Subscripts 0,1,2 used with the aforementioned parameters refer to the cart, first (bottom) pendulum and second (top) pendulum correspondingly.
Parameter value m0=1,5 kg, m1=0,5 kg, m2= 0,75 kg, L1= 0,5 m, L2= 0,75 m.
Where θ1 and θ2 denotes the angle(in radians) of the pendulum from the vertical, dθ1/dt and dθ2/dt are angular velocities. G=9,8 m/s2 is the gravity constant. m0 is mass of the cart, m1 is mass of the first pendulum link, m2 is mass of the second pendulum link. L1 is length of
the first pendulum link, L2 is the second pendulum link. You will solve this double link inverted pendulum using Takagi-Sugeno Method. Firstly, You will find the Dynamic Equations of this system. Finding the premise variables you will design Fuzzy rules with consequent terms which is called State Equations. After that you will design system Matrices, Input(Control) Matrices, Output Matrices. There will be Midterm exam homework. Up to this point, the next ones will be Final homework, After Solving the state equations of each rule in MATLAB program, you will draw the curves of each state variables in MATLAB and interpret them
1. “You measured the diameter, d, of the pendulum bob using a ruler and a digital caliper. List all of the diameters of the bob as measured by both instruments. Determine the range of measured values for both instruments by calculating the difference between the maximum and minimum recorded values for the group. Compare the relative sizes of these two ranges and draw a conclusion about the precision of these two methods of measuring d. Repeat this analysis for the measurements of the thickness of the 100 gram mass.Compare the size of the range of ruler measurements of the pendulum bob diameter to the size of the range of ruler measurements of the thickness of the 100 g mass. If one is much larger than the other, which is it and why is it so much larger?
2. For the group of measurements of T in V-2(B), calculate T, vTand vT . vTis the standard deviation of the calculated values for T and vTis the standard deviation of the mean. Report T = T ± vT.
3. For each value of m used in V-4, you recorded three values of xm. Using x0 from posi-tion 2 in Figure M0-2, determine the three values of x for each value of m. Tabulate m, xm and x. Plot m vs. x. Whenever plotting a linear relation, be sure to include a trendline and the equation of the trendline in the plot. You should plot all three calculated values of x as a single set of data on one plot. Using LINEST in Excel, calculate the slope s, uncertainty in the slope vs, the intercept b and the uncertainty in the intercept vb. Report the slope and the intercept as s ±vs and b ±vb. From these, determine and report k ±vk.
4. Using one of the measurements of xo with a deliberate parallax error (e.g., posi-tion 1 or position 3 in Figure M0-2), recalculate all of your values of x. With these new values of x and using LINEST, recalculate the slope and intercept of the data. Tabulate m, xm and the recalculated values of x. Compare the value of the slope calculated with these data to the slope calculated in VI-3. Recalculate and report k ±vk. Compare the value for k determined in VI-3 with the value for k determined in VI-4″
M0 Powerpoint Video（Should be really help for lab report ,Let me know if you can’t open it）： https://drive.google.com/file/d/1l01UcKlzsX-rqLGJRILYHbcwL8TgGiWq/view
You are only responsible for completing the sections listed on the title page.（important）
TextBook link: https://ublearns.buffalo.edu/ultra/courses/_181429_1/cl/outline I have already bought It All of the experimental steps are in it, and you need to read it. Also Lab report question are inside.
We have Data already, So use it for this lab report. Please let me know if you need any more information from me.
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