Embedded Systems Design - March 2008 - (Page 20)

0308esd.p16to25 2/14/08 3:50 PM Page 20 cover feature The membership function for the input variables Error, and Cerror. y 0x1AAA NM NS ZE PS PM Fuzzified data resulting from Error equal to 0x30 (x-axis) and Cerror equal to 0x10 (x-axis). Array NM NS ZE PS PM X1[ ] 0x0 0x0 0x196A 0x13F 0x0 X2[ ] 0x0 0x0 0x19D6 0x6A 0x0 Table 1 -0x5000 Figure 2 -0x3554 -0x1AAA 0 0x1AAA 0x3554 0x5000 The fuzzified membership function for the input variable Error: X1[]. y 0x1AAA NM NS ZE 0x13F -0x5000 -0x3554 -0x1AAA 0 0x1AAA 0x3554 0x5000 0x196A PS PM Figure 3 The fuzzified membership function for the input variable Cerror: X2[]. y 0x1AAA NM NS ZE 0x6A -0x5000 -0x3554 -0x1AAA 0 0x1AAA 0x3554 0x5000 0x19D6 PS PM Figure 4 membership sets are triangular-shaped and overlap to provide good response. Each set has a maximum value of 0x1AAA. This differs from typical fuzzy logic literature, which sets the maximum range equal to one. Using a maximum value of 0x1AAA for the range reduces computational complexity. Speciﬁcally, the multiplying operation is reduced to either a series of additions or subtractions rather than converting to and from a ﬂoating point number. The resulting fuzziﬁcation of the input variables produces a vector with ﬁve components that correspond to the fuzzy membership sets NM, NS, ZE, PS, PM. The value (y-axis) of each component represents the degree of membership for that crisp input value. The vectors containing the fuzziﬁed values of Error and Cerror are denoted by arrays X1[] and X2[] respectively. For example, with Error equal to 0x30 (x-axis), and Cerror equal to 0x10 (x-axis), the resulting fuzziﬁed data are shown in Table 1. Figures 3 and 4 graphically show the resulting fuzziﬁed values for Error and Cerror. FUZZY INFERENCE RULES Fuzzy inference rules operate on the fuzziﬁed data to determine the system’s behavior. Speciﬁcally, the fuzziﬁed data is applied against the rule table. Linguistically, this is where the input data Error and Cerror are compared with the rule table. The rule table contains membership set components NM, NS, ZE, PS, and PM, depending on the control surface. The output is “inferred” from the valid or “ﬁred” rules. The inference process is described by pseudo code in Listing 1. Table 2 shows the initial rule base for the motor control surface. The inference rule table. NM NM NS ZE PS PM NM NM NM NS ZE Cerror:X2[] NS ZE NM NM NS ZE PS NM NS ZE PS PM PS NS ZE PS PM PM PM ZE PS PM PM PM Error: X1[] Table 2 As mentioned during the design section, ﬁve membership sets are deﬁned for variables Error and Cerror: 1. NM: Negative Medium 2. NS: Negative Small 20 3. ZE: Zero 4. PS: Positive Small 5. PM: Positive Medium Figure 2 shows the membership sets for variables Error and Cerror. The MARCH 2008 | embedded systems design | www.embedded.com http://www.embedded.com

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Embedded Systems Design - March 2008 Contents #Include Programming Pointers Designing DSP-based Motor Control Using Fuzzy Logic Hardware/Software Verification Enters the Atomic Age Efficient CRC Calculation with Minimal Memory Footprint Programming Your Own Microcontroller Advertising Index Break Points Marketplace

Embedded Systems Design - March 2008

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