Application of some new tools to robust stability analysis of spark ignition engines: a case study

An analysis of the stability of a spark ignition engine is carried out to demonstrate the applicability of some new tools for robustness analysis. First, a brief introduction to the model of the engine at idle speed is provided. Then, frequency domain characterizations of both the engine and the controller are seen to depend on a set of uncertain parameters. Based on physical realizability considerations, three sets of uncertain parameters are used. Subsequently, the problem of robust stability is posed in terms of a polynomial whose root set is required to be in the open left half plane. To complete the specification of the robust stability problem, it is important to specify which intermediate values of the uncertain parameters are feasible; i.e., uncertain parameter values other than those associated with the three operating points. In this regard, the two “intermediate value models” which are used involve polytopes of polynomials in the appropriate polynomial and parameter spaces. Then, robust stability analyses are carried out graphically by employing the notions of “value set” and “zero exclusion”. It turns out that robust stability is established for both models