Intelligent Tuning of Fuzzy Controllers by Learning and Optimization - Fuzzy Modeling and Control: Theory and Applications - page 144

Table 7.1 Neuro-fuzzy algorithms. Relevant characteristics and parameters
Characteristics

ANFIS TNFIS

and parameters (Martin and Guerra 2009 ) (Gajate et al. 2010 )

(Gajate et al. 2012 )

Structure Single-input/single-output Single-input/single-output

Type of membership functions Gaussian Gaussian

Membership functions 2 Variable each run (maximum 5)

Fuzzy inference system Takagi-Sugeno Mamdani

Number of rules 2 Variable each run (maximum 5)

Iterations 5 20

Learning rate 0.0001 0.0001

Training algorithms Back propagation Back propagation

Training data set 139 samples 139 samples

choosing these parameters, the goal is to find a tradeoff between the accuracy and
the quality of the dynamic response.
ANFIS uses a training set of 139 data to create an initial neuro-fuzzy system. Then
it uses a set of 134 validation data to adjust the membership functions and rules of
the initial neuro-fuzzy system. However, in TNFIS the model is created and adjusted
based on only the neighbors closest to the input (up to 5 neighbor samples) of the
entire training set (139 data). The summary of the parameters andmain characteristics
of both neurofuzzy systems are summarized in Table 7.1 .
In order to compare the two systems, the integral of time-weighted absolute error
( ITAE )( 7.13 ), the integral of the time-weighted squared error ( ITSE )( 7.16 ), and
the integral of the squared time-weighted squared error ( IT 2 SE )( 7.14 ) are used as
performance indices. The overshoot ( Ovt ) was also included in the comparative study
due to the influence of transient dynamics on useful tool life.

T

te 2 ITSE = ( t ) dt (7.16)

0

The results of the experimental tests using 17-4PH are shown in Figure 7.8 .
Drilling-force behaviour is depicted as a solid line for ANFIS and as a dashed-
dotted line for TNFIS. The TNFIS-IMC system fulfills the design requirements with
a fast closed-loop response and small overshoot. Table 7.2 lists the corresponding
performance indices calculated using actual data (e.g., drilling force, time) recorded
in real-time from an actual experimental test in an industrial environment. While at
first glance the behaviour of the ANFIS and the TNFIS seems to be very similar,
the TNFIS performs better on the IT 2 SE and ITAE criteria, and worse on overshoot
than the ANFIS. In sum, the TNFIS presented better performance indices while
maintaining a good dynamic response.