Gain-Scheduling Control of Port-Fuel-Injection Processes Andrew White, Jongeun Choi, Ryozo Nagamune, and Guoming Zhu Abstract— In this paper, we first obtain an event-based sampled discrete-time linear system to represent a port-fuel- injection process based on wall-wetting dynamics, and formu- late it as a linear parameter varying (LPV) system. The system parameters used in the engine fuel system model are engine speed, temperature, and load. These system parameters can be measured in real-time through physical or virtual sensors. A gain-scheduling controller for the obtained LPV system is then designed based on the numerically efficient convex optimization or linear matrix inequality (LMI) technique. The simulation results show the effectiveness of the proposed scheme. I. I NTRODUCTION Increasing concerns about global climate change and ever- increasing demands on fossil fuel capacity call for reduced emissions and improved fuel economy. Vehicles equipped with a port-fuel-injection fuel system have been widely used today; and vehicles equipped with a direct-injection (DI) fuel system have been introduced to markets globally. In order to improve DI engine full load performance at high speed, Toyota introduced an engine with a stoichiometric direct injection system with two fuel injectors for each cylinder (see [1]). One is a DI injector generating a dual- fan-shaped spray with wide dispersion, while the other is an intake port injector. The dual-fuel system introduces one additional degree of freedom for engine optimization to reduce emissions with improved fuel economy. The use of gasoline port-fuel-injection and ethanol DI dual-fuel system to substantially increase gasoline engine efficiency is de- scribed in [2]. The main idea is to use a highly boosted small turbocharged engine to match the performance of a much larger engine. Direct injection of ethanol is used to suppress engine knock at high engine load due to its substantial air charge cooling resulting from its high heat of vaporization. This shows that with the introduction of DI fuel systems for the internal combustion engine, port-fuel-injection fuel systems will be part of the engine fuel system for improved engine performance, which is the main motivation for us to revisit the air-to-fuel ratio control problem for a port-fuel- injection fuel system. The control of air-to-fuel (A/F) ratio is an increasingly important control problem due to the federal and state emis- sion regulations. Spark-ignited internal combustion engines are operated at a desired air-to-fuel ratio since the highest conversion efficiency of a three-way catalyst occurs around Andrew White, Jongeun Choi and Guoming Zhu are with the Department of Mechanical Engineering, Michigan State University {whitea23, jchoi, zhug}@egr.msu.edu Ryozo Nagamune is with the Department of Mechanical Engineering, Department of Mechanical Engineering, University of British Columbia nagamune@mech.ubc.ca stoichiometric air-to-fuel ratio. Due to the introduction of internal combustion engines with dual fuel systems (port- fuel-injection and DI), control of both A/F ratio and fuel ratio (ratio of port-fuel-injection fueling vs. total fueling) becomes a part of the combustion optimization problem [3]. There have been several fuel control strategies developed for internal combustion engines to improve the efficiency and exhaust emissions. A key development in the evolution was the introduction of a closed-loop fuel injection control algo- rithm [4], followed by the linear quadratic control method [5], and an optimal control and Kalman filtering design [6]. Specific applications of A/F ratio control based on observer measurements in the intake manifold were developed in 1991 [7]. Another approach was based on measurements of exhaust gases A/F ratio measured by the oxygen sensor and on the throttle position [8]. Hedrick also developed a nonlinear sliding mode control of A/F ratio based upon the oxygen sensor feedback [9]. Continuing research efforts of A/F ratio control include adaptive approaches [10], [11], observer-based controllers [12], H ∞ controllers [13], model predictive controllers [14], sliding mode controllers [15], and linear parameter-varying controllers [16], [17], [18]. The conventional A/F ratio control for automobiles uses both closed-loop feedback and feedforward control to have good steady state and transient responses. For a spark-ignited engine equipped with a port-fuel- injection system, the wall-wetting dynamics is commonly used to model the fuel injection process; and the wall-wetting effects are compensated on the basis of simple linear models that are tuned and calibrated through engine tests. These models are quite effective for an engine operated at steady state or slow transition conditions but they are difficult to be used at fast transient and other special operational conditions, for instance, during engine cold start. One of the approaches to model the wall-wetting dynamics during engine cold start is to describe it using a family of linear models to approximate the system dynamics at a given engine coolant temperature, speed and load conditions, that is, to translate the fuel system model into a linear parameter varying (LPV) system. As stated earlier, the use of LPV modeling to control the A/F ratio of a port-fuel- injection system has been reported by [16], [17], [18]. In [18], a continuous-time, LPV model is developed considering only engine speed as a time-varying parameter. Due to the simplicity of the model used, the issue of engine cold start is not addressed. Furthermore, the control synthesis method used in [18] relies on gridding the parameter space at a finite number of grid points. In [17], a large variable time delay is present in the air-fuel 2010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02, 2010 WeB19.2 978-1-4244-7427-1/10/$26.00 ©2010 AACC 1453