Abstract
This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.
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Abbreviations
- H u :
-
fuel lower heating value (kJ/kg)
- I :
-
crank shaft load inertia (kg m 2)
- L th :
-
stoichiometeric air/fuel ratio (14.7)
- ṁ ap :
-
air mass flow into the intake port (kg/sec)
- ṁ at :
-
air mass flow past the throttle plate (kg/sec)
- ṁ EGR :
-
EGR mass flow (kg/sec)
- ṁ f :
-
engine port fuel mass flow (kg/sec)
- ṁ ff :
-
fuel film mass flow (kg/sec)
- ṁ fi :
-
injected fuel mass flow (kg/sec)
- ṁ fv :
-
fuel vapor mass flow (kg/sec)
- n:
-
crankshaft speed (krpm)
- p a :
-
ambient pressure (bar)
- P b :
-
load power (kW)
- P f :
-
friction power (kW)
- p i :
-
manifold pressure (bar)
- P p :
-
pumping power (kW)
- R:
-
gas constant (here 287 × 10−5)
- T a :
-
ambient temperature (degrees Kelvin)
- T EGR :
-
EGR temperature (degrees Kelvin)
- T i :
-
intake manifold temperature (degrees Kelvin)
- t d :
-
time delay of fuel injection systems
- u :
-
throttle position (degrees)
- V d :
-
engine displacement
- V i :
-
manifold + port passage volume (m 3)
- η i :
-
indicated effiency
- λ:
-
air/fuel ratio
- Δτ d :
-
injection torque delay time (sec)
- κ:
-
ratio of specific heat = 1.4 for air
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Shi-Wei Wang PhD student, Liverpool John Moores University; MSc in Control Systems, University of Sheffield, 2003; BEng in Automatic Technology, Jilin University, 2000; Current research interests automotive engine control, model predictive control, sliding mode control, neural networks.
Ding-Li Yu obtained B.Eng from Harbin Civil Engineering College, Harbin, China in 1981, M.Sc from Jilin University of Technology, Changchun, China in 1986 and PhD from Coventry University, U.K. in 1995, all in control engineering. He is currently a Reader in Process Control at Liverpool John Moores University, U.K. His current research interests are in process control, engine control, fault detection and adaptive neural nets. He is a member of SAFEPROCESS TC in IFAC and an associate editor of the IJMIC and the IJISS.
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Wang, SW., Yu, DL. Adaptive air-fuel ratio control with MLP network. Int J Automat Comput 2, 125–133 (2005). https://doi.org/10.1007/s11633-005-0125-y
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DOI: https://doi.org/10.1007/s11633-005-0125-y