EE324 LAB REPORT
Lab 1
Stephen Nelson
Introduction:
The objective of this lab was to familiarize ourselves with Simulink. Additionally we used Simulink to study the system response of seemingly unrelated systems. This lab also introduced us to deriving differential equations for input output relationships.
Prelab:
Argue that the integrator system is LTI and therefore it is characterized by its impulse response. Assume: ( ) ( ) ( ) ( ) ( ) ( )
( )
( ) ( ) ( )
( )
Superposition holds therefore the integrator is linear. Assume: ( ) ( ) ( ) ( ) ( ) ( )
Therefore the integrator is time invariant. Making the integrator a LTI system. I then verified the integrators impulse response shown below. ( ) ( ) ( ) ( ) ( )
I then created a Simulink model to verify the impulse response of the integrator this will be shown on page 2.
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The above Simulink model gives the following output.
The Simulink output is a unit step. However the ramp at the beginning is caused because the discrete impulse is not ideal. The next step in the prelab was to compute the Laplace transform of the integrator and to find the ROC. ( ) ( ) ROC: ( )
Lab:
In the following sections I will detail my Simulink investigation into an electrical system and a mechanical system.
Electrical system
For the first part of this lab I investigated the electrical system shown on page 3. I first derived an equation relating I(t) and V(t) and then I constructed a Simulink model of the system.
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Equation: ( )
( )
( )
( )dt
From this equation I then created the Simulink model shown below.
The outputs for the Simulink model are given on page 4.
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H=100mH, C=1mF, R=1k
H=100mH, C=1mF, R=1M
Analysis
In the first set of simulation parameters the circuits acts a Normal RLC circuit whose transients end after a short length of time. However, in the second simulation the R value is so large that the circuit acts as an LC circuit and oscillates. Page 4 of 6
Mechanical system:
For the mechanical system I derived the equation relating f(t) and V(t) and then created a Simulink model for the system. Equation: ( )
( )
( )
( )
The output for this model is shown on page 6.
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Analysis
The mechanical system has the same Simulink model as the RLC circuit did. The mass(M) relates to the capacitor(C), the spring(K) relates to the inductor(L) and the dampener (B) relate to the resistor (R).
Conclusion:
This lab introduced the use of Simulink to solve differential equations. Additionally, it showed that two seemingly unrelated systems can have the same Simulink model.
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