SENSITIVITY ANALYSIS
OF LOW COST FUZZY CONTROLLED SERVO SYSTEMS
Stefan Preitl, Radu-Emil Precup and Zsuzsa Preitl
“Politehnica” University of Timisoara, Dept. of Automation and Applied Informatics
Bd. V. Parvan 2, RO-300223 Timisoara, Romania
Phone: +40-256-4032-29, -30, -24, -26, Fax: +40-256-4032-14
E-mail: spreitl@aut.utt.ro, rprecup@aut.utt.ro, zsuzsap@aut.utt.ro
Abstract: The paper performs the sensitivity analysis with respect to the parametric
variations of the controlled plant in the case of low cost fuzzy control systems
dedicated to servo systems, with focus on solving the tracking control problem for a
class of wheeled mobile robots with two degrees of freedom used in mining
technologies. A new development method for Takagi-Sugeno PI-fuzzy controllers is
proposed, based on applying the Extended Symmetrical Optimum method to the basic
linear PI controllers in a cascaded control system structure. Original sensitivity models
are derived. The approaches are validated by a case study. Copyright © 2005 IFAC
Keywords: sensitivity analysis, fuzzy control, second-order systems, PI controllers,
servo systems, dynamics.
1. INTRODUCTION
The considered class of controlled plants
(abbreviated CPs) is characterized by the transfer
functions H
P
(s):
)] 1 ( /[ ) (
Σ
+ = sT s k s H
P P
, (1)
where k
P
is the plant gain and T
Σ
represents the small
time constant or the sum of parasitic time constants.
The CPs with the transfer functions (t.f.s) of the
second-order systems in (1) can approximate well
enough the servo systems used in several
applications including the control of mobile robots.
Low cost automation (LCA) involves the use of low
cost control equipment and of control solutions that
can be developed and implemented relatively easy.
LCA solutions employ control structures and
algorithms with dynamics that can ensure good
control system (CS) performance in many situations.
A second-order system (1) can be placed on the
lower hierarchical level of complex, large-scale
systems. The assurance of good CS performance for
these systems by means of LCA solutions represents
a necessity.
One way to fulfil the goal of good CS performance
by means of LCA solutions for the CP (1) is
represented by conventional control under the form
of PI controllers (Åström and Hägglund, 1995).
Another way to fulfil the mentioned goal is
represented by the use of fuzzy control with
dynamics due to the flexible nonlinear input-output
static map ensured by the fuzzy controllers (FCs) that
can compensate (based on the designers’ experience)
the model uncertainties, nonlinearities and
parametric variations of the CP. Actual applications
of fuzzy control in the field of mobile robots are
those reported in (Saffiotti, 2001; Hwang and Liu,
2004). But, although the reported simulation and
experimental results are acceptable, relatively small
research effort has been focussed on the systematic
analysis of these fuzzy control systems (FCSs)
including their stability or sensitivity analysis due to
the nonlinearity of the FCs and of the CPs (Gartner
and Astolfi, 2000; Cuesta and Ollero, 2002; Precup
and Preitl, 2004).
The development of fuzzy controllers for the linear
CPs (1) is considered as a first step in the development
of complex control structures including these plants.