Optimal tuning of scaling factors and membership functions for mamdani type PID fuzzy controllers



This study addresses the problem of tuning
Mamdani-type fuzzy Proportional-Integral-Derivative
controllers by solving a constrained nonlinear optimisation
problem. Two different schemes are discussed. One considers
merely the scaling factors optimisation, while assuming the
membership functions width unchanged. In second
methodology both scaling factors and membership functions
width adjusted. The cost function under minimisation is chosen
as the closed loop performance index, with the system
dynamics described by a nonlinear model. In addition, a set of
constraints to the optimisation problem are taken into account,
namely bounds on scaling factors, control actions and also on
the system outputs. For the second approach, extra constraints
on membership functions width are also included in problem
formulation. Experimental results carried out on a Multi-Input
Multi-Output benchmark system shows the out-performance
of considering the optimising of both scaling factors and
membership function widths.


2015 International Conference on Control, Automation and Robotics, May 2015


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