Project 3

Fuzzy Control Logic

Daniel Arreguin JassoEduardo Ruiz MaresGuillermo SánchezLuis Antonio Reyes

Automated Control Laboratory

November 24th, 2015

ObjectivesBe able to understand and apply the knowledge of Fuzzy Control Logic to program a Fuzzy controller for the Control Station used in previous projects.

Introduction to Fuzzy LogicFuzzy Logic comes out after the difficulty of describing results of any process or analysis with exact numbers or forms, when the result can be explained only with words; when parameters are unidentifiable or imprecise to define in certain conditions. Fuzzy controllers define the dependence between inputs and outputs through the declaration of certain IF-THEN rules. Similar to the way a human thinks and acts.

We can say a fuzzy controller is based on qualitative analysis of the system, so first is needed to identify these properties.The main characteristic of this controller is that it allows a grade of membership of the elements in a set, going from 0 - 1. This means that a certain value can belong partially 20% to some range and the rest to other. So the system evaluates the rules assigning an output according to the grade of membership of the input to the set.

Features of a membership functionCore: The region of the universe with full membership in a set.Support: The region of the universe that is not zero in a set.Boundaries: Values with non-zero membership, but not a full one.

Explanation of the PI-Fuzzy Controller.The fuzzy controller that we used for this practice uses two inputs and one output, being our inputs our error and the derivative of that error, and our output is our manipulation.

We used for the inputs and output triangle functions to control our system, using a smaller function for the input than the output, this because in this way we can control easier the values of our manipulation based in our error and the differential of the error.

For our first VI we use three memberships and for our second VI we used 7 memberships. And for our exit we used 7 memberships.

First VI Input

Second VI Input

To control the first input values we used 9 rules, and for our second input values we used 49 rules to control it.

We used a template to understand how the rules work and how to relation them.

The number of combinations of rules change depending on the number of inputs that we have making possible n combinations.

Tuning of the PI-Fuzzy ControllerFor tune in the controller we started using one input, making a SISO system, furthermore we realized that was very hard to control our sistem with only one input so we used a MISO system to controll it. Using diferent numbers of memberships for both inputs.We realized that we needed to establish logic values for this memberships in order to get the value of manipulation that we wanted in our output.Once we put our memberships and rules correctly, we could saw that the controller was beginning to compensate and it didnt took a long time to reach the value of SP.

The outputs selected was the error and the differential of the error, it means the subtraction about the actual error less an anterior sample of the error. The output must be a gradient of the operation variable, so the output of this controller must be added to the anterior manipulation to solve the new operation variable that the System needs.We need to use a proportion factor to minimize the big fluctuation given by the output of the PI-Fuzzy system.

VI with 3 memberships VI with 7 memberships

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We don't know why when error and delta-error is equal to zero the output is different to zero. even if the only rule that cover Zero is 1.

Charts of the temperature process response with PI-FUZZY controllerIn the following images we can see how the graphs of manipulation and temperature behaves when a setpoint of 25 is set.

In this last image we can see when the system reaches the setpoint level. Also, the proportion factor in a value of 20 means that we need a fifth of total range, it is 100 ,which is shorter range in order to work properly .

Charts of the temperature comparing PID versus PI-FUZZY controllerPID Controller PI-Fuzzy Controller

We can see that the process variable reach the set point faster than PI-Fuzzy does, however, the system has a overshoot that still stabilizing until long time after. The PI-Fuzzy controller can not linearize

the operation variable until the system shows an insignificant error, is very slowly to reach the set point, but it remain once it reach it.

long time after, we can see that PID has not stabilized yet there are a very small fluctuation

By the other hand, PI-Fuzzy remains with no change once the Process variable reach the set point

General commentsIn the part of the membership we have a issue about the relation between inputs and outputs. The manner to solve this problem was to center all the membership around the zero, on this way when the error and the differential of the error is Zero the output will be Zero activating only one rule of available rules.

We need a very short range in the output, it means that the works better with a range (-10,10) instead a range (-100,100), we realize about this in the behavior of the OP, it seems like a sawtooth while it must be almost linear, a factor in the output of the PI-Fuzzy controller was necessary to improve the operation variable and by consequence the the Process variable.

Individual Conclusions

Daniel Arreguín:In this practice you can learn a completely new method for my Control, fuzzy methodology could help control systems even when you have defined the transfer function, which can be very helpful. But it is necessary that memberships are well defined and the rules that control these memberships are very precise.

Guillermo:

In this practice we learned about a fuzzy method of control which is a different method that we can apply depending on what are we looking for. One of the advantages that we saw of this method is that once it reaches the setpoint it remains but it has the disadvantage that it is slower.

Jose Eduardo Ruiz Mares: With this practice we learned how fuzzy logic control is applied to a system, we saw that it wasn't easy to try to understand quickly this method because it takes a time to get how it works but with this method some kind of systems, like inestable systems could be easy to control with this method.

Luis Antonio:For me, Fuzzy controller toolkit in Labview was a little tricky at the beginning because I’ve never heard of it but through investigation we found what was it about. It is interesting in the fact that it acts similar to a human behavior. Fuzzy controller achieved a very stable level after some time, it reacts slower but more precise than our PID.