Fuzzy Logic

Abstract The allocation of scarce business resources is becoming a major problem for management nowadays. Limited by lack of resources, management needs to make project selection decisions under the constraints of available information, and often makes decisions based on incomplete information. Traditionally, quantitative techniques dominate decision-making in selecting management information systems (MIS) projects. However, encapsulating or simply discarding the qualitative concerns makes a project economically sound but not operationally sound. This is often the reason that causes a project to fail. This paper establishes a model by incorporating fuzzy logic as a decision tool, which smoothly aids decision makers dealing with uncertain or incomplete information without losing existing quantitative information

What's so great about Fuzzy Logic?

More and more these days, we hear about fuzzy logic being used in high tech research fields and government laboratories. We see on the news or read in scientific magazines that scientists and researches from all over the world are using fuzzy logic to solve or simulate complex systems and problems which until now have proven too complex to comprehend even to the brightest minds of the day. With all this talk about fuzzy logic, one must wonder what it is, and how it could potentially apply to him. The answer to this question is much different than you would think. Fuzzy logic is actually much more simple than standard linear or mathematical logic which we have come to know. Fuzzy logic is designed to simulate human thought much more closely than the standard programming code used in most industries. For example, the PLC code for a certain holding tank might incorporate multiple IF-THEN statements to control the speed of agitation in the tank based on fill level. However, in fuzzy logic, the agitation is controlled via several statements which might read, "If the level in the tank is LOW, SLOW the agitator down." This version of code is much more similiar to the way humans would think in that it incorporates certain predefined levels of imprecession into the decision making process. The benefits of using fuzzy logic are vast and include: 1) Reduced development time/cycle 2) Simplifies design complexity 3) Reduces time to market 4) Improves control performance 5) Simplifies implementation 6) Reduces hardware costs A reduction in development time can be realized by eliminating unecessary steps previously incorporated in the development of standard PID controllers such as developing linear models of sensors, actuators, and drives. It can also eliminate the need to generate a simplified control loop using standard control theory. In essence, you move straight from identifying the problem to generating the fuzzy logic control to implementing. Once implemented, changes can easily be made by modifying the fuzzy logic statements or parameters rather than developing an entirely new PID controller. A simplification in the design complexity can be realized by utilizing only a few rules which are in plain english that can control an entire system. This system may have required multiple lines of code using standard practice. This reduction in programming time and the fact that most people are able to learn this method, given that it utilizes few rules all in english language format, rather quickly greatly reduces the complexity of the design. Fuzzy logic can reduce the time to market by greatly reducing the development time spent on software generation. Since the system is much less complex than traditional controllers,

and since it can be shared and understood more readily by separate groups or teams, it can greatly reduce the troubleshooting and commissioning times necessary for most control systems thus reducing the time to market of the package. By using fuzzy logic, control performance and response time can be greatly improved much easier than with standard systems of linear equations. Take for example the problem of heating up a room to a desired temperature. The time it takes to heat the room is critical as is the exact temperature of the room at any given time. As time progresses, the goal would be to heat the room to the exact desired temperature as fast as possible without overshooting or undershooting, and to maintain the temperature. Under normal conditions, this would require combining a system of linear and non-linear equations in order to achieve the correct amount of response time and damping. However, with fuzzy logic, only a few statements must be made to properly heat the room at very fast response times. Fuzzly logic can simplify implementation by controlling multiple inputs and outputs with one IF-THEN statement as opposed to traditional code which may require multiple lines to adress each variable. For instance, if an output is driven by a combination of inputs, and IF-THEN statement combined with an AND or OR statement can be used to control the entire system very effectively. Fuzzy logic requires much less memory space and processing power/time to operate than standard code which uses look-up tables etc. Look up tables, for instance, on standard code may take up 64Kb of memory where as Fuzzy logic requires less than 0.5Kb for labels and object code. In summary, fuzzy logic is definitely not just designed to aid high tech research or problems. It appears that it has very real applications in today's society and industry. Does anyone have any experience either using or dealing with examples of fuzzy logic in your day to day lives?

Why Use Fuzzy Logic? •

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An Alternative Design Methodology Which Is Simpler, And Faster ○

Fuzzy Logic reduces the design development cycle

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Fuzzy Logic simplifies design complexity

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Fuzzy Logic improves time to market

A Better Alternative Solution To Non-Linear Control ○

Fuzzy Logic improves control performance

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Fuzzy Logic simplifies implementation

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Fuzzy Logic reduces hardware costs

Fuzzy Logic is a paradigm for an alternative design methodology which can be applied in developing both linear and non-linear systems for embedded control. By using fuzzy logic, designers can realize lower development costs, superior features, and better end product performance. Furthermore, products can be brought to market faster and more cost-effectively.

An Alternative Design Methodology Which Is Simpler, And Faster In order to appreciate why a fuzzy based design methodology is very attractive in embedded control applications let us examine a typical design flow. Figure 4 illustrates a sequence of design steps required to develop a controller using a conventional and a Fuzzy approach. Using the conventional approach our first step is to understand the physical system and its control requirements. Based on this understanding, our second step is to develop a model which includes the plant, sensors and actuators. The third step is to use linear control theory in order to determine a simplified version of the controller, such as the parameters of a PID controller. The fourth step is to develop an algorithm for the simplified controller. The last step is to simulate the design including the effects of nonlinearity, noise, and parameter variations. If the performance is not satisfactory we need to modify our system modeling, re-design the controller, re-write the algorithm and retry. With Fuzzy Logic the first step is to understand and characterize the system behavior by using our knowledge and experience. The second step is to directly design the control algorithm using fuzzy rules, which describe the principles of the controller's regulation in terms of the relationship between its inputs and outputs. The last step is to simulate and debug the design. If the performance is not satisfactory we only need to modify some fuzzy rules and re-try. Although the two design methodologies are similar, the fuzzy-based methodology substantially simplifies the design loop. This results in some significant benefits, such as reduced development time, simpler design and faster time to market: Fuzzy Logic reduces the design development cycle With a fuzzy logic design methodology some time consuming steps are eliminated. Moreover, during the debugging and tuning cycle you can change your system by simply modifying rules, instead of redesigning the controller. In addition, since fuzzy is rule based, you do not need to be an expert in a high or low level language which helps

you focus more on your application instead of programming. As a result, Fuzzy Logic substantially reduces the overall development cycle. Fuzzy Logic simplifies design complexity Fuzzy logic lets you describe complex systems using your knowledge and experience in simple English-like rules. It does not require any system modeling or complex math equations governing the relationship between inputs and outputs. Fuzzy rules are very easy to learn and use, even by non-experts. It typically takes only a few rules to describe systems that may require several of lines of conventional software. As a result, Fuzzy Logic significantly simplifies design complexity. Fuzzy Logic improves time to market Commercial applications in embedded control require a significant development effort a majority of which is spent on the software portion of the project. Development time is a function of design complexity, and the number of iterations required in a debugging and tuning cycle. As we explained above, a fuzzy based design methodology addresses both issues very effectively. Moreover, due to its simplicity the description of a fuzzy controller not only is transportable across design teams, but also provides a superior media to preserve, maintain, and upgrade intellectual property. As a result, Fuzzy Logic can dramatically improve time to market.

A Better Alternative Solution To Non-Linear Control Most real life physical systems are actually non-linear systems. Conventional design approaches use different approximation methods to handle non-linearity. Some typical choices are, linear, piecewise linear, and lookup table approximations to trade off factors of complexity, cost, and system performance. A linear approximation technique is relatively simple, however it tends to limit control performance and may be costly to implement in certain applications. A piecewise linear technique works better, although it is tedious to implement because it often requires the design of several linear controllers. A lookup table technique may help improve control performance, but it is difficult to debug and tune. Furthermore in complex systems where multiple inputs exist, a lookup table may be impractical or very costly to implement due to its large memory requirements. Fuzzy logic provides an alternative solution to non-linear control because it is closer to the real world. Non-linearity is handled by rules, membership functions, and the inference process which results in improved performance, simpler implementation, and reduced design costs: Fuzzy Logic improves control performance In many applications Fuzzy Logic can result in better control performance than linear, piecewise linear, or lookup table techniques. For instance, a typical problem associated with traditional techniques is trading-off the controller's response time versus overshoot. For the simple one-input temperature controller example this is illustrated in Figure 5:

The first linear approximation for the desired curve generates a slow output response with no overshoot, which implies that the room would be too cold for a while. The second linear approximation results in faster response with an overshoot and subsequent fluctuations, which implies that the temperature will be uncomfortable for a period of time. With fuzzy logic we can use rules and membership functions to approximate any continuous function to any degree of precision. Figure 6 illustrates how we can approximate the desired control curve for our temperature controller using four points (or four rules). We can also add more rules to increase the accuracy of the approximation (similar to a Fourier transform), which yields an improved control performance. Rules are much simpler to implement and much easier to debug and tune than piecewise linear or lookup table techniques. IF temperature IS cold THEN force IS high IF temperature IS cool THEN force IS medium IF temperayure IS warm THEN force IS low IF temperature IS hot THEN force IS zero Rules are not like a lookup table because the fuzzy arithmetic interpolates the shape of the non-linear function. The combined memory required for the labels and fuzzy inference is substantially less than a lookup table, especially for multiple input systems. As a result, processing speed can be improved as well. Another example of robust control that can be achieved with Fuzzy Logic is the classical problem of the inverted pendulum. A conventional controller for the pendulum depends on system parameters such as length, weight, and mass. If the parameters change, then we need to re-design our controller. With fuzzy control this is not necessary because a fuzzy system is robust. Aptronix has demonstrated an actual device where we can vary the weight or length of the pendulum and the system is still stable using the original set of rules.

By using a more natural rule-based approach which is closer to the real world, Fuzzy control can offer a superior performance and a better trade-off between system robustness and sensitivity, which results into handling non-linear control better than traditional methods. Fuzzy Logic simplifies implementation The one input temperature controller presented so far has helped us illustrate some fundamental concepts, however real life control is much more complex in nature. Most control applications have multiple inputs and require modeling and tuning of a large number of parameters which makes implementation very tedious and time consuming. Fuzzy rules can help you simplify implementation by combining multiple inputs into single if-then statements while still handling non-linearity. Consider a modified version of the temperature controller example, with two inputs, temperature and humidity and the same output, fan_speed (Figure 7). This example can be described with a small set of rules as follows: IF temperature IS cold AND humidity IS high THEN fan_spd IS high IF temperature IS cool AND humidity IS high THEN fan_spd IS medium IF temperature IS warm AND humidity IS high THEN fan_spd IS low IF temperature IS hot AND humidity IS high THEN fan_spd IS zero IF temperature IS cold AND humidity IS med THEN fan_spd IS medium IF temperature IS cool AND humidity IS med THEN fan_spd IS low IF temperature IS war m AND humidity IS med THEN fan_spd IS zero IF temperature IS hot AND humidity IS med THEN fan_spd IS zero IF temperature IS cold AND humidity IS low THEN fan_spd IS medium IF temperature IS cool AND humidity IS low THEN fan_spd IS low IF temperature IS warm AND humidity IS low THEN fan_spd IS zero IF temperature IS hot AND humidity IS low THEN fan_spd IS zero A linear approximation requires handling each input separately which multiplies design effort. Similarly, a piecewise linear approach requires the design of several controllers and is costly to implement. A lookup table seems more appropriate for this problem but it takes time to develop, debug and tune. For example, if we assume that each input requires eight bits, a lookup table would require 64K entries which makes it very time consuming to implement (Figure 8). Using Fuzzy Logic we can describe the output as a function of two or more inputs linked with operators such as AND. This relationship can also be represented in a table form illustrated in Figure 8. The fuzzy approach requires significantly less entries than a lookup table depending upon the number of labels for each input variable. Rules are much easier to develop, and simpler to debug and tune compared to a lookup table.

Another example of simplicity is the classical control problem of the double stage inverted pendulum. Using conventional programming, this problem is extremely difficult, or impossible to implement. Aptronix has demonstrated a physical model of the 2stage inverted pendulum which was accomplished using only 30 rules. The software portion of the project took only two days to develop. Fuzzy Logic reduces hardware costs Using a lookup table the two-input temperature controller requires 64Kb of memory, while the fuzzy approach is accomplished with less than 0.5Kb of memory for labels and object code combined. This difference in memory savings implies a cheaper hardware implementation. In addition, conventional techniques in most real life applications require complex mathematical analysis and modeling, floating point algorithms, and complex branching. This typically yields a substantial size of object code which requires a high end DSP chip to run. Fuzzy Logic enables you to use a simple rule based approach which offers significant cost savings, both in memory and processor class. As an example, consider again the 2-stage inverted pendulum, whose model is equivalent to a second order differential equation. With a traditional approach, the model requires a high end workstation to develop, and the controller is extremely difficult or very costly to implement. For example, a non-linear equation would require a costly high end processor to cope with calculation intensity, while a lookup table would require a huge amount of memory. Aptronix's 2-stage pendulum was developed on a PC, runs on a low cost 8-bit microcontroller and requires under 1Kb of memory. This achievement demonstrates that we can use existing low end hardware to tackle an order of magnitude more complex applications. Back to FIDE © 1996-2000, Aptronix Inc.