Lyapunov-Based Nonlinear Feedback Control Design for Exhaust Gas Recirculation Loop of Gasoline Engines

Abstract

For gasoline engine with an exhaust gas recirculation loop, a challenging issue is how to achieve maximum brake efficiency while providing the desired torque. This paper presents a solution to this challenging issue via dynamical control approach which consists of two phases: optimal equilibrium point generation and feedback regulation of the optimized operating mode. First, a mean-value model is developed to represent the dynamical behavior of the intake manifold and exhaust manifold focused on gas mass flows. Then, the control scheme is constructed based on the control-oriented model. Mainly, the optimal set-points are designed by solving the optimal programming problem of maximizing the brake efficiency under demand torque constraint which is the first control design stage, and the dynamical model to the feedback stabilization regulation control for improving transient performance is at the second stage. Lyapunov-based design is used for the derivation of the state feedback law. Furthermore, the proposed exhaust manifold pressure estimator is also coupled into the controller to replace the cost prohibitive exhaust pressure sensor. Finally, experimental validations on the test bench are provided to evaluate the proposed controller.

Nonlinear observer-based exhaust manifold pressure estimation and fault detection for gasoline engines with exhaust gas recirculation

“…where x EGR , non and x EGR , PI are the EGR ratios estimated by the nonlinear observer and the sliding-mode proportional integral (PI) observer, 24 respectively, where m · ^ EGR , PI is the estimated EGR mass flow by the PI observer in the study by Jiang and Shen. 24…”

Air Path Dynamics Control and Efficiency Optimization with Scenario Approach for Gasoline Engines

“…The target 2ZR-FXE engine (22) provided by Toyota is an advanced hybrid application engine which is equipped with EGR and intake VVT system. Unlike the traditional EGR system, the EGR gas of this engine is transported to the intake port and distributed into each cylinder directly, which implies there is little mixing effect between the EGR gas and intake air in the intake manifold (22) . And, we can assume that the EGR gas always be inducted into the cylinder from the EGR valve.…”

“…ideal gas equation and mass conversation law (1,21) with the assumptions in (22) , the intake manifold and exhaust manifold dynamic modeling (22) can be described as following: The torque modeling (24) is summarized as:…”

“…is the standard deviation, and For a given PDF, the probability can be computed in a finite interval. And, the σ ≤ 0.02μ can be interpreted in a probabilistic perspective, which means the probability of the the exhaust manifold pressure estimator, which is proposed by the authors' previous research (22) , is used here to substitute to the physical sensor.…”

Design and experimental validation for nonlinear control of internal combustion engines with EGR and VVT

“…Meanwhile, an experimental comparison between linear-quadratic regulator and model predictive control are presented by Kang and Shen [11]. In the paper [12], the problem of EGR control is solved by using nonlinear model and Lyapunov design to find the nonlinear feedback control law.…”