Embedded Systems Design - March 2008 - (Page 22)

0308esd.p16to25 2/14/08 3:50 PM Page 22 cover feature Listing 1 Inference rules pseudo code. MinValue = MaxValue = 0 Y[0..N] = 0; For (I = 0 to N) { for (j = 0 to M) { MinValue = Min{X1[I], X2[M]}; // compare each X1 element to X2 element and store // smaller value // store max value found among X2 members If (Max{X1[I], X2[M]} > MaxValue) // { MaxValue = Max{X1[I], X2[M]}; } // add max value to output vector function deﬁned by // membership rules MaxValue += output_vector_member(x); } } Defuzzified output vector table. Array NM NS ZE PS PM Y[ ] 0x0 0x13F 0x196A 0x0 0x0 Table 3 In the earlier example, output vector Y[] is shown in Table 3. DEFUZZIFICATION Defuzziﬁcation is the process of converting fuzzy data back into crisp value data. For the purpose of this application the defuzziﬁed value determines the duty cycle of the PWM signal used to drive the motor. The duty cycle is determined by using the modiﬁed centroid calculation function. The defuzziﬁcation approach used here takes the centroid function and multiplies it by a coefﬁcient. The modiﬁed calculation is also known as the centroid point calculation function. This approach provides additional precision over the centroid calculation function. The centroid point calculation is obtained by the center point of the function that is the result of the multiplication of the output membership function by the output vector Y[]. The formula for the centroid point calculation is: Defuzziﬁed Value = Σ_Y[i] X multCoeff[I] / Σ Y[i] where Y[i] are the i-th elements of the output vector, and multCoeff[i] are the multiplying coefﬁcients of the output membership function. The index i has a range of i = 1 to i = 5. Figure 5 shows the graphical representation of the output membership function used by this application with the coefﬁcients of [-0x10, -0x8, 0x0, 0x8, 0x10]. Using the example output vector Y[] = [0x0, 0x13F, 0x196A, 0x0, 0x0], the following defuzziﬁcation output value is calculated: Defuz = 0 X (-16) + 319 X (-8) + 6506 X (0) + 0 X (8) + 0 X (16) / 0 + 319 + 6506 + 0 + 0 = -2552 / 6825 => -0.37391 FUZZY LOGIC DEFINITIONS Centroid calculation function: used for producing an exact output value by calculating the center of gravity of the union of areas bound by membership functions and the input variable axes. Defuzziﬁcation: a general method for determining the best exact or “crisp” output of a given fuzzy set, defuzziﬁcation uses the centroid calculation function or a similar function to generate a crisp output. Fuzziﬁcation: a method for converting a “crisp” input value to a fuzzy membership function. The resulting fuzzy value is a member of a multivalued set. Fuzzy control system: a control system based on fuzzy IF-THEN rules that use fuzzy sets for input and output. Fuzzy inference system: a collection of fuzzy IF-THEN rules. Fuzzy logic: logic that uses linguistic variables to describe a system. Examples include: “fast,” “slow,” and “medium.” Fuzzy set: any set that allows its members to have different “grades” of membership. Each member may be expressed by a continuous number between zero and one: [0,1]. This contrasts to Boolean logic that limits set members to a value of either zero or one. Fuzzy system: a system whose variables range over states that are fuzzy sets. Membership function: the mapping of a fuzzy set that associates each set member with its grade of membership. 22 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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