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Enhancing Optimal Weight Tuning in H
Loop-shaping Control with
Particle Swarm Optimization
Philippe Feyel
1
, Gilles Duc
2
and Guillaume Sandou
2
1
SAGEM (SAFRAN Group), Optronics & Defense division, 100 Avenue de Paris, 91344 MassyCedex, France
2
SUPELEC Systems Sciences (E3S), Automatic Control Department, 3 rue Jolio-Curie, 91192 Gif-sur-Yvette, France
Keywords: Particle Swarm Optimization, H
Control, Loop-shaping.
Abstract: The H
loop-shaping controllers have proven their efficiency to solve problems based on complex industrial
specifications. However, the design is based on the tuning of weighting filters to reformulate all the
specifications, which is a time consuming task requiring know-how and expertise. This paper deals with the
use of Particle Swarm Optimization (PSO) algorithm for tuning the weighting filters. Whereas this topic has
already been investigated in lots of works especially using evolutionary algorithms, we propose here to
enhance the optimization process by working on the definition of a generic fitness function from a general
high-level specification, and by relaxing constraints on weights structure. The developed methodology is
tested using a real industrial example and leads to satisfactory results.
1 INTRODUCTION
H
synthesis is an efficient tool in robust control.
Among several design methodologies, the loop-
shaping procedure (McFarlane and Glover, 1992)
has strong advantages in the industrial framework. It
is based on the definition of weighting filters to
reformulate the desired specifications of the closed-
loop. An optimization step, based on the H
theory,
is then used to compute the final controller. The
main advantage of this design procedure is that the
weighting filter selection step allows the use of
linear transfer functions with decoupled intuition
and classical considerations on the open-loop gain
(bandwidth, low-frequency gain, etc). However,
choosing the “best” filters to capture as well as
possible complex specifications (mixing for instance
linear and nonlinear considerations) is difficult and
often time-consuming. Indeed, the classical
approach relies on an oriented “try and error”
procedure: the design problem is first simplified by
neglecting some nonlinear or disturbance
phenomena and/or some specifications. The
controller is then validated using time-domain
simulations of a full model. Several iterations are
thus generally needed in the development process.
Further, some expertise is often required to
reformulate specifications and to define well suited
weighting filters. This issue is worsened when the
final goal is not only to satisfy some specifications,
but also to optimize the closed-loop performance.
Since the emergence of H
theory, lots of works
have been done to optimize the weight selection
process. In (Lanzon, 2005) weighing functions are
set by a quasi-convex optimization problem.
Although effective, the main difficulty of such
approaches is related to the necessary open-loop
frequency specification framework used for the
optimization process. This is usually not
straightforward to obtain from a complex high-level
specification and the efficiency of the method often
relies on the expertise of the designer.
To avoid the frequency declination task, other
approaches based on stochastic optimization have
been considered. For instance in (Chipperfield,
Dakev, Fleming and Whidborne, 1996), weighing
functions of low order are selected with an
evolutionary algorithm. Based on stochastic
optimization, such works prove that complex criteria
can be considered in the Automatic control field
even if their gradients are not available, the only
requirement being the capability of evaluating the
fitness function.
The main improvements proposed in this paper
rely on:
the definition of the fitness function. This is of
course a crucial point in the optimization procedure.
For that purpose, we propose a method to build a
120
Feyel P., Duc G. and Sandou G..
Enhancing Optimal Weight Tuning in H8 Loop-shaping Control with Particle Swarm Optimizations.
DOI: 10.5220/0004552801200127
In Proceedings of the 5th International Joint Conference on Computational Intelligence (ECTA-2013), pages 120-127
ISBN: 978-989-8565-77-8
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)