Embedded Systems Design Europe - March 2008 - (Page 16)

cover feature 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 ﬁned for variables Error and Cerror: 1. 2. 3. 4. 5. NM: Negative Medium NS: Negative Small ZE: Zero PS: Positive Small PM: Positive Medium The inference rule table. NM NM NS ZE PS PM NM NM NM NS ZE NS Cerror:X2[] ZE NM NS ZE PS PM PS NS ZE PS PM PM PM ZE PS PM PM PM Error: X1[ ] NM NM NS ZE PS Table 2 of input variables. For this application, motor control input variables are rotational error (Error) and change in rotational error (Cerror), which are taken from the PID controller model discussed earlier. Error is the absolute error from one sample time to the next. Similarly, Cerror is the change in Error 16 from one sample time to the next. The formulas for each are: Error = SetSpeed – CurrentSpeed Cerror = Error – PreviousError As mentioned during the design section, ﬁve membership sets are de- Figure 2 shows the membership sets for variables Error and Cerror. The 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 (xaxis), 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 MARCH 2008 | embedded systems design europe | www.embedded.com/europe 014-015-016-018-020-021_EETE.ind16 16 5/03/08 12:49:29 http://www.embedded.com/europe

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Embedded Systems Design Europe - March 2008 Distributors to Increase Embedded Focus Kontron and Quanta to Join Forces Coverity Raises $22m as European Business Booms Help is at Hand for Europe's Industrial Control Developers Milestones in Embedded Systems Microsoft is Recruiting for Embedded Center in Aachen European Designers to Win Cash for Green Designs Duo Work on Smaller Form Factor Europe Invests in Real-Time Java for Multicore Systems Curtiss-Wright Buys Pentland Systems Designing DSP-Based Motor Control Using Fuzzy Logic Lower the Cost of Intelligent Power Control with FPGAs Virtualizing Embedded Linux Back to the Future: Manchester Encoding Is Multicore Hype or Reality New Products Advertising Contacts

Embedded Systems Design Europe - March 2008

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