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Lab 5a Tips

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Pre-Lab

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State-Space Form

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Steady State Conditions

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Transfer Functions

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Step response of

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In-Lab

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Post-Lab

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Lab 5a Solutions

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Pre-Lab

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(1)
(2)
(3)

State Space Form (2 points)

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Solve equations (1) and (2) for and .

Steady State Form (2 points)

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Simplify (2 points)

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Transfer Functions(2 points)

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Combine equations (1)-(3) to eliminate . First solve (1) and (3) for

Then substitute the result into (2).

Convert the resulting equation to the frequency domain through application of Laplace transforms. Note that we choose the capital form of (), when in the frequency domain. Also, it is safe to assume .

Solving the resulting equation for yeilds

Finally, solve the above equation for the transfer functions

and

and (2 points)

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Using the first transfer function above, solve for given . In other words, solve the following

.

We use a Laplace transform table to look up the transform for an exponential approach

then if we let

we can express as

.

Given

we have

and

Lab 5b Solutions

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Pre-Lab

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(1)
(2)
(3)
(4)

Solving equation (1) for and substituting into equation (2) results in

Simplifying

Now equations (3) and (4) can be substituted into the above equation to produce

Applying some trigonometry the above can be rewritten as

(4 points)

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(3 points)

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(3 points)

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Post-Lab 6b

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Lab 7a

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Post-Lab

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The Fourier series of a 2π-periodic function ƒ(x) that is integrable on [−ππ], is given by

where

and

In question 2, you are being asked to find the fundamental component of the fourier series of the functions vas, vbs, and vcs. The fundamental component is the component with the lowest freqency, specifically:

To find the coefficients an and bn from the equations above, the integral must be broken down into the sum of integrals over continuous regions.

Other

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