Dimensionless robust control with application to vehicles

The selection of a nominal plant model and an uncertainty representation is a central design choice for a robust controller design. In this brief, we examine the choice of both a plant model and an uncertainty representation from a dimensionless viewpoint. We develop a dimensionless representation of a linear bicycle model for vehicle dynamics that is suitable for a generalized vehicle analysis. Within such a dimensionless framework, the average of vehicle parameters becomes well defined thereby giving a nominal vehicle. Additionally, it becomes easy to develop perturbations of the vehicle model about the nominal one that reasonably encompass all production vehicles. These uncertainty bounds are then used to generate a robust controller suitable for any vehicle. Tighter uncertainty bounds result from the dimensionless analysis versus a dimensioned one and therefore provide less conservative controllers. For the purposes of demonstration, the focus of this brief is a lateral-positioning control task. The resulting control design approach is demonstrated on a scaled experimental vehicle as well as through simulations.