Problem 10.1
Develop a fuzzy inference system for a robot, where the force exerted at the hand and the velocity of the hand are the inputs and the % power to the actuators is the output.
Estimated student time to complete:---
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Force; Small, Average, Large
Velocity; Slow, Fast, Fast, Very-Fast Outputs: Power; Low, Medium, High, Very-High The fuzzy sets are (arbitrary numbers):
The rules are:
The resulting output is:
Changing the rules or the membership functions will change this result.
Problem 10.2
Develop a fuzzy inference system for a washing machine. The inputs are how dirty the fabrics are and how much clothes are being washed, and the output is the wash time.
Estimated student time to complete:---
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Dirty; Not-Much, Some, Very.
Clothes; Small, Med, Much, A-Lot.
Outputs: Wash-Time; Five, Ten, Twenty, Thirty The fuzzy sets are:
The rules are:
The resulting output is:
Changing the rules or the membership functions will change this result.
Problem 10.3
Develop a fuzzy inference system for a barbecue. The inputs may be the thickness of the steak and how cooked or rare it is desired to be. The output may be the temperature of the flame and/or the time of cooking.
Estimated student time to complete:
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Thickness; See-Through, Average, Hefty
How Cooked; Rare, Medium-Rare, Medium, Well-Done Outputs: Temp; Low, Medium, High
Time; Three, Five, Eight, Ten The fuzzy sets are:
The rules are:
The resulting out puts are:
And
Problem 10.4
Develop a fuzzy inference system for an automatic gearbox. The inputs are the speed of the car and the load on the engine, and the output is the gear ratio of the transmission.
Estimated student time to complete:
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Speed; Slow, Medium, Cruise, Fast, Maximum Load; Low, Average, High
Outputs: Gear-Ratio; Fourth, Third, Second, First The fuzzy sets are:
The rules are:
Changing the rules or the membership functions will change this result.
Problem 10.5
Develop a fuzzy logic system for a vision system in which the inputs are the intensities of the three colors of red, green, and blue (RGB) in a color image and the output is the relationship of the combination to the colors of the rainbow.
Estimated student time to complete:
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Color-Red; Red-Off, Red-Medium, Red-High
Color-Green; Green-Off, Green-Medium, Green-High Color-Blue; Blue-Off, Blue-Medium, Blue-High
Outputs: Color; Black, Red, Orange, Yellow, Green, Cyan, Blue, Violet, White The fuzzy sets are:
The rules are:
Problem 10.6
Develop a fuzzy inference system for grading a robotics course. The inputs are your effort level in the course and your exam grade, and the output is your letter grade.
Estimated student time to complete:
Prerequisite knowledge required: Text Section(s) 10.3-10.9 Solution:
As in any other design problem, the solution is not unique. For example, different inputs and outputs may be selected, different fuzzy sets may be chosen, the ranges selected may be different, and alternate rules may be assigned. Therefore, not only the solution is not unique, the result will also differ. This suggested solution may only be used as a guide.
This solution is implemented on the MATLAB Fuzzy Toolbox. You may use this or any other available system.
In this solution, the inputs, outputs, the sets, and the rules are as follows:
Inputs: Effort; Low, Medium, High Exam-Grade; eA, eB, eC, eD, eF Outputs: Course-Grade; A, B, C, D, F The fuzzy sets are:
The rules are:
The resulting out put is:
Changing the rules or the membership functions will change this result.
APPENDICES
Problem A.1
Show that the determinant of a matrix can be calculated by picking any row or column.
Estimated student time to complete: 10-15 minutes Prerequisite knowledge required: Text Section(s) A.1 Solution:
For an arbitrary matrix:
a b c aei afh bdi bfg cdh ceg A d bi ch e ai cg f ah bg
dbi dch eai ecg fah fbg A b di fg e ai cg h af cd
bdi bfg eai ecg haf hcd
= − − − + −
They are all the same.
Problem A.2
Calculate the determinant of the following (4 × 4) matrix.
1 1 0 0
0 1 2 0
3 0 1 1
1 0 0 1
A
⎡ ⎤
⎢ ⎥
⎢ ⎥
=⎢ ⎥
⎢ ⎥
⎣ ⎦
Estimated student time to complete: 5 minutes
Prerequisite knowledge required: Text Section(s) A.1.
Solution:
( )
( ) ( ( ) )
detA=1 1 1 0− − + −0 0 1 0 2 3 1− − − + − = + =0 0 0 1 4 5
Problem A.3
Calculate the inverse of the following matrix using method 1:
⎥⎥
Estimated student time to complete: 5-10 minutes Prerequisite knowledge required: Text Section(s) A.1.
Solution:
Problem A.4
Calculate the inverse of the following matrix using method 2:
1 0 1
Estimated student time to complete: 10-15 minutes Prerequisite knowledge required: Text Section(s) A.1.
Solution: