“Gains Tuning of Fuzzy PID Controllers for MIMO Systems: A Performance-Driven Approach

Authors

Abstract

A new methodology for tuning the scaling factors, or
gains, of fuzzy proportional-integral-derivative controllers, by taking
explicitly into account the closed-loop system performance is
proposed in this study. The solution is obtained by solving a nonlinear
constrained optimization problem, considering a set of constraints
on the scaling factors of the Mamdani-type fuzzy system,
and on the plant’s inputs and outputs. Two distinct approaches are
presented, which are associated with the optimization being carried
out offline or in real time. The offline tuning scheme assumes
the system dynamics described by a nonlinear model, while for the
real-time implementation, the plant’s dynamics is locally approximated
by a linear model, with the underlying parameters recursively
updated. In order to cope with rather stringent sampling
time requirements, the constrained online optimization problem is
implemented based on the grid computing paradigm. Given the
adaptive nature of the real-time scheme, time-varying dynamics
and unknown disturbances can be accommodated in such a way
that the closed-loop performance is effectively maximized, while
avoiding wind-up phenomena induced by the integrator term. The
proposed tuning methodologies are assessed on a benchmark threetank
system and compared against a conventional-based tuning
approach. Results from experiments illustrate the feasibility of the
proposed approaches and also all the relevance in optimal control
systems based on Mamdani-type fuzzy controllers.

Journal

IEEE Transactions on Fuzzy Systems, Vol. 23, #4, pp. 757-768 2015

DOI