MATLAB Control Systems RLC Circuit Queries

[DarrenMK]

Hi there, we recently completed a laboratory session on MATLAB relating to an RLC Circuit and arrive at a code and relevant inputs and got our graphs as shown below.

I was just wondering if anyone know if these are correct and make any sense? Or any other comments appreciated.

We also have to prepare a lab report on our findings and derive our TF from first principles

G(s) = s/(RC) / s^2 + s/(RC) + 1/√(LC) is what we have. How do I go about derivation?

The code and other information is shown below. Transfer function:
0.3333
-----------------------
s^2 + 0.3333 s + 0.4082

Enter a value for Kp 1
Enter a value for Ti 2
Enter a value for Td 3
Enter a value for Hs1

Hs =

1


Transfer function:
2 s^2 + 0.6667 s + 0.3333
-----------------------------
2 s^3 + 0.6667 s^2 + 0.8165 s

ForwardPathTransferFunction

Transfer function:
2 s^2 + 0.6667 s + 0.3333
-----------------------------
2 s^3 + 0.6667 s^2 + 0.8165 s

FeedbackPathTransferFunction

FeedbackPathTransferFunction =

1

OpenLoopTransferFunction

Transfer function:
2 s^2 + 0.6667 s + 0.3333
-----------------------------
2 s^3 + 0.6667 s^2 + 0.8165 s

ClosedLoopTransferFunction

Transfer function:
4 s^5 + 2.667 s^4 + 2.744 s^3 + 0.7666 s^2 + 0.2722 s
----------------------------------------------------------------
4 s^6 + 6.667 s^5 + 6.377 s^4 + 3.833 s^3 + 1.433 s^2 + 0.2722 s

ErrorRatio

Transfer function:
2 s^3 + 0.6667 s^2 + 0.8165 s
------------------------------------
2 s^3 + 2.667 s^2 + 1.483 s + 0.3333

PrimaryFeedbackRatio

Transfer function:
4 s^5 + 2.667 s^4 + 2.744 s^3 + 0.7666 s^2 + 0.2722 s
----------------------------------------------------------------
4 s^6 + 6.667 s^5 + 6.377 s^4 + 3.833 s^3 + 1.433 s^2 + 0.2722 s

CharacteristicEquation

Transfer function:
2 s^3 + 2.667 s^2 + 1.483 s + 0.3333
------------------------------------
2 s^3 + 0.6667 s^2 + 0.8165 s

The graphs which were gotten from the above inputs were as follows;

http://img560.imageshack.us/img560/9556/stuffo.jpg

Are they what you would expect from such a system? What exactly do they show?

Any other help or comments appreciated

 

[MisterX]

We also have to prepare a lab report on our findings and derive our TF from first principles

G(s) = s/(RC) / s^2 + s/(RC) + 1/√(LC) is what we have. How do I go about derivation?

Check any materials you were provided with. It may have a schematic or specify the locations of input and output quantities. I would expect those to be input and output voltages.

Start by writing down the differential equation(s) for the circuit in terms of input and output quantities, in the time domain. Once the Laplace transform is applied to these differential equation(s), you may solve for the transfer function. The transfer function is the transformed output divided by the transformed input.