Embedded Systems Design Europe - March 2008 - (Page 18)

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); } } 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 Figure 6 shows the graphical representation of the centroid point calculation for the output vector Y[]. HARDWARE DESCRIPTION The eZdsp2812 board is used in this motor control application. At the heart of the eZdsp board is the TMS320F2812 DSP. The TMS320F2812 is a 150-MHz device that uses timer T1 running at 20 kHz for generating PWM1-6 signals, and timer T2 running at 40 kHz for executing interrupt service routines (ISRs). Additionally, the input capture pins CAP1-3 are used to collect speed 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. 18 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 MARCH 2008 | embedded systems design europe | www.embedded.com/europe 014-015-016-018-020-021_EETE.ind18 18 5/03/08 12:49:43 http://www.embedded.com/europe

Table of Contents Feed for the Digital Edition of Embedded Systems Design Europe - March 2008

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

For optimal viewing of this digital publication, please enable JavaScript and then refresh the page. If you would like to try to load the digital publication without using Flash Player detection, please click here.