Neural network model-based automotive engine air/fuel ratio control and robustness evaluation

doi:10.1016/j.engappai.2008.08.001

Engineering Applications of Artificial Intelligence

Volume 22, Issue 2, March 2009, Pages 171-180

https://doi.org/10.1016/j.engappai.2008.08.001 Get rights and content

Abstract

Automotive engines are multivariable system with severe non-linear dynamics, and their modelling and control are challenging tasks for control engineers. Current control of engine used look-up table combined with proportional and integral (PI) control and is not robust to system uncertainty and time varying effects. In this paper the model predictive control strategy is applied to engine air/fuel ratio control using neural network model. The neural network model uses information from multivariables and considers engine dynamics to do multi-step ahead prediction. The model is adapted in on-line mode to cope with system uncertainty and time varying effects. Thus, the control performance is more accurate and robust compared with non-adaptive model based methods. To speed up algorithm calculation, different optimisation algorithms are investigated and performance compared. Finally, the developed method is evaluated on a well-known engine benchmark, a simulated mean value engine model (MVEM). The simulation results demonstrate the effectiveness of the developed method.

Introduction

Automotive engines have been a major source of air pollution, especially in metro area. Governments set strict emission standards for engines to reduce the air pollution. Reducing pollutant emissions is an imperative and a continuous challenge for the automotive industry. For spark-ignition (SI) engines, in term of control engineering, the target is to maintain the air/fuel ratio (AFR) at stoichiometric value (14.7) for both steady state and transient operation, which is a best solution to minimum emission and a widely accepted balance between power output and fuel consumption. AFR influences the effect of emission control because its stoichiometric value ensures the maximum efficiency of three-way catalysts (TWC). Variations of greater than 1% below 14.7 can result in significant increase of CO and HC emissions. An increase of more than 1% will produce more NO_x up to 50% (Manzie et al., 2001, Manzie et al., 2002). However, the dynamics of air manifold and fuel injection of SI engines are very fast, severely non-linear and with constraints imposed on the states and inputs (Balluchi et al., 2000; De Nicolao et al., 1996; Tan and Saif, 2000; Vinsonneau et al., 2003). Therefore, they present a challenge problem to control engineers.

Many of the current production of fuel injection controllers utilize feed-forward control with a mass airflow sensor located upstream of the throttle, plus a proportional and integral (PI) type feedback control. The feed-forward control is simply implemented with look-up tables, which requires a laborious process of calibration and tuning. Furthermore, it is difficult to apply this method since it needs the output magnitude information that is not available in the AFR control (Mooncheol et al., 1998). A variety of researches have been conducted during the last decade on advanced control strategies on AFR. Onder and Geering (1993) made an LQR regulator to improve the AFR control. It obtained fairly good AFR performance when throttle angle ranging from 4° to 8°, but is impractical due to heavy computations resulting from the high order of linearized model. Choi and Hendricks (1998) made an attempt at developing an observer-based fuel injection control algorithm to improve AFR control by using sliding mode. This analytic design method is in good agreement with the binary nature of the oxygen sensor signal. However, the controller is effective only when the throttle change is not rapid, since the controller depends mainly on feedback sensor information (Mooncheol et al., 1998).

Because of the attractive power on approximating, neural networks have been successfully used in a wide range of control applications. They provide researchers a black-box method to describe the complex process accurately in input–output models. A non-linear model predictive control (MPC) scheme for AFR based on a radial basis function (RBF) neural network model is developed in this paper. The RBF network is on-line adapted to model engine parameter uncertainty and severe non-linear dynamics in different operating regions. Based on the multi-step ahead prediction of the AFR, an optimal control is obtained to maintain the stoichiometric value when engine speed and load change. Two types of non-linear optimization algorithms are implemented to generate the optimal control signals of fuel injection according to the inputs from the RBF model: (1) Secant method and (2) reduced Hessian method. In both cases, satisfactory AFR control results are obtained by using MPC scheme, but the first method uses considerable less time than the second one for computation. Finally, the comparisons between two algorithms are presented regarding the performance and time cost.

Section snippets

SI engine dynamics

Engine control system analysis and design based on engine simulation models are much more economical than using a real engine test bed in both industrial practice and scientific research. The developed control will then be evaluated on real test engine under realistic model-plant mismatch and noise provided the test engine is available. The engine model adopted in this paper is referred to as the mean value engine model (MVEM) developed by Cho and Hendricks (1989), which is a widely used

Adaptive neural network model

The advantage of using adaptive neural network is that it can track the time-varying properties of the process to provide efficient information to the controller, under circumstances where the process parameters are changing (Chang, 2001). RBF with Gaussian transfer function is chosen in this application as it has been shown that RBFN could map a non-linear function arbitrarily well and possesses the best approximation property (Girosi and Poggio, 1999). The K-means algorithm is used for centre

Control system structure

The idea of model predictive control with neural network has been introduced in details by Draeger, et al. (1995). The strategy is shown in Fig. 6. The obtained adaptive RBF neural network is used to predict the engine output for N₂ steps ahead. The non-linear optimizer minimizes the errors between the set point and the engine output by using the cost function, $J (k) = \sum_{i = k + N_{1}}^{k + N_{2}} [msp (i) - \hat{y} (i)]^{2} + ξ \sum_{i = k}^{k + N_{u}} [{\dot{m}}_{fi} (i) - {\dot{m}}_{fi} (i - 1)]^{2}$ Here, N₁ and N₂ define the prediction horizon. ξ is a control weighting

Robustness evaluation

Air leakage can ruin performance, boost exhaust temperature, and raise emissions. In the engine model we are using, the parameter ${\dot{m}}_{ap}$ stands for the airflow rate into the engine port, which is shown in Eq. (4). When air leakage happens, the lost of air into the cylinders will result in the decrease of ${\dot{m}}_{ap}$ , this will fool the ECU into over fuelling. To test the system robustness to deal with air leakage problem, a 20% model mismatch is introduced on the airflow rate into engine port, which is

Conclusions

In this paper, an adaptive RBF model-based MPC is applied to AFR control of automotive engines. The simulation results validated that the developed method can control the AFR to track the set-point value under disturbance of changing throttle angle. To meet the requirement for fast optimization in engine control, a one-dimensional optimization method, Secant method, is implemented in the MPC and is compared with a multi-dimensional method, the reduced Hessian method. Simulations show a much

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Citation Excerpt :
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Neural network model-based automotive engine air/fuel ratio control and robustness evaluation

Abstract

Introduction

Section snippets

SI engine dynamics

Adaptive neural network model

Control system structure

Robustness evaluation

Conclusions

Control Engineering Practice

Neurocomputing

Engineering Application of Artificial Intelligence

Automotive engine control and hybrid systems: challenges and opportunities

Proceedings of the IEEE

A reduced Hessian method for large scale constrained optimization

SIAM Journal of Optimization

Numerical experience with a reduced Hessian method for large scale constrained optimization

Computational Optimization and Applications

Automotive power train modelling for control

Transaction of the ASME—Journal of Dynamic Systems Measurement and Control

An observer-based controller design method for improving air-fuel characteristics of spark ignition engines

IEEE Transaction on Control Systems Technology

A comparison of neural network control algorithms

IEEE Transaction on Neural Network