Less conservative polytopic LPV models for charge control by combining parameter set mapping and set intersection

In order to apply LPV gain scheduling to charge control of a spark ignited engine a polytopic LPV model was derived. This model suffers from overbounding, i.e. the LPV model displays more behavior than the underlying nonlinear model. As a consequence, the controller derived for this model does not fulfill the closed loop performance requirements. This paper presents a method for the generation of less conservative representations; the approach is based on a recently proposed technique for constructing LPV models - parameter set mapping - with tighter parameter sets. Since with this method the new parameter set is not a subset of the original one, improved performance is likely but not guaranteed. The approach proposed here improves this method by constructing the intersection of the original and the mapped parameter set, thus guaranteeing less overbounding. This approach is applied to the LPV model of the charge control model to demonstrate that it improves the quality of the desired representation in the sense of the induced pound₂ gain. Moreover, the application of this method to a set of similar models illustrates that with this approach less conservative models and better control performance for all representations can be achieved.