Real-Time System Identification and Control of Engine System Using Least Squares Learning and Simplex Tessellation

Abstract

To aid in engine control for achieving the stable combustion of varying cetane level fuels, a computationally efficient algorithm for the online learning of an engine model based on real-time input and output measurements is developed. Innovations in engine technology has led to the feasibility of robust, multi-fuel engine systems capable of operating on unknown or non-ideal fuel types. To attain such performance, advanced control strategies must be implemented in order to achieve stable engine combustion using such fuels. The method developed in this work, based on piecewise-linear modeling via discrete nodes and recursive linear least squares is first derived for the one-dimensional system of injection timing and combustion phasing. The learning model is then used for adaptive feedforward and feedback control of the SISO system in simulation using a gaussian process model as a virtual engine. The algorithm is then extended to the two-input/two-output system of injection timing and fuel mass and their effect on combustion phasing and indicated mean effective pressure (IMEP). Data generated using computational fluid mechanics is used to supplement experimental data in the development of the 2D model. The theory of barycentric and affine coordinates is introduced and applied to the concept of piecewise planes to approximate nonlinear surfaces. The learning model is utilized in an adaptive MIMO feedforward algorithm to control the engine to a desired combustion phasing and IMEP. Additionally, a decoupled integral feedback control scheme is presented and shown effective in simulation. A generalization of the learning algorithm for higher dimensions is made in order to model higher order systems. Specifically, simplex tessellation and barycentric coordinates as regressor coefficients are shown to generalize node locating and updating in arbitrary dimensions. The generalized learning algorithm is applied to a synthetic three-input data set in order show feasibility of the model for higher order nonlinear systems. The algorithm developed in this work is a unique, generalized, data-driven model capable of the real-time learning and control of multi-dimensional systems. The computational efficiency and generalization of the method allows for the real-time system identification of engine systems that are operating in unknown or untested environments. Existing engine models lack the efficiency to perform at the operating times seen in internal combustion engines. Implemented in a physical engine, the developed algorithm could be used for adaptive modeling of the system when undergoing a fuel or environmental change, which in turn can be used to aid in adaptive control of the engine. In commercial application, the real-time learning model could be used to decrease or eliminate the traditional in-house testing of engines required for lookup table generation, which would in turn decrease the time and cost in getting the engine to final application.