Question

As an exercise move the Data cursor to find i. The gain for imaginary axis crossing ii. The value of the pole and the gain at the breakaway point. Now move the data cursor for the pair of complex poles that have an overshoot of 40%. Find the value of K required to get that closed loop pole. Move rest of the data cursors such for the same value of gain K. this will give the location of all closed loop poles of the system for a specific value of gain. For the value of gain at which overshoot is 40%, is the second order approximation valid?

          As an exercise move the Data cursor to find

i. The gain for imaginary axis crossing
ii. The value of the pole and the gain at the breakaway point.

Now move the data cursor for the pair of complex poles that have an overshoot of 40%.
Find the value of K required to get that closed loop pole.

Move rest of the data cursors such for the same value of gain K. this will give the location of all closed loop poles of the system for a specific value of gain.

For the value of gain at which overshoot is 40%, is the second order approximation valid?

Show more…

As an exercise move the Data cursor to find

i. The gain for imaginary axis crossing
ii. The value of the pole and the gain at the breakaway point.

Now move the data cursor for the pair of complex poles that have an overshoot of 40%.
Find the value of K required to get that closed loop pole.

Move rest of the data cursors such for the same value of gain K. this will give the location of all closed loop poles of the system for a specific value of gain.

For the value of gain at which overshoot is 40%, is the second order approximation valid?

Added by Susan R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/02/2023

Step 1

First, we need to find the gain for the imaginary axis crossing. To do this, move the data cursor to the point where the root locus crosses the imaginary axis. Note the value of the gain at this point. Show more…

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As an exercise move the Data cursor to find i. The gain for imaginary axis crossing ii. The value of the pole and the gain at the breakaway point. Now move the data cursor for the pair of complex poles that have an overshoot of 40%. Find the value of K required to get that closed loop pole. Move rest of the data cursors such for the same value of gain K. this will give the location of all closed loop poles of the system for a specific value of gain. For the value of gain at which overshoot is 40%, is the second order approximation valid?

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