Problem # 01
Question 1
Given
The impedance of the inductor in the s domain is
The circuit can be drawn in s domain as follows
So the current flowing through the inductor can be found using current division rule as
So the transfer function is
Another way of finding the transfer function:
The voltage across the inductor is
The current flowing through the resistor is
Here the voltage across the resistor is same as the voltage across the inductor. So
Now applying Kirchoff’s Current Law we get
Substituting the values of L and R we get
Taking Laplace Transform on both sides under zero initial conditions, we get
So the transfer function is
We got the same answer
To find the poles and zeros
The poles are at
There are no zeros. So the pole - zero map will be
To find the step response
Step response is the response of the system when a unit step input is applied. So
Taking Laplace Transform, we get
So
Taking Partial Fraction expansion, we get
So
Taking Inverse Laplace Transform, we get
So the step response of the circuit is
Question 2
To find the state and output equation.
The state is
The input is
We have already shown the current equation in question 1 as
Substituting the state variables and input we get
So
Substituting the values of R and L
The output is
So the state equation is
The output equation is
Question 3
From the equation,
We can write
The output is
So the block diagram is
Question 4
Simulation Using MATLAB
MATLAB Code
clc;
clear all;
close all;
n = [1];
d = [0.1 1];
sys = tf(n, d);
step(sys);
grid
After executing we get
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
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