Architecture Diagram Of Mamdani Type Of Flc Computer Science Essay

Published:

Over the past few decades, lots of researches had been accomplished on different methods and principles in order to expand and enhance the control filed. Many methods and patterns were developed and the knowledge is still increasing. People are trying to emulate the human intelligence and reflect that on new types of systems and machines. The conventional knowledge and methods that were developed in the past are considered the key element in the modern control systems or what is called nowadays "Intelligent Control System". Obviously, the boundaries will be shifted tomorrow and this "intelligent control" today will become just a "control".

Many of the recent control problems cannot be studied and solved by the conventional difference and deferential mathematical equations. Instead, modern methodologies have been developed in recent days which are part of the "intelligent control" [1].

However, intelligent control is considered as interdisciplinary because it depends on theories and principles from different fields like control, computer science and operations research [1]. However, these theories cannot be applied straightforwardly in the control field; they should be combined with the conventional control principles in order to design a developed control system [2]. Areas relevant to intelligent control, in addition to conventional control include hybrid systems, planning and knowledge based systems, machine learning, search algorithms, fault diagnosis and control reconfiguration, predicate logic, automata, Petri nets, neural nets and fuzzy logic [1].

Lady using a tablet
Lady using a tablet

Professional

Essay Writers

Lady Using Tablet

Get your grade
or your money back

using our Essay Writing Service!

Essay Writing Service

The influence of intelligent control could be noticed in many applications involving different areas such as robotics, automation, communications, manufacturing and traffic control [1]. Moreover, its hardware implantation requires an advance sensors, actuators, computation technology and communication networks [1].

In order to understand what is meant by intelligent control and how was it developed, it is very important to recognize the difference between conventional and intelligent control.

1.1 Conventional and Intelligent Control

Conventional control methods are part of the intelligent control and there are applied to solve low level control problems. Moreover, intelligent control is involved in more general progressions and control objectives. Therefore, the intelligent control aims to get the advantage of conventional control to solve more complex problems [2].

Intelligent Control depends entirely on the computational capabilities, while it is not involved in all conventional control studies. Moreover, intelligent control requires a data memory in order to save certain parameters that are measured previously and take immediate actions without the need to readapt with the new conditions [1].

Furthermore, intelligent control have many characteristics which helps to control complex systems and make it different such as adaptation, learning, planning, fault diagnosis, control reconfiguration, coping with large amounts of data, accomplishing and setting control goals, etc [1,2].

Another difference is in the structure of the controlled system. In conventional control, the system or plant is separate from the controller and each one has its own design. The controller can be designed or redesigned as required, while the plant is fixed. On contrary, in intelligent control there is no separation between the plant and the controller and they should be designed together. This makes the design of the intelligent control more challenging and complex [1].

2.0 Definition of Intelligent Control Systems

Intelligent control system could be defined through a number of characteristics that determine its intelligent level and how far it could be reliable.

One of the important dimensions on the intelligent systems is the adaption, where the system should has the ability to take proper actions whenever unusual conditions occur. Moreover, the system should be able to learn from previous conditions in order to take quick response and ensure low uncertainty on the specified task [1, 2].

The adaption and learning involve the ability to analyze, organize and convert data into ordered information which could be applied to eliminate ignorance and uncertainty.

Another characteristic is to plan for future and the capability to distinguish unexpected events and objects. This allows the system to reassign its subgoals that will lead to the success of the main goal [1].

In summary, intelligent systems have some fundamental dimensions such as adaption, learning and high level of autonomy whenever it is required to deal with any changes or complexity.

3.0 History and Major Contributors

3.1 History

Lady using a tablet
Lady using a tablet

Comprehensive

Writing Services

Lady Using Tablet

Plagiarism-free
Always on Time

Marked to Standard

Order Now

In the third century B.C. the Greek Ktesibios in Egypt invented the water clock which considered at that time as the first feedback device. This useful device was also shown in Baghdad in 1258 A.D.

First control inventions depended entirely on the human intuitive. There were no methods that could be used to develop that. In 1769, James Watt's flyball governor decided to allow the steam engine vehicles work with regulated speed. In 1868, J.C. Maxwell was the first who convert the plant behavior into a mathematical model which was an extremely important step in the control field. He succeeds to describe the instability problems, which faced flyball governor, using differential equations methods [2].

During the past 120 years, control field developed dramatically and by many noticeable progressions. As in 1930s and 1940s most of the control problems were studied using frequency domain and Laplace transforms methods. However, the state space and optimal methods were on the spot line in the 1950s and 1960s. Later on, robust, adaptive and stochastic methods were introduced as well as computation technology which considered the beginning of new era of the "Intelligent Control" [2].

This term was created in the 1970s though several earlier terms were used such as Learning Control and Self-organizing Control [1]. The development on the control methods during the past few decades allowed to deal and control more complex systems.

Looking for the history of the intelligent control in particular, it is noticed that in 1950s there was an increasing attention on the certainty equivalence principle which focus mainly on ignoring uncertainty and consider the estimates value as true one. In 1951, scientists were able to design and test a self-organizing controller which was used to control a combustion engine and operate it under optimal conditions. In the period of 1957-1961, dynamic programming techniques were developed which considered a major step in the optimization methods. Moreover, in 1970s-1980s, more studies were done on the area of self-tuning methods and the usage of computation abilities in order to maintain stability. In addition, in 1980s, process control was introduced to develop the self-tuning methods [3].

3.2 Major Contribution

The attention on using intelligent control is increasing nowadays. Many organizations and educational institutes tend to implement and involve intelligent control concepts such as fuzzy and neural controls in their projects.

One example is intelligent control system designed by Hitachi to control the subway train of the city of Sendai in Japan. This system is considered as one of the earlier systems that used fuzzy control. In this system the power and brake levers are determined by notch position which changes according to the train's acceleration and deceleration. Changing the notch position frequently or in great increments may affect the objectives of the train's trip such as passengers' comfort, safety, on time arrival, energy consumption, and accurate stoppage in the specified stop.

A simulation program attached to the train predicts the speed, stopping position and the arrival time for each notch position. Next is the rule of the fuzzy controller which studies these variables and determines which are most suitable for the mentioned objectives. Then the notch position will be changed accordingly [4].

Another example is on the heating and cooling systems. In Japan, individual rooms in the household are heated separately using "Kerosene Fan Heater". These heaters used vaporized oil to produce heat. The main constrain of this heater is the long time needed to vaporize the oil and start producing the required heat.

Many companies such as Matsushita, Sanyo, Hitachi, and Sharp succeed to apply neural network techniques to develop different approaches in controlling these heaters. For example, the heaters of Sanyo have the ability to learn the users' pattern in using the heater. Therefore, the heater will start heating in advance. On the other hand, Sharp's heaters provide the user with the ability to determine the desired temperature of a room in a specific desired time. The neural control role is to learn the required heating time and switch on the heater accordingly [4].

According to references 1 and 2, some of the advanced intelligent systems that were designed in NIST's (National Institute for Standards and Technology) RCS (Real-time Control System) are "Robot vision-based object pursuit; robot deburring; composites fabrication; automated manufacturing research facility; robot machine loading/unloading for a milling workstation; multiple autonomous undersea vehicles; NASA space station telerobotics; army field material handling robot; DARPA submarine automation; coal mine automation; and army unmanned land vehicles".

4.0 Principles

Lady using a tablet
Lady using a tablet

This Essay is

a Student's Work

Lady Using Tablet

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

Examples of our work

Intelligent control system is designed in such a way that it can autonomously achieve a high level goal, while its components, plant models and control laws are not completely defined, it is either because they were not known at the design time or because they changed unpredictably. Moreover, an intelligent system must be highly adaptable to significant unexpected changes, and so learning is also essential. It must be able to deal with significant complexity, and this leads to certain types of functional architectures such as hierarchies [1,2].

Fuzzy control, Neural networks, genetic algorithms, planning systems, expert systems, and hybrid systems are all areas and principles behind designing an intelligent control system [5]. This paper will discuss the first three principles that are used to design intelligent control system.

4.1 Fuzzy Logic Control (FLC)

Fuzzy logic controllers are being used successfully in an increasing the number of applications to both consumer electronics and automobile industry. The usual decision making process to control a dynamical system in a fuzzy logic control framework is structured as a set of if < situation > then < action > rules where both situation and action have suitable fuzzy representations. Generally, FLCs are mostly used for complex systems and mathematically fuzzy systems. Thus the performance of an FLC depends on human knowledge about the system and the knowledge accomplishment techniques to convert human knowledge to appropriate fuzzy if-then rules [5].

One of the most popular fuzzy control systems is the Mamdani type fuzzy logic control where the controller is designed directly based on the consequences on error variables. Any control problem in FLC model is broken down into IF-Then rules that define the desired controller output response for a given system input conditions [5]. The rules can be generated from an expert or it can be obtained from various observations. For a small region of an input space, the rules should tell as how we control the system. Usually error and change in an error are input variables, and the control action is the output variable for an FLC. Imprecise

The complete architecture of a Mamdani type of FLC is illustrated below in figure 1.

Plant

Crisp to Fuzzy interface fuzzification

Actuators

Sensors

Fuzzy to crisp interface defuzzification

Interface mechanism

(Rule evaluation)

Fuzzy Rule Base

Figure 1. Architecture Diagram of a Mamdani type of FLC

The figure above illustrates how the fuzzy control operates. Before connecting the controller to the system, the IF-THEN rules should be defined to the controller. At normal condition the system will operate normally until the sensors of the system detect an error. After that the error will go to the fuzzy controller to check what situation this error gives (fuzzification). Then the situation will be evaluated through the interface mechanism. After the evaluation, the controller will take an action to control the situation happened (defuzzification). This action then will be sent to the actuators to move the plant to the satisfactory condition [6].

Each situation [input] should be tested individually so that the controller should recognize the action that should be taken accordingly. After that all the situations and actions should be saved in the intelligent control [5,6].

4.2 Genetic Algorithms

Genetic Algorithms (GA) is a technique where a population of strings (chromosomes), which encode candidate solutions (individuals) to an optimization problem, evolves toward better solutions. The advantage of the GA techniques is that it is independent of the complexity of the performance index considered [7].

In GA, the current approximations of the parameters form what are called "individuals". These individuals are grouped together and encoded as strings (chromosomes) [7]. The initial population is randomly generated. Then the performance of these individuals will be evaluated using fitness function which is a measure of how good the chromosomes under evaluation are according to the optimum solution [7]. After that several genetic operators are done accordingly. The fittest individuals that have the best performance in the current population will be used to generate the new population; this is called "selection". Then the cross-over procedure comes where large groups of individuals exchange genetic information with one another [7].

If the optimum solution was not achieved, the genetic operators should be done again till obtaining the optimum solution or reaching a lack of improvement and a certain fitness [7].

Figure 2. Genetic Algorithm

4.3 Neural Networks:

Neural networks work just like the human brain. The network is composed of a large number of interconnected elements (neurons) that are working in parallel to solve a certain problem.

A simple neuron

Neural Networks is a device that has many inputs and one output. Two modes of operation are there for neural networks; the training mode and the using mode. In the training mode, the neuron is trained to fire [or not] when specific input is detected. In the using mode, if the input does not belong to the list of input patterns that are previously specified, the firing rule is used to determine whether to fire or not depending on the other inputs [8].

The firing rule is simply decides whether to fire of not depending and relating all the inputs together in certain input is not defined. A simple firing rule can be illustrated by using Hamming distance technique. The rule is as discussed below:

Some of the training patterns cause a node to fire (give it a value of 1). Where other patterns cause the node not to fire (give it a value of 0). If the pattern is not defined, it compares its inputs with the nearest pattern to it. If the nearest pattern causes the node to fire, it will fire. If the nearest pattern causes the node not to fire, it will not fire. Sometimes, there will be a tie between the two actions (same distance), in this case the state remains as undefined [8].

For example, a 3-input neuron is set to output 1 (Fire) when the inputs (X1,X2 and X3) is 111 or 101 and is set to output 0 (not to fire) when the inputs is 000 or 001. Then, the truth table before applying the firing rule is as follows;

Table 1: truth table before firing rule

X1

0

0

0

0

1

1

1

1

X2

0

0

1

1

0

0

1

1

X3

0

1

0

1

0

1

0

1

Output

0

0

0/1

0/1

0/1

1

0/1

1

As an example of how the firing rule works, take the pattern 010. It differs from 000 in 1 element, from 001 in 2 elements, from 101 in 3 elements, and from 111 in 2 elements. As a result, the nearest pattern to 010 is 000 which belongs has an output of 0 (not to fire) [8]. Therefore the firing rule requires that the neuron should not fire when the input is 010. But in the case of 011, it differs from 000 in 2 elements, from 001 in 1 element, from 101 in 2 elements, and from 111 in 1 element. As noticed that its nearest pattern is both 001 and 111, which represents two different actions. In this case the state of this pattern will stay undefined (0/1).

By applying the firing in every column for the previous truth table;

Table 2: truth table after firing rule

X1

0

0

0

0

1

1

1

1

X2

0

0

1

1

0

0

1

1

X3

0

1

0

1

0

1

0

1

Output

0

0

0

0/1

0/1

1

1

1

5.0 Examples on Intelligent Control Techniques and MATLAB simulation

5.1 Fuzzy Control

To make the idea of the fuzzy logic control more understandable, let's illustrate the rule base by an example of a single link manipulator.

You may like to fuzzify input and output variables of the controller e, é, and u in such a way that if e is negative and é is positive the output u is zero and so on. See table 3:

Table 3: rules of fuzzy control

Rule

e

é

u

1

Negative

Positive

Zero

2

Zero

Positive

Negative

3

Positive

Positive

Negative

What if we want to use the fuzzy logic control in PD controllers? This example will use a single link manipulator to design a fuzzy PD controller. The dynamics is expressed as:

Óª+10 sin(Ó¨)= Ï„

Where Óª is the link position from the vertical, Ó¨' is the link acceleration, and Ï„ is the applied torque.

Taking x1= Ó¨, x2=Ó¨', as the state variables of system. And u= Ï„ as the output of the controller and the input to the system. The state equations are written as:

X1 = X2

X2 = -10 sin X1 + u

By setting the PD gains as KP = 50, and KD = 5. The output of the PD controller can be expressed as follows:

u= 50e + 5é

Where e = X1 - Xd1 and Xd1 is the desired state for X1. Setting Xd1=1, the system is simulated (see figure 3)

Figure 3: Simulation results for fuzzy controller

It can be noticed from figure 3 that the range of the input é is from (-4,4) in rad/s, if the range of the other input which is e is from (-1,1). The corresponding range for the control action (tourqe) is found to be (-20,20) Nm. If we want to limit the maximum torque to 20 Nm so we need to make a fuzzy rule that whenever the torque goes above 20 or lower than -20, the output of the controller should always gives steady state error which is 20. A Matlab program is written for the above example and including the fuzzy rule.

clear all;

x1(1,1)=0;

x2(1,1)=0;

x1d=1;

x2d=0;

dt=0.01;

for i=1:500

e(i,1)=(x1d-x1(i,1));

edot(i,1)=(x2d-x2(i,1));

u(i,1)=50*e(i,1)+5*edot(i,1);

if(u(i,1)>20)

u(i,1)=20;

elseif(u(i,1)<-20)

u(i,1)=-20;

end

x1(i+1,1)=x1(i,1)+dt*(x2(i,1));

x2(i+1,1)=x2(i,1)+dt*(-10*sin(x1(i,1))+u(i,1));

end

plot(e)

grid on

figure

plot(edot)

grid on

figure

plot(u)

grid on

5.2 Genetic Algorithm

Another simple example is on the GA technique. Suppose the fitness function is set to be f(x) = x2, with x is integer in the interval of [0, 31]. According to reference 9, the following steps illustrate the basic rules and methods used in GA techniques in solving optimization problems.

Determine the number of bits required and the binary representation for integers. In this example, 5 bits are needed to represent integers up to 31.

Determine the population size (n). This step done by either random assumption or due to certain limitations. The population in this exampled is assumed to be n = 4.

Random generation of the initial population. As the population in this example is 4, there must be 4 chromosomes with 5 bits each; e.g., 01001 10110 10001 01101.

Next step is to convert the binary representation of each chromosome to its integer value.

01001 = 9 10110 = 22 10001= 17 01101= 13

Use the fitness function f(x) = x2 to calculate the fitness value

9  81 22  484 17  289 13  169

Select two chromosomes as "parents" for crossover. This selection based on the fitness value and Pi (the probability of i th chromosome or string). One law of calculating Pi is:

Table 4 summarized the entire calculation procedures. The summation of the fitness values for all strings is 1023. Moreover, the sum of the four probabilities is equal to 1 as expected. Most importantly, string number 2 has the highest fitness value and probability to be selected in the next generation.

Table 4: Summary of basic example on GA

String number

Initial Population

x or integer value

Fitness Fi, f(x) = x2

Pi

1

01001

9

81

0.08

2

10110

22

484

0.47

3

10001

17

289

0.28

4

01101

13

169

0.17

Sum

1023

1.00

Max

484

0.47

6.0 Recent Development

There are many recent developments on intelligent control that enhance the performance and overcome previous disadvantages. One of these developments is the fuzzy neural network.

6.1 Fuzzy Neural Network

This type of control combines two types of control, the fuzzy control and the neural network. It is also called neuro-fuzzy system. The main principle of neuro-fuzzy is to use the approximations methods of neural network in order to find the parameter of the fuzzy system [10].

Comparing Fuzzy control to the neural networks:

Both techniques can be used effectively in solving problems without the need of having a mathematical model [10].

Neural networks depend entirely on observed examples and it has the ability to learn from scratch. Therefore there is no need to have a previous knowledge about the problem. On the other hand, the fuzzy control does not have the ability to learn, and it requires prior knowledge about the problem [10].

Fuzzy control requires straightforward description of the input and output variables. In other words, if there is any error in the knowledge, the fuzzy system should be tuned again [10].

In conclusion, having the fuzzy neural network allows combining the advantages and excludes the disadvantages of both fuzzy systems and neural network. Therefore, scientists and researchers were able to end up with an enhanced system that can be designed using the fuzzy rules with learning abilities and without the need for previous knowledge.

7.0 Conclusion

Intelligent Control is related to Digital Control Systems (DCS) in many ways. First of all, the principles and the techniques of state space which are covered in DCS are used frequently in intelligent control. The example of Fuzzy Logic Control which was discussed earlier depends on state variables.

Moreover, it was shown earlier that conventional and intelligent controls have different structure according to the plant and controller. The controller is separated from the plant in the conventional control while they are not separated in the intelligent control. Relating this to DCS, it is obvious that most of the systems studied are mainly conventional systems as each of the plant and the controller could be represented by a separated block diagram and transfer function.

Another advantage of studying DCS is the ability to use MATLAB and be familiar with its control toolbox and the most important and used commands in the control field. For example, the MATLAB code of neural network ensures having steady state value if the output exceeds a specified value. This logic have been studied in DCS and used regularly in its MATLAB applications.

In conclusion, it is obvious that control is a very huge field and it is a comprehensive knowledge. Most of the topics in control depend on each other and it is difficult to ignore the relation between them. For example intelligent control, robust control, nonlinear control, etc have common techniques that are used in solving the control problem such as Fuzzy Logic Control and Genetic Algorithm.