EXACT AND LINEARISED NEURAL PREDICTIVE CONTROL
A TURBOCHARGED SI ENGINE EXAMPLE
G. Colin*, Y. Chamaillard*, G. Bloch**, G. Corde***, A. Charlet*
* Laboratoire de Mécanique et d’Energétique (LME, EA1206) – France
8, rue Léonard de Vinci – 45072 Orléans Cedex 2 – +33 (0)2 38 41 70 50
** Centre en Recherche en Automatique de Nancy (CRAN, UMR CNRS 7039) – France
*** Institut Français du Pétrole (IFP) – France
guillaume.colin@univ-orleans.fr
KEYWORDS
Neural Networks – Predictive Control – Non-linear
Control – Engine Control – Real Time Implementation
ABSTRACT
This paper describes a real-time control method for
non-linear systems based on Model Predictive Control.
The model used for the prediction is a neural network
because of its ability to represent non-linear systems, its
ability to be derivated and its easiness to be used. The
feasibility and the performance of the method, based on
on-line linearization, are demonstrated on a
Turbocharged SI Engine application, where the
simulation models used are very accurate and complex.
The results allow to implement the control scheme in
real time.
INTRODUCTION
Theoretical issue
Model Predictive Control (MPC) or Receding
Horizon Control (RHC) has become an attractive control
strategy especially for linear processes or non-linear
large time constant processes. MPC uses an explicit
model to predict the future response of the process and
an algorithm which optimizes future process behavior. In
general, MPC is formulated as solving on-line a finite
horizon open-loop optimal control problem subject to
system dynamics and constraints involving states and
control (Clarke et al., 1987).
Linear MPC uses a linear model to predict the process
behaviour, so that the solution or a part of the solution
could be calculated off line. Linear MPC has dozens of
variants: model predictive heuristic control (Richalet et
al., 1978), Dynamic Matrix Control (Cutler and
Ramaker, 1979), state space MPC (Lee et al., 1994), ...
For a good introduction to the theoretical and practical
issues associated to linear MPC, see (Garcia et al.,
1989), (Morari and Lee, 1999), (Qin and Badgwell,
2003). Many systems are, however, non-linear by nature,
and linear models are often inadequate to describe such
processes. This motivates the development of Non-linear
Model Predictive Control (NMPC) (Findeisen and
Allgöwer, 2002). Due to the use of a non-linear model,
NMPC strategy is based on solving a non-convex
optimization problem on-line, which requires an
important computational burden.
Besides, because of their ability to represent nonlinear
process with good flexibility and accuracy, neural
networks have become popular to model various systems
as discrete black boxes (Bloch and Denoeux, 2003). So
the ability of the NMPC to make accurate predictions can
be enhanced if a neural approach is used instead of a
standard non-linear modeling technique (Nørgaard et al.,
2000) and the associated control scheme is then called
Neural Predictive Control. Another advantage of using
neural networks is the easiness of model derivating, so
that a linear model could be extracted at each sample
time and used for the controller design, leading to
linearized predictive control (Blet et al., 2002).
Practical issue
European emissions standards impose to reduce fuel
consumptions and pollutants emissions for Spark Ignited
engines (Powers and Nicastri, 2000). Nowadays,
downsizing (reduction of the engine size) appears as a
major way for reducing fuel consumption while
maintaining advantage of the low emission capability of
the three ways catalytic system (Lecointe and Monnier,
2003; Mille, 2003). Turbocharging is one of the pertinent
ways to realize an efficient downsizing. On the other
hand, engine control is necessary to consider an efficient
engine torque control (Corde, 2002), which includes
notably the control of ignition coils, fuel injectors and air
actuators (throttle, turbocharger, etc…). The air actuators
controllers currently used are PID controllers which lead
into problems of overshoot and bad set point tracking. A
solution of this control problem is Neural Predictive
Control (Lennox et al., 2001). Very few works deal with
real-time implementation of NMPC or the works are
applied to plants that have a large time constant
(Soloway and Haley, 1996; Haley et al., 1999; Sorensen
et al., 1999). For the real-time implementation, we need
a solution for the optimization problem which should not
be an intensive iterative procedure and linearized
predictive control could be chosen.
Main Contributions
This work deals with a real-time control method for
non-linear systems based on Neural Predictive Control.
Therefore, the main contributions of this work are the
possible real time implementation of the method on
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