → s¯ := τp1 s. We obtain G(¯s). l to obtain the dimensionless Divide the resulting transfer function G(¯s) by kτp1 ¯ s). transfer function G(¯ Steps (ii) and (iii) leave the dimensional transfer function unaltered, that is G(s) = ¯ s) is G(¯s).
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. The use of the transfer function representation or the state space representation in control theory depends on the type of problems to be solved.
In the following section we show how dimensional analysis helps to circumvent these problems. 2 General procedure The dimensionless representation of dynamical systems reduces the number of parameters of the dynamical system. In this way we may gain some simplicity on the system representation. The parameters reduction by the dimensionless transfer 52 Application of dimensional analysis in systems modeling and control design function representation is limited to two parameters. Despite the limit on the parameters reduction capabilities, the dimensionless representation may enable the graphical representation in two or three dimensions of expressions that, otherwise, would not be possible to represent graphically.