2. Consider the system with the following configuration. r(t) Ke y(t) Kp Tp8 +1 Let Kp = T, = 1. Choose three different K. values to represent each of the following cases: (1) overdamped, (2) underdamped, and (3) critically damped.

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2. Consider the system with the following configuration.
r(t)
Ke
y(t)
Kp
Tps +1
S
Let K, = T, = 1. Choose three different K, values to represent each of the following cases: (1) overdamped,
(2) underdamped, and (3) critically damped.
(a) Plot the unit-step responses of the three cases on the same figure.
(b) For the case of an underdamped system, compute the maximum value of the response and the time it
occurs. Verify your answer from the plot.
(c) Please study the formula that computes an approximate value of the 2% settling time of the standard 2nd
order system. Compute the 2% settling time and verify your answer from the plot.
Note that you need to provide your own Matlab codes and/or Simulink diagrams. Be little more creative. For
example, before you choose an underdamped & value, you can try out few different values that satisfy <1 to
observe the behaviour of the respective step response. Use the "insert" function ("text arrow" function under
it) with on the Matlab's figure window, label all the plots.
1
Transcribed Image Text:2. Consider the system with the following configuration. r(t) Ke y(t) Kp Tps +1 S Let K, = T, = 1. Choose three different K, values to represent each of the following cases: (1) overdamped, (2) underdamped, and (3) critically damped. (a) Plot the unit-step responses of the three cases on the same figure. (b) For the case of an underdamped system, compute the maximum value of the response and the time it occurs. Verify your answer from the plot. (c) Please study the formula that computes an approximate value of the 2% settling time of the standard 2nd order system. Compute the 2% settling time and verify your answer from the plot. Note that you need to provide your own Matlab codes and/or Simulink diagrams. Be little more creative. For example, before you choose an underdamped & value, you can try out few different values that satisfy <1 to observe the behaviour of the respective step response. Use the "insert" function ("text arrow" function under it) with on the Matlab's figure window, label all the plots. 1
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