Question

Design a parallel RLC circuit to have an a) overdamped, b) underdamped, and c) critically damped voltage response. Use matlab to plot the responses on the same graph, labeling each response with the component parameter values. What are the pros/cons of each type of second-order design?

Answer 1

Design

Tpype the fallowing program in matlab

% overdamped
R=20;
L=0.01;
C=0.000001;
num = 1;
den = [L*C L/R 1];
sys1 = tf(num,den);
subplot(3,1,1)
step(sys1);
title('overdamped responce')
% underdamped
R=100;
L=0.01;
C=0.000001;
num = 1;
den = [L*C L/R 1];
sys2 = tf(num,den);
subplot(3,1,2)
step(sys2);
title('underdamped responce')
%critically damped
R=50;
L=0.01;
C=0.000001;
num = 1;
den = [L*C L/R 1];
sys3 = tf(num,den);
subplot(3,1,3)
step(sys3);
title('critically damped responce')

The responce of the system is shown below

pros/cons

Overdamped

The system returns (exponentially decays) to equilibrium without oscillating.

Critically damped

The system returns to equilibrium as quickly as possible without oscillating.

Underdamped

The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero.