IC_FinalReport_WorkSoFarv4

Bruno Diaz and George RosenbaumIntelligent Control - EE 4733

Final Project Report

INTRODUCTION:

A fuzzy controller must be designed for a fan actuated, imbalanced lever and fulcrum. A

lever has a fixed weight and a magnet on one side, and a battery operated fan on the other. A

Hall Effect sensor detects the distance of the magnet from the ground, and represents this as a

non-zero number. The fan voltage must be controlled to balance the distance of the weight from

the floor so as to keep the lever balanced. This system is mathematically complex, which makes

modeling a transfer function very difficult. So a fuzzy logic controller is favored in this scenario.

Two different fuzzy logic controllers’ rulesets will be investigated. One controller

contains three rules, and another contains five rules. Then a method of increasing performance

by making changes to how error is read will be explored.

PROCEDURE:

The method for making these controllers will require a combination of observation,

intuition, and trial-and-error. The best way to design a good controller requires the user to know

the advantage of fuzzy logic over traditional “crisp” logic. Crisp logic has very discrete states

that the controller must stay in. As a result, such controllers can easily end up on the border of

two different states, getting stuck and unable to move to the desired target. This can only be

defeated with many redundant rules that slowly “fade” into the desired operation by creating lots

of states. This process is tedious, time consuming, and very difficult to update and experiment

with.

With fuzzy logic, the user can actually fade into the desired operation by allowing

multiple states at the same time. This reduces the number of states needed, eliminating brute-

force redundancy and allowing for more intuitive design. The amount of each state used can be

controlled easily, allowing for infinite states generated in a gradient of effect.



The fuzzy logic technique we used was the DOF which will serve as the controller in the

algorithm shown below.

The DOF method is essentially shown below.

The range of different sensor values must first be collected using “s.inputSingleScan()” to

find the universe for error. Use this command once when the sensor is far away, and again when

the sensor is close. These values will be different depending on the Hall sensor and the magnet

being sensed. A third target voltage must also be found with “s.inputSingleScan()” so the

controller will know what voltage to track.

The universe generated from these values will not actually be the lowest and highest

value the sensor records. Instead the difference between the two values is calculated, which was

found to be about. 5703, and the universe will range from the negative difference to the positive

difference. This should create an error universe of about [-5703, 5703].

With the universe found, the rules and gain change are experimentally created until the

controller becomes reliable and effective. The gain change that is the weights attached to du after

the defuzzified output is found to be most effective around 0.1.

The rules specify what state the controller is in, and the gain value alters how quickly the

fan voltage is allowed to change. The three rule controller has a “too high” state (called P), a “too



low” state (called N), and a “just right” state (called Z). The 5 rule controller has a “very high”

state (called PB), a “slightly high” state (called PS), a “just right state” (also called Z), a “slightly

low” state (called NS), and a “very low” state (called NB).

For the three rule controller, most of the universe was taken up by the “P” and “N” states.

The “Z” state takes is a narrow triangle placed on the target. Depending on how large the

controller gain is, the controller will require more room to fade from an outer state to the “Z”

state. With a 5 rule controller, care must be taken in how large the “PS” and “NS” states are, as

the controller can easily be stuck in these states if they are made too large. But careful design of

these rules will provide faster response and steadier tracking.

The boundaries chosen for the 3 rule controller were

N=trapmf(Err_X, [(-.5703 -.5703 -.5 .2)]);Z=trimf(Err_X, [(-1*.03) mid .03]);P=trapmf(Err_X, [.2 .5 .5703 .5703 ]);

For the 3 rule controller, the boundaries for the “N” and “P” controller are left very large.

Without any finer way of specifying rules, the “Z” rule had to be left slightly large. The

controller eventually works, but has a lot of overshoot and takes a long time to settle.

The boundaries for the 5 rule controller were

PB=trapmf(Err_X, [-.5703 -.5703 -.4 -.2]);PS=trimf(Err_X, [-.3 -.25 -.2]);Z=trimf(Err_X, [-.02 0 .02]);NS=trimf(Err_X, [.2 .25 .3]);NB=trapmf(Err_X, [.2 .4 .5703 .5703]);

For this controller we found improvement in performance by narrowing the Z boundary

so that we could have the fan could be leveled out at the VR more easily and evenly since we

were noticing that the fan would level of at a height near the VR but wouldn’t reach it for some

time.



We also introduced a new feature to improve both controllers, referred to in this paper as

“future tracking.” While making the original controllers, a delay was noticed between a change

in voltage and effecting the operation of the fan. If the fan is set to a certain voltage that levels

out at a certain height we can see that it takes some time before it reaches that height, which

appears to take about 30 to 40 steps. This presents a problem since within those 40 steps the error

will still show up and the controller will continue to increase the voltage unnecessarily, causing

extreme overshoot. To remedy this problem, the error that the fan will have in the future is also

calculated in the adjusted algorithm seen below.

This is accomplished by creating a buffer that stores the last several values of recorded

voltages, the size of which can be controlled with the variable PD. Then it uses the latest point

and the oldest point in the buffer to calculate the slope of the fan speed relative to those two

points. The right length of the buffer has to be found, a buffer too short may be subject to erratic

behavior from noise and a buffer too long may not respond fast enough to changes. For our

purposes we found a buffer size of 3 to be adequate. After the slope has been found multiply that

by PF which represents how far we want to assume this will continue into the future (we choose



30 steps) and add that to the current voltage. That becomes our future voltage and we subtract

our target voltage “VR” from that to get our error.

MAIN RESULTS:

We performed experimentally found our value for the weight in front of du to be 0.15.

We then ran two for the 3 and 5 rules using the original algorithms and another two for the

adjusted 3 and 5 rule algorithms. The results of all four experiments are shown below, with a VR

of 2.1 V.



The same controllers were used on a different my VTOL board with a VR of 2.15, which

changed the behavior of the circuit somewhat. While there was some performance improvement

with the original algorithm the adjusted remained consistent.

3 rules original 5 rules original



3 rules adjusted 5 rules adjusted

CONCLUSION AND DISCUSSION:

Approximating even a 3-rule controller is difficult for crisp logic. For any mode of

operation where a fuzzy logic uses a combination of states, a crisp controller must use a

completely unique state. This results in a crisp controller that has many different states that are

very close to each other, more lines of code, more chances to make mistakes, and more difficulty

changing the behavior of the controller to add better performance. There are room for

performance an issue we had with the controller

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