A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation

Ackmece, A. Behcet

Carson, John M., III

NASA Technical Reports Server

NASA Tech Briefs, May 2007 33
A model predictive control (MPC) al-
gorithm that differs from prior MPC al-
gorithms has been developed for con-
trolling an uncertain nonlinear system.
This algorithm guarantees the resolv-
ability of an associated finite-horizon op-
timal-control problem in a receding-
horizon implementation.  Given a
feasible solution to the finite-horizon
optimal control problem at an initial
time, resolvability implies the ability to
solve the optimal control problem at
subsequent times.
Originally developed for the control
of spacecraft in the proximity of small
celestial bodies, the algorithm can also
be applied to other systems (such as in-
dustrial and automotive systems) for
which robust feedback control may be
required. The algorithm consists of a
feedforward and a feedback component.
The feedforward part is computed by
the on-line solution of the finite-horizon
optimal control problem with the nomi-
nal system dynamics, with a relaxation of
the initial state constraint at each com-
putation.
The feedback component makes this
relaxation possible, which in turn guar-
antees resolvability and asymptotic sta-
bility once an initial feasible solution is
obtained at the start of a maneuver. The
feedback part involves off-line design of
a feedback control policy based on the
uncertainty bounds in the dynamical
model of the system. Consequently, this
algorithm is robust to system uncertain-
ties that are explicitly accounted for in
the design of the feedback portion of
the control input.
This explicit characterization of the ro-
bustness to the uncertainties (which can
easily be extended to external distur-
bances) is particularly desirable in a real-
time autonomous control application.
Furthermore, the ability to solve for an
open-loop trajectory during a maneuver
enables model updates (possibly based
on real-time information) into the con-
trol problem to reduce model uncer-
tainty and improve optimality for the
open-loop trajectory. The algorithm has
been shown to be robustly stabilizing
under state and control constraints with a
region of attraction composed of initial
states for which solution of the finite-hori-
zon optimal control problem is feasible.
This work was done by A. Behçet Açkmeçe
and John M. Carson III of Caltech for NASA’s
Jet Propulsion Laboratory. Further informa-
tion is contained in a TSP (see page 1).
The software used in this innovation is
available for commercial licensing. Please
contact Karina Edmonds of the California
Institute of Technology at (626) 395-2322.
Refer to NPO-42754.
A Robustly Stabilizing Model Predictive Control Algorithm
The algorithm can be applied to industrial and automotive systems.
NASA’s Jet Propulsion Laboratory, Pasadena, California
Information Sciences
A mathematical model describes the
evaporation of drops of a hydrocarbon
liquid composed of as many as hundreds
of chemical species. The model is in-
tended especially for application to any
of several types of kerosenes commonly
used as fuels. Like evaporating-multi-
component-fuel-drop models described
in several previous NASA Tech Briefs arti-
cles, the present model invokes the con-
cept of continuous thermodynamics, ac-
cording to which the chemical
composition of the evaporating multi-
component liquid is described by use of
a probability distribution function
(PDF). However, as described below, the
present model is more generally applica-
ble than is its immediate predecessor.
The present model is built on the one
reported in “Statistical Model of Evapo-
rating Multicomponent Fuel Drops”
(NPO-30886), which appears elsewhere
in this issue. To recapitulate: The PDF in
that model is a superposition of two func-
tions and, accordingly, is denoted a dou-
ble PDF. It is a function of the molecular
weight plus five other parameters. Unfor-
tunately, some of those other parameters
depend on the class of homologous hy-
drocarbon species, so that it becomes
necessary to have a double PDF for each
such class entering the fuel composition.
The introduction of multiple double
PDFs would make the computation very
cumbersome, negating the advantage of
the continuous-thermodynamics formu-
lation. The derivation of the present
model is driven by the concept of a uni-
fied thermodynamic representation of
three classes of homologous hydrocar-
bons (alkanes, naphthenes, and aromat-
ics) that constitute the principal compo-
nents of kerosenes. Somewhat more
specifically, it is sought to characterize
the hydrocarbons in each homologous
series by unified reference temperatures,
pressures, and other parameters that de-
pend only on molecular weights and
thermodynamic quantities.
The derivation leads to a new version
of the double PDF, in which the square
root of the molecular weight occupies
the position previously occupied by the
molecular weight and other parameters
are modified accordingly. By design, this
version of the double PDF applies to the
three major homologous series in
kerosene; hence, it is not necessary to
use multiple double PDFs. An additional
advantage of this formulation is that it is
valid over the subcritical region in the
pressure range from 1 to 15 bars (0.1 to
1.5 MPa).
The model has been tested on three
kerosenes used as aircraft and rocket
fuels: Jet A, JP-7, and RP-1. The present
Modeling Evaporation of Drops of Different Kerosenes
One model applies to all three classes of hydrocarbon constituents.
NASA’s Jet Propulsion Laboratory, Pasadena, California
https://ntrs.nasa.gov/search.jsp?R=20090041645 2019-08-30T08:17:36+00:00Z


A Robustly Stabilizing Model Predictive Control Algorithm

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server