Embedded Systems Design - March 2008 - (Page 18)

0308esd.p16to25 2/14/08 3:50 PM Page 18 cover feature termine system behavior, rather than complex math equations. For example, IF the error (E) is equal to NM and + Hysteresis Ιρ ΔΙ Voltage current 3-Phase I dt change in error (CE) is equal to PS, inverter – controller Position then the change in the armature voltcy decoder age (CV) is equal to NS. The number Speed controller of rules used is based on the experience of the designer and the knowledge of Encoder cε ε the system. Thus, for our system the d/dt number of rules used is 25, which is +– ω d/dt based on our basic PID controller ωρ model using the PID’s control surface. Figure 1 In order to energize the armature, the CV fuzzy output must be converted back to a crisp output. This process is 1. Deﬁne inputs, outputs, and the natively, CE is negative iff the current called defuzziﬁcation. A popular controller’s range of operation. speed is greater than the set speed. method of defuzziﬁcation called the 2. Deﬁne fuzzy membership set func- When close to the set speed CE altercenter of gravity method is used; I’ll tions and rules. nates between positive and negative discuss it in greater detail later. 3. Tune the engine. values. CV is the energizing voltage apThe last step of design is to adjust plied to the armature. This voltage is the membership functions and rules. Figure 1 shows the block diagram of expressed in implementation as a pulse This stage is also referred to as tuning. the BLDC controller model. Tuning is used to imThe ﬁrst step is to deﬁne prove the performance Instead of math formulas, a fuzzy-logic the relevant inputs and outof the FL controller. puts of the model. The inOnce designed, the controller uses fuzzy rules to make a puts are the error (E), which controller is ready to decision and generate an output; is the current error between be implemented. how cool is that? the set speed (SS) and the The FL controller current speed (CS). The othimplementation is er input is the change in error (CE), width modulation (PWM) duty cycle. made up of three modules. They are which is the difference between the The next step is to deﬁne the fuzzy fuzziﬁcation, rule-base, and defuzziﬁcurrent error, and the previously calcu- membership set functions, variables cation. The following sections discuss lated error (PE). The output is the and rules. In order to work, non-fuzzy the modules as related to the FL-BLDC change in armature voltage (CV), (crisp) inputs and outputs must be implementation. which is the difference between the converted into fuzzy ones. Conversion current armature voltage (CAV) and is performed by using linguistic variFUZZIFICATION the stored value of the previous armaables to represent input and output Fuzzificaton is the process of convertture voltage (PAV). The resulting ranges. These are also referred to as ing crisp value data into fuzzy data. model equations are as follows: fuzzy variables. Fuzzy variables are used The resulting fuzzy data conversion is to partition a region of values for based on the degree of fuzzy set memE = SS – CS membership functions. For example, bership of input variables. For this apCE = E – PE ﬁve variables are used to map the inplication, motor control input variCV = CAV – PAV puts and output. They are negative ables are rotational error (Error) and medium (NM), negative small (NS), change in rotational error (Cerror), Motor speed units are in revoluzero (Z), positive small (PS), and posiwhich are taken from the PID contions per minute (RPM), and E detertive medium (PM). The model’s inputs troller model discussed earlier. Error is mines how close we are to the target and outputs are membership set functhe absolute error from one sample speed. So for E > 0 motor speed is betions that are described over the range time to the next. Similarly, Cerror is low set speed. Alternatively, E < 0 indiof operation by the ﬁve fuzzy variables. the change in Error from one sample cates that the motor is spinning faster Instead of math formulas, an FL time to the next. The formulas for than the set speed. CE determines concontroller uses fuzzy rules to make a each are: troller direction to adjust. CE is posidecision and generate an output; how tive if and only if (iff) the current cool is that? FL rules are in the form of Error = SetSpeed – CurrentSpeed speed is less than the set speed. AlterIF-THEN statements. Fuzzy rules deCerror = Error – PreviousError BLDC motor The BLDC controller block diagram. 18 MARCH 2008 | embedded systems design | www.embedded.com http://www.embedded.com

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

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

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.