# lab4 - R1 1m L1 1u C1 1K R2 Figure 1: Simple RLC circuit...

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Objectives: Learn to use MATLAB software Learn to derive the state space model Procedure: Part A: 1. Find the transfer function of the circuit shown in figure (1) 2. Using MATLAB, find the inverse Laplace of the transfer function for a unit step function. 3. Using MATLAB, plot the step response of the function. Part B: 1. Find the state space model for the system. 2. Using the state space model and MATLAB software, derive the transfer function. 3. Compare the result of part A and B. Analysis For this lab we had to solve for the transfer function of figure 1 by hand and then use mathlab to find the inverse laplace when the input is a unit step. After this we then had to plot the step response using the same software. The first step to calculate the transfer function of the RLC circuit was to assign current loops I 1 and I 2 and then use mesh analysis to derive the two loop equations. Vout Vin 1K

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Unformatted text preview: R1 1m L1 1u C1 1K R2 Figure 1: Simple RLC circuit Loop 1: 2 1 1 1 ) 1 ( I Cs Cs R I V in-+ = Loop 2: 1 2 2 1 ) 1 ( I Cs R Ls Cs I-+ + = Transfer Function: 2 2 1 2 ) ( + + = s s G s Inverse laplace ) ( ) sin( ) ( t u t e V t t-= Figure 2:Step Response of the Circuit For part B of the lab, we had to find the state space model for the circuit in figure 1. For this situation, V C and I L selected as state variables since they are linearly independent from each other. C I RC V RC V dt dV L C t C--= ) ( L C L I L R L V dt dI-= Figure 3:State Space matrix Conclusion: The lab was simple and straight forward. I hate getting the state space variables but its understandable that when one has a huge system to consider and breaks it into little portions using state space variable technique, then use matlab to simplify it or get the transfer function....
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## This note was uploaded on 10/24/2011 for the course ELET 3700 taught by Professor Grubb during the Spring '11 term at North Texas.

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lab4 - R1 1m L1 1u C1 1K R2 Figure 1: Simple RLC circuit...

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