Dimensional analysis for robust control of planar vehicle dynamics

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. Copyright © 2007 John Wiley & Sons, Ltd.     

An anti-windup technique for LMI regions

The anti-windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities, such as saturation, for a given linear time-invariant plant and controller. This paper presents a linear matrix inequality (LMI) based method that attempts to minimize performance deterioration while explicitly restricting the anti-windup closed loop dynamics. The restriction placed on the dynamics is described via LMI regions, which is a form of regional pole placement. Finally, the techniques discussed in this paper are demonstrated on an electro-hydraulic testbed.     

A KYP Lemma for LMI Regions

In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.