Dimensional analysis for robust control of planar vehicle dynamics

Yan Li, Brandon Hencey, Andrew Alleyne

Research output: Contribution to journalArticlepeer-review


Most engineered systems with similar functions, which are designed under strict external constraints, share similar dynamics. Using a dimensionless model as system representation, a dimensionless robust controller can be designed and implemented for a class of dynamically similar systems that are different in physical dimension. Dimensionless transformations of timescale, inputs and outputs determine a nominal plant model and plant-to-plant uncertainties in a dimensionless form. Using parameter-dependent normalization, a normalized dimensionless model can be derived that has lower levels of plant-to-plant uncertainty than previous formulations (IEEE Trans. Contr. Syst. Technol. 2005; 13(4):624-630). The benefit of this dimensional analysis is demonstrated by the dynamic analysis of different types of planar vehicle systems. Numerical results show that, by using dimensional analysis, it is possible to obtain a controller that is robust to plant-to-plant parametric uncertainties among specific classes of systems designed with widely varying physical dimensions.

Original languageEnglish (US)
Pages (from-to)587-616
Number of pages30
JournalInternational Journal of Robust and Nonlinear Control
Issue number6
StatePublished - Apr 2008


  • Dimensional analysis
  • Modelling for robust control
  • Parametric uncertainty
  • Robust control design
  • Time scaling
  • Unstructured uncertainty
  • Vehicle dynamics

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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