Fuzzy modeling and control of a spark ignition engine idle mode

In this paper, a MIMO nonlinear discrete time model of the idle mode of an SI engine is first developed using a fuzzy logic model in the form of a nonlinear radial basis function expansion. The inputs are the throttle angle and the ignition advance and the outputs are the idle speed and manifold pressure. The model is validated using nonlinear correlation tests for MIMO systems. Phase portrait analysis is used to study the global dynamic behavior of the plant, in order to find periodic motions and equilibrium points of the system. Optimal state trajectories are used as entries to a fuzzy logic expansion to approximate the distorted control surface of the plant. The resulting FAM or fuzzy controller smoothens the control surface, and consequently, the transitions of the state trajectories from a different initial condition to another in its path to the equilibrium. Both the model and controller parameters are optimized using a modern version of an evolutionary algorithm, called covariance matrix adaptation-evolution strategies (CMA-ES).