Real-time Adaptive Control Using Neural Generalized Predictive Control
Pam Haley,NASA Langley Research Center -
p.j.haley@larc.nasa.gov
Don Soloway, NASA Ames Research Center – don@ptolemy.arc.nasa.gov
Brian Gold,Langley Aerospace Research Summer Scholar -
bgold@vt.edu
Abstract
The objective of this paper is to demonstrate the feasibility of a
Nonlinear Generalized Predictive Control algorithm by showing
real-time adaptive control on a plant with relatively fast time-
constants. Generalized Predictive Control has classically been
used in process control where linear control laws were formulated
for plants with relatively slow time-constants. The plant of
interest for this paper is a magnetic levitation device that is
nonlinear and open-loop unstable. In this application, the
reference model of the plant is a neural network that has an
embedded nominal linear model in the network weights. The
control based on the linear model provides initial stability at the
beginning of network training. In using a neural network the
control laws are nonlinear and online adaptation of the model is
possible to capture unmodeled or time-varying dynamics.
Newton-Raphson is the minimization algorithm. Newton-Raphson
requires the calculation of the Hessian, but even with this
computational expense the low iteration rate make this a viable
algorithm for real-time control.
1. Introduction
Generalized Predictive Control (GPC) belongs to the class of
Model-Based Predictive Control (MPC) techniques and was first
introduced by Clarke and his co-workers in 1987 [1,2,3]. Linear
model predictive control has a long reputation as a powerful
control tool in industrial control processes [4,5,6]. However
nonlinear model predictive control is still viewed as an academic
tool mainly because of the difficulties associated with reliable
construction of a nonlinear model [7].
In the predictive control scheme the model is used to predict the
future behavior of the system due to both known and unknown
input effects. The accuracy of the model prediction directly
determines the quality and effectiveness of the control law and is
the primary consideration during implementation. The
construction of the model can be either derived from fundamental
principles, based on empirical data, or, as in this paper, a
combination of the two. A detailed discussion about the modeling
and identification as it applies to nonlinear model predictive
control can be found in [7].
A nonlinear model that is constructed from fundamental principals
could be globally valid over the entire input space depending on
the assumptions that are made. The derivation can be extremely
rigorous and often leads to very high order models, which can
introduce complications for real-time computation. Empirical
modeling is the process of transforming available input output data
into meaningful input output relations. The main limitation of a
model based on observations is that the prediction capability is
only valid for the region spanned by the data so nothing can be
said about the accuracy of the predictions based on extrapolations.
The magnetic levitation (MAGLEV) system presents significant
challenges for neural network modeling and predictive control.
The challenge for the neural network model is online learning for
the MAGLEV system. The challenge for the controller is to
compute real-time control laws for the MAGLEV system that has
dynamics that are considered to be relatively fast, especially for a
MBC scheme. In this paper the neural network model is
initialized with a nominal linear model. The control based on the
linear model provides initial stability at the beginning of network
training. The neural network is then allowed to learn the
unmodeled dynamics of the nonlinear plant thus combining
fundamental and empirical modeling. This paper also
demonstrates the feasibility of this NGPC implementation by
establishing real-time control at 500 Hertz while adapting the
neural network model online. All results are using a single-input
single-output system.
In the next section the Experimental Setup will be described
followed by discussions of the Neural Generalized Predictive
Control, Forming the MAGLEV Model (Fundamental Principles),
Neural Network Model, Real-time Adaptive Control, and
Conclusions and Recommendations.
2. Experimental Setup
The plant to be controlled is a magnetic levitation or MAGLEV
device. Magnetic levitation is a means of suspending an object in
space by controlling the magnetic force produced by current
flowing through a magnetic coil. The MAGLEV device used for
this work has two coils that are positioned side by side to suspend
two one-inch metal balls in the air by the electromagnetic force
due to the DC magnet above it. This device is capable of two
degrees-of-freedom (DOF), vertical translation and rotation [8].
The MAGLEV device can be used as a 1DOF single-input single-
output (SISO) system that commands only vertical translation of a
single metal ball or a 2DOF multi-input multi-output (MIMO)
system that also produces rotation through two separate vertical
translations of two metal balls connected by a nonferrous rod.
This paper presents results for the SISO 1DOF MAGLEV device
only.
The MAGLEV device is comprised of two DC magnets, a current
drive system, two light sources, and two photosensors. Each of
the DC magnets is made of 3800 turns of gage-22 magnet wire
wrapped about a one-inch diameter low carbon steel core that is
Analog
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Figure 1. Magnetic Levitation System