ME 349 University of South Alabama Electrical Systems Matlab Coding Task

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Engineering

ME 349

University of South Alabama

ME

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The University of Alabama ME 372 Homework 5 Please put all your solutions into ONE file (preferably PDF, or MS-Word) and upload it on ualearn.blackboard.com anytime before the due date and time. Late, hardcopy, or emailed homework is not accepted. ELECTRICAL SYSTEMS 1. CFN (Textbook) Problem 6.3. 2. For the electrical circuit shown below, a) show that state space equations are: di 1 dt L le-ec) dt e Also write the state-space equations in matrix form L b) Write a Matlab code and function) using integration technique to find the system response under the following conditions: 1) Initial conditions: when t = 0, i = 0.75, e. = 2.5. II) Time span: 1 = 0 to 15s. III) Consider R = 10, C = 0.11, L =2.5, and e=0. IV) output is y=i. Submit ALL Matlab codes and plot of y as functions of time. Correct labeling must be used for the horizontal and vertical axes. E370 HH M Moh
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Explanation & Answer:
2 Questions
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Explanation & Answer

Done dude😎 Reach me in case of needed modifications 😇

a)
Applying Kirchhoff’s voltage law on the large mesh we get

𝑒𝑖 = 𝐿

𝑑𝑖
+ 𝑒𝑐
𝑑𝑡

Rearranging the equation above
𝑑𝑖
𝑑𝑡

=

1
𝐿

𝑒𝑐

𝑖1 =

(𝑒𝑖 − 𝑒𝑐)

(1)

(Ohm’s law)

𝑅

𝑖2 = 𝑐 ∗

𝑑 𝑒𝑐
𝑑𝑡

Applying Kirchhoff’s current law on the shown node above we get

𝑖 = 𝑖1 + 𝑖2
𝑖 =

𝑒𝑐
𝑑 𝑒𝑐
+ 𝑐 ∗
𝑅
𝑑𝑡

Rearranging the equation above
𝑑 𝑒𝑐
𝑑𝑡

=

1
𝐶

(𝑖 −

𝑒𝑐
𝑅

)

(2)

State space

b) Using MATLAB, a function and a script were built using ODE45
The function

The script

The results

Done 😎

Problem CFN 6.3

Applying Kirchhoff’s current law at node 2 we get
i1 = i2 + i3

Substituting we get (1)

Applying Kirchhoff’s current law at node 3 we get
iL + iR2 = iR3

Substituting we get (2)

Applying the conditions R1 = 6 , R2 = 2 , R3 = 12, R4 = 3 , L=3 , (1) becomes (3) as follows

And (2) becomes (4) as follows

Now, we differentiate eq (4) to get (...


Anonymous
Awesome! Perfect study aid.

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