# 0.7 System identification for the torsional plant

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The objective of this lab is to review of the behavior of second-order systems. Students will gain a better understanding of the importance system identification. Students will also develop a hands-on understanding of the concept of hardware gain and why it will play a crucial role in controller design. System Identification will be implemented in LabVIEW using the System Identification Toolkit.

## Objectives

• Understand the dynamic equivalence between rotational and translational systems.
• Perform system identification using two different methods and compare the results.

## Pre-lab

• Assume that the least squares estimate has already been found for the unloaded and loaded sine sweep tests, so ${\stackrel{ˆ}{x}}_{\mathrm{d1}}$ , ${\stackrel{ˆ}{x}}_{\mathrm{d2}}$ , ${\stackrel{ˆ}{x}}_{\mathrm{d3}}$ , ${\stackrel{ˆ}{\stackrel{ˉ}{x}}}_{\mathrm{d1}}$ , ${\stackrel{ˆ}{\stackrel{ˉ}{x}}}_{\mathrm{d2}}$ , ${\stackrel{ˆ}{\stackrel{ˉ}{x}}}_{\mathrm{d3}}$ are known values. Formulate the linear least squares equation to estimate the 9 individual plant parameters. In other words, find the $y$ vector and $H$ matrix that would go into the equation $y=Hx+\epsilon \phantom{\rule{0ex}{0ex}}$ where the vector of parameters to be estimated, $x$ , is defined as $x=\left[\begin{array}{c}{J}_{\mathrm{d1}}\\ {J}_{\mathrm{d2}}\\ {J}_{\mathrm{d3}}\\ {c}_{1}\\ {c}_{2}\\ {c}_{3}\\ {k}_{1}\\ {k}_{2}\\ {k}_{hw}\end{array}\right]\phantom{\rule{0ex}{0ex}}$
• Outline the experimental steps you will take to identify the torsional plant using the second-order model method similar to Lab #2. Your procedure should allow you to find ${J}_{\mathrm{d1}},{J}_{\mathrm{d3}},{c}_{1},{c}_{3},{k}_{1},{k}_{2},$ and ${k}_{hw}$ . You may exclude the procedure for identifying the inertia and damping for disk 2. When formulating your procedures, remember that disks 2 and 3 can be clamped, disk 1 cannot.

## System identification using least squares

• Configure the plant with all three disks rotating freely and no brass weights attached.
• Perform a 1638 count (0.5V) linear sine sweep from $0$ to $8Hz$ with a sweep time of $20$ seconds. When the execution is complete, enter a file name such as $\mathit{3DiskSweepUnloaded}$ and save the raw data from the front panel.
• Now load two $0.5kg$ brass weights onto each of the three disks so their centers are $9.0cm$ from the axis of rotation.
• Perform the sine sweep again. Enter a file name such as $\mathit{3DiskSweepLoaded}$ and save the raw data.
• You are now ready to identify the system parameters using least squares estimation.

## System identification using second-order model

• Follow the steps you outlined in the pre-lab to identify the system parameters using the second-order model method.

## Post-lab

• Complete the table below; remember to include units.
• How close are your least-squares values compared to your second-order model values. Can you explain any discrepanciesbetween them. Which method do you think is more accurate?

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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Sherica
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Uday
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or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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J, combine like terms 7x-4y
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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Cied
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Porter
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Porter
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Cesar
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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