Page 192 - The Mechatronics Handbook

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The defuzzification process converts two or more fuzzy-valued outputs to one real-valued output.
There are many defuzzification methods, such as center of gravity (COG) and center of area (COA),
available for different applications (Passino and Yurkovich, 1998). By COA approach, the real-valued
control signal, u, was determined by the domain and the memberships of the selected fuzzy control
commands, µ(u i ), using the following equation:

n
()du
u = ∑ i=1 u i m u i (10.34)
----------------------------------
n
()du
∑ i=1 m u i
The COA method naturally averages the domains of selected fuzzy control commands, and thus reduces
the sensitivity of the system to noise. The use of a COA approach increased the robustness and accuracy
of the control.
The performance of the fuzzy controller depends on the appropriation of domain definition for both
input and output fuzzy variables. Properly defined fuzzy variables for a specific E/H system will improve
the stability, accuracy, and nonlinearity compensation of the fuzzy controller. Normally, a triangular
fuzzy membership function, µ FV , was defined by domain values of a i , a j , and a k , for each fuzzy value
(FV) in the fuzzy controller.

m NL a 1 a 1 a 2
m NM a 1 a 2 a 3
m NS a 2 a 3 a 4
m A = = (10.35)
m ZE a 3 a 4 a 5
m PS a 4 a 5 a 6
m PM a 5 a 6 a 7
m PL a 6 a 7 a 7

where µ A is a set of fuzzy membership functions for each fuzzy input or output variable; a t , a k are the
boundaries; and a j is the full membership point of the fuzzy value.
Equation (10.35) uses a set of seven domain values to define seven fuzzy values in the real-valued operating
range. The tuning of the fuzzy controller was to determine the domain values for each of the fuzzy values.
The following vector presents the domains of fuzzy membership functions for a particular variable:

A = { a 1 a 2 a 3 a 4 a 5 a 6 a 7 } (10.36)

10.7 Programmable Electrohydraulic Valves

Proportional directional control valves are by far the most common means for motion control of hydraulic
motors or cylinders in fluid power systems (McCloy, 1973). Normally, a proportional direction control
valve uses a sliding spool to control the direction and the amount of fluid passing through the valve. For
different applications, the spool in a proportional direction control valve is often specially designed to
provide the desired control characteristics. As a result, valves are specific and cannot be interchangeable
even if they are exactly of the same size. The multiplicity of such specific valves make them inconvenient and
costly to manufacture, distribute, and service. To provide a solution to these problems, researchers at the
University of Illinois at Urbana-Champaign (Book and Goering, 1999; Hu et al., 2001) developed a generic
programmable electrohydraulic (E/H) control valve. A generic programmable valve is a set of individually

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