Embedded Systems Design Europe - March 2008 - (Page 15)

cover feature to partition a region of values for membership functions. For example, ﬁve variables are used to map the inputs and output. They are negative medium (NM), negative small (NS), zero (Z), positive small (PS), and positive medium (PM). The model’s inputs and outputs are membership set functions that are described over the range of operation by the ﬁve fuzzy variables. Instead of math formulas, an FL controller uses fuzzy rules to make a decision and generate an output; how cool is that? FL rules are in the form of IF-THEN statements. Fuzzy rules determine system behavior, rather than complex math equations. For example, IF the error (E) is equal to NM and change in error (CE) is equal to PS, then the change in the armature voltage (CV) is equal to NS. The number of rules used is based on the experience of the designer and the knowledge of the system. Thus, for our system the number of rules used is 25, which is based on our basic PID controller model using the PID’s control surface. In order to energize the armature, the CV fuzzy output must be converted back to a crisp output. This process is called defuzziﬁcation. A popular method of defuzziﬁcation called the center of gravity method is used; I’ll discuss it in greater detail later. The last step of design is to adjust the membership functions and rules. This stage is also referred to as tuning. Tuning is used to improve the performance of the FL controller. Once designed, the controller is ready to be implemented. The FL controller implementation is made up of three modules. They are fuzziﬁcation, rule-base, and defuzziﬁcation. The following sections discuss the modules as related to the FL-BLDC implementation. FUZZIFICATION Fuzziﬁcaton is the process of converting crisp value data into fuzzy data. The resulting fuzzy data conversion is based on the degree of fuzzy set membership 15 trol also has a shorter development cycle compared to PID controllers, and thus a faster time-to-market. This article discusses the process of using FL algorithms to control BLDC motors using a Texas Instruments c28xx ﬁxedpoint family of DSPs. BLDC CONTROL MODEL DEVELOPMENT Before constructing the FL engine, we must ﬁrst develop a model to base the design on. FL controllers use heuristic knowledge and express the design using a linguistic description of the model. Rather than develop a model from scratch, we’ll use the PID controller model as a starting point. Once developed and implemented, the FL controller is improved by adjusting its parameters. In general, there are three design steps for developing a FL BLDC controller: 1. Define inputs, outputs, and the controller’s range of operation. 2. Define fuzzy membership set functions and rules. 3. Tune the engine. Figure 1 shows the block diagram of the BLDC controller model. The ﬁrst step is to deﬁne the relevant inputs and outputs of the model. The inputs are the error (E), which is the current error between the set speed (SS) and the current speed (CS). The other input is the change in error (CE), which is the difference between the cur- rent error, and the previously calculated error (PE). The output is the change in armature voltage (CV), which is the difference between the current armature voltage (CAV) and the stored value of the previous armature voltage (PAV). The resulting model equations are as follows: E = SS – CS CE = E – PE CV = CAV – PAV Motor speed units are in revolutions per minute (RPM), and E determines how close we are to the target speed. So for E > 0 motor speed is below set speed. Alternatively, E < 0 indicates that the motor is spinning faster than the set speed. CE determines controller direction to adjust. CE is positive if and only if (iff) the current speed is less than the set speed. Alternatively, CE is negative iff the current speed is greater than the set speed. When close to the set speed CE alternates between positive and negative values. CV is the energizing voltage applied to the armature. This voltage is expressed in implementation as a pulse width modulation (PWM) duty cycle. The next step is to deﬁne the fuzzy membership set functions, variables and rules. In order to work, non-fuzzy (crisp) inputs and outputs must be converted into fuzzy ones. Conversion is performed by using linguistic variables to represent input and output ranges. These are also referred to as fuzzy variables. Fuzzy variables are used www.embedded.com/europe | embedded systems design europe | MARCH 2008 014-015-016-018-020-021_EETE.ind15 15 5/03/08 12:49:13 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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