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Ecet 402 Lab 6

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ECET-402 Week 6 Lab Worksheet Name: John Natale
Block Diagram Simplification and Step/Impulse Responses
Please complete this worksheet and submit to week 6 lab dropbox
This worksheet serves as coversheet

1. Determine the overall transfer function of the system given below by hand as discussed in pre-lab. Please show your work and type the equations if you can.

TF=(Y(s))/(X(s))=((s^3+3s^2+3s+2)/(〖2s〗^4+6s^3+15s^2+12s+5))/(1+(s^3+3s^2+3s+2)/(〖2s〗^4+6s^3+15s^2+12s+5)×2/s)=(s^4+3s^3+3s^2+2s)/(2s^5+6s^4+17s^3+18s^2+11s+4)

TF=(Y(s))/(X(s))=(s^4+3s^3+3s^2+2s)/(2s^5+6s^4+17s^3+18s^2+11s+4)

2. Determine the overall transfer function of the system shown above using MATLAB. Copy the MATLAB code and the overall transfer function obtained and paste them below:

>> nG1 = [1 0];
>> dG1 = [1];
>> G1 = tf (nG1, dG1) Transfer function:

>> nG2 = [1];
>> dG2 = [1 1];
>> G2 = tf (nG2, dG2)

Transfer function: 1
-----
s + 1 >> nG3 = [1];
>> dG3 = [1 0];
>> G3 = tf (nG3, dG3) Transfer function:
1
- s >> nG4 = [1 2];
>> dG4 = [1 2 5];
>> G4 = tf (nG4, dG4) Transfer function: s + 2
-------------
s^2 + 2 s + 5 >> nG5 = [2];
>> dG5 = [1 0];
>> G5 = tf (nG5, dG5) Transfer function:
2
- s >> G6 = series (G1, G2)

Transfer function: s
-----
s + 1 >> G7 = parallel (G3, G6) Transfer function: s^2 + s + 1
-----------
s^2 + s >> G8 = feedback(G7, 1) Transfer function: s^2 + s + 1
---------------
2 s^2 + 2 s + 1 >> G9 = series (G8, G4) Transfer function: s^3 + 3 s^2 + 3 s + 2
---------------------------------
2 s^4 + 6 s^3 + 15 s^2 + 12 s + 5 >> TF = feedback (G9, G5) Transfer function: s^4 + 3 s^3 + 3 s^2 + 2 s
------------------------------------------
2 s^5 + 6 s^4 + 17 s^3 + 18 s^2 + 11 s + 4

3. Are the results in steps 1 and 2 the same? Comment if they are not.

Yes, they are the same.

4. Determine the unit step response of the overall system using the MATLAB command described in the pre-lab. Copy the unit step response and paste it below.

5. Determine the impulse response of the overall system using the MATLAB command described in the pre-lab. Copy the impulse response and paste it below.

6. Is the overall system stable?

Yes, the system is stable.

7. Submit the worksheet to week-6 dropbox.

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