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Online linearization-based neural predictive control of air–fuel ratio in SI engines with PID feedback correction scheme

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Abstract

Model predictive control (MPC) frequently uses online identification to overcome model mismatch. However, repeated online identification does not suit the real-time controller, due to its heavy computational burden. This work presents a computationally efficient constrained MPC scheme using nonlinear prediction and online linearization based on neural models for controlling air–fuel ratio of spark ignition engine to its stoichiometric value. The neural model for AFR identification has been trained offline. The model mismatch is taken care of by incorporating a PID feedback correction scheme. Quadratic programming using active set method has been applied for nonlinear optimization. The control scheme has been tested on mean value engine model simulations. It has been shown that neural predictive control with online linearization using PID feedback correction gives satisfactory performance and also adapts to the change in engine systems very quickly.

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Abbreviations

H u :

Fuel lower heating value (kJ/kg)

EVO:

Exhaust valve opening BBDC

IVO:

Intake valve opening BTDC

I :

Engine inertia (kg m2)

N :

Crankshaft speed (rpm)

P f :

Frictional power (kW)

P p :

Pumping power (kW)

P b :

Load power (kW)

P man :

Manifold pressure (bar)

P amb :

Ambient pressure (bar)

R :

Gas constant

T amb :

Ambient temperature (K)

T delay :

Transport delay (s)

T EGR :

EGR temperature (K)

T man :

Manifold temperature (K)

V man :

Manifold volume (m3)

V d :

Engine displacement (l)

e v :

Volumetric efficiency

k b :

Loading factor

\( \dot{m}_{\text{at}} \) :

Air mass flow past the throttle (kg/s)

\( \dot{m}_{\text{ap}} \) :

Air mass flow into the intake port (kg/s)

\( \dot{m}_{\text{EGR}} \) :

EGR mass flow (kg/s)

\( \dot{m}_{\text{f}} \) :

Fuel flow into intake port (kg/s)

\( \dot{m}_{\text{ff}} \) :

Fuel film mass flow (kg/s)

\( \dot{m}_{\text{fi}} \) :

Injected fuel mass flow (kg/s)

\( \dot{m}_{\text{fv}} \) :

Fuel vapour mass flow (kg/s)

n :

Crankshaft speed (krpm)

n cyl :

Number of cylinders

η i :

Indicated efficiency

α:

Throttle angle (degrees)

θ:

Spark advance (degrees)

θmbt :

MBT spark advance (degrees)

λ:

Relative air/fuel ratio

τf :

Fuel evaporation time constant (s)

γ:

Ratio of specific heats for air (1.4 for air)

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Authors and Affiliations

  1. Department of Mechanical Engineering, MNNIT, Allahabad, 211004, India

    Samir Saraswati & Satish Chand

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  1. Samir Saraswati
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  2. Satish Chand
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Correspondence to Samir Saraswati.

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Saraswati, S., Chand, S. Online linearization-based neural predictive control of air–fuel ratio in SI engines with PID feedback correction scheme. Neural Comput & Applic 19, 919–933 (2010). https://doi.org/10.1007/s00521-010-0419-z

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