<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>

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Author:

Itamar Bocher

18-Jan-2012

Audit:

Omer Yagel

084735 Control Theory

Home Assignment #9

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Given the following Unit feedback control system:

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

Find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= to get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EoYGVfX3NzYEYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEnMC4wMDEyRidGMy1GMDYtUScmc2RvdDtGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGUi1JJW1zdWJHRiQ2JS1GLDYlUSJSRicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnLUYjNiUtRks2JFEiMEYnRjNGWkZnbi8lL3N1YnNjcmlwdHNoaWZ0R0Zdb0Yz

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

We know that 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 and because the system is type 1 we can use the relation 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JSFH

Therefore,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVLX192R0YoJCIrTExMTCQpISIoNyNGLg==

So,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiS0c2IiQiK0xMTEwkKSEiKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E0L0kiS0c2IiQiK0xMTEwkKSEiKEYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDk5NjcpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

The value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrTExMTCQpISIo

JSFH

JSFHJSFH

Find the system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjR01GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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print(); # input placeholder

NyQkIisoUl8rbiIhIiokIiYrKyIhIiM=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JC1GLDYlUSxQaGFzZU1hcmdpbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJHN5c0YnRjRGNy9GOFEnbm9ybWFsRidGKw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIis5YEokNCIhIiokIituJHlEMyohIik=

print(); # input placeholder

NiI=

The system margins:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHTUdGKCQiKyhSXytuIiEiKjcjRi4=

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JS1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUTs3JCQiKzlgSiQ0IiEiKiQiK24keUQzKiEiKUYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDk5OTYpRicvJSV2aWV3R1EmbGFiZWxGJy1GIzYjLUkjbW5HRiQ2JFEiMUYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQiKzlgSiQ0IiEiKjcjRi4=

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Design correction network LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEdfX2NgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn So we will get 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. Explain every step.

<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>

The design requirement is 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 deg.

From previous article we found

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrOWBKJDQiISIq

JSFH

Therefore,we need to advance the PM by:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEjNDBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSgmbWludXM7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrcCVvMSpRISIp

We need to add phase, that is why we will use a lead correction network

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

We will always take a bit more than the value we need in order to get to the requirement LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn because the gain curve will get larger when we add the correction network, and the phase will get a bit larger.

Let choose

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYCZwaGk7X19tYEYnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSM0NEYnRjMtRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkg=

. Using the eq.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

we can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.JSFH

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

L0kiYUc2IiQiK24uL11iISIq

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EzL0kiYUc2IiQiK24uL11iISIqRicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTAwODUpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

The gain of lead correction network,

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

Setting

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, therefore,

SSZmYWxzZUclKnByb3RlY3RlZEc=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JJGFic0clKnByb3RlY3RlZEc2I0knR19fc3lzRzYiJCIrayJbWkMlISM1

And in db:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19zeXNHRigkISs9OSdIVyghIio3I0Yu

Searching in the bode plot (Art 2) this gain (in db) we will get the frequency, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EsYHdfXyZwaGk7fmBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRJjEzMy4yRidGMy1GMDYtUSJ+RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRlJGMw==. For an Optimal solution, let set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHdfX21gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EsYHdfXyZwaGk7fmBGJ0Yz.

Using the eq.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

We can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

L0kkdGF1RzYiJCIrcnl1Jz0kISM3

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E2L0kkdGF1RzYiJCIrcnl1Jz0kISM3RicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTAxMDkpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

So, the correction system is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiK0t6bG88ISM2IiIiRilGKSwmRiQkIityeXUnPSQhIzdGKUYpISIi

JSFH

Building the new Transfer function:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EpYEdfX25ld2BGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYsNiVRIkdGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictRjA2LVEnJnNkb3Q7RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRlYtRiw2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCosSSJzR0YoISIiLCYiIiJGM0YwJEYzRjFGMSwmRjNGM0YwJEYzISIkRjEsJkYwJCIrS3psbzwhIzZGM0YzRjMsJkYwJCIrcnl1Jz0kISM3RjNGM0YxJCIrTExMTCQpISIoNyNGLg==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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print(); # input placeholder

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print(); # input placeholder

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For the correction system we design, the

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print(); # input placeholder

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<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>

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Given the following Unit feedback control system:

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Draw the system Bode plots, and find the system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRI0dNRidGL0YyRjk=.

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

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print(); # input placeholder

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print(); # input placeholder

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The system margins:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHTUdGKCQiKyc9RD1fJCEiKjcjRi4=

JSFH

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQiKyZIazM+IiEiKTcjRi4=

JSFH

Design correction system of the type Phase Promotion in order to get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzNUYnRjlGOQ==.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

JSFH

The design requirement is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzNUYnRjlGOQ== deg.

From previous article we found

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrJkhrMz4iISIp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Therefore,we need to advance the PM by:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEjMzVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSgmbWludXM7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrMGQ4NEIhIik=

We need to add phase, that is why we will use a lead correction network

Let choose

. Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

we can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiYUc2IiQiIiQiIiE=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EvL0kiYUc2IiQiIiQiIiFGJy8lK2FjdGlvbnR5cGVHUTxtYXBsZXNvZnQuY29tOmxhYmVsKEwxMDU3NClGJy8lJXZpZXdHUSZsYWJlbEYnRjovRjNRJ25vcm1hbEYn

The gain of lead correction network,

Setting

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JJGFic0clKnByb3RlY3RlZEc2I0knR19fc3lzRzYiJCIrIXAtTngmISM1

And in db:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19zeXNHRigkIStdREByWiEiKjcjRi4=

Searching in the bode plot (Art 1) this gain (in db) we will get the frequency, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EsYHdfXyZwaGk7fmBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRJTIuNjJGJ0YzLUYwNi1RIn5GJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGUkYz. For an Optimal solution, let set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHdfX21gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EsYHdfXyZwaGk7fmBGJ0Yz.

Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

We can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kkdGF1RzYiJCIrIilwaS5BISM1

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E2L0kkdGF1RzYiJCIrIilwaS5BISM1RicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTA1NTgpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

So, the correction system is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiK1Y0KTNoJyEjNSIiIkYpRiksJkYkJCIrIilwaS5BRihGKUYpISIi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Building the new Transfer function:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCosSSJzR0YoISIiLCZGMCIiIiIiI0YzRjEsJkYwRjMiIiRGM0YxLCZGMCQiK1Y0KTNoJyEjNUYzRjNGMywmRjAkIisiKXBpLkFGOkYzRjNGMSIjPzcjRi4=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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print(); # input placeholder

NyQkIitpcm9ubyEiKiQiK0JOZiozJUYl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiw2JVEsUGhhc2VNYXJnaW5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSdOZXdTeXNGJ0YyRjUvRjZRJ25vcm1hbEYnRis=

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print(); # input placeholder

NyQkIissYzkoZiMhIikkIisqPm09aiMhIio=

As we can see, we got the system margins and their frequency: GM=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E6NyQkIitpcm9ubyEiKiQiK0JOZiozJSEiKkYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDEwNjAxKUYnLyUldmlld0dRJmxhYmVsRictRiM2Iy1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Yr

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print(); # input placeholder

JCIraXJvbm8hIio=

PM=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E7NyQkIissYzkoZiMhIikkIisqPm09aiMhIipGJy8lK2FjdGlvbnR5cGVHUTxtYXBsZXNvZnQuY29tOmxhYmVsKEwxMDYwMylGJy8lJXZpZXdHUSZsYWJlbEYnLUYjNiMtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGKw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrLGM5KGYjISIp

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We haven't reach the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we want. Let take a larger LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiVRIm1GJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y9Rj8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIjpGJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWEY1

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

Let choose

. Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

we can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.JSFH

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiYUc2IiQiK2c4IWYrIiEiKQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E0L0kiYUc2IiQiK2c4IWYrIiEiKUYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDEwNjg5KUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=

The gain of lead correction network,

Setting

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JJGFic0clKnByb3RlY3RlZEc2I0knR19fc3lzRzYiJCIrKCl5KUg6JCEjNQ==

And in db:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19zeXNHRigkISsmUmJEKyIhIik3I0Yu

Searching in the bode plot (Art 1) this gain (in db) we will get the frequency, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EsYHdfXyZwaGk7fmBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRJjMuNDY3RidGMy1GMDYtUSJ+RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRlJGMw==. For an Optimal solution, let set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHdfX21gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EsYHdfXyZwaGk7fmBGJ0Yz.

Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

We can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kkdGF1RzYiJCIrOEhHJTQqISM2

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E2L0kkdGF1RzYiJCIrOEhHJTQqISM2RicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTA2NDYpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

So, the correction system is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiK106Jno5KiEjNSIiIkYpRiksJkYkJCIrOEhHJTQqISM2RilGKSEiIg==

JSFH

Building the new Transfer function:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCosSSJzR0YoISIiLCZGMCIiIiIiI0YzRjEsJkYwRjMiIiRGM0YxLCZGMCQiK106Jno5KiEjNUYzRjNGMywmRjAkIis4SEclNCohIzZGM0YzRjEiIz83I0Yu

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIiskKTN2RDUhIikkIisjeldecichIio=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIis/JlxhZiQhIikkIiszKj4sWSQhIio=

We got the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we wanted.

JSFH

So the correction system is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiK106Jno5KiEjNSIiIkYpRiksJkYkJCIrOEhHJTQqISM2RilGKSEiIg==

Draw the fixed system Bode plots. What is the system Band width?

<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

In order to find the bandwidth, we will search in the Phase graph above the frequency which the phase =-180 deg, 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjQndGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmYXBwcm94O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEid0YnRi9GMi1GIzYlLUYsNiVRJyYjOTY2O0YnL0YwRj1GOUYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRJTYuNTRGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZW8tSSZtZnJhY0dGJDYoLUYsNiVRJHJhZEYnRi9GMi1GIzYlLUYsNiVRJHNlY0YnRmZuRjlGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZncC8lKWJldmVsbGVkR0Y9RjktRiw2I1EhRidGOQ==JSFH

JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

During changes in the steady state, the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5is now LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDEwMEYnRjlGOQ==. Dose it possible to achieve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzNUYnRjlGOQ== for this gain using correction system of the type Phase Promotion?

JSFH

<Text-field style="Heading 2" layout="Heading 2">Art. 4</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkISshXGRkLyIhIikkIitWKCpbXEMhIio=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIStaKzskKUchIikkIisoWyh5Jj0lISIq

The system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjR01GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn are:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHTUdGKCQhKyFcZGQvIiEiKTcjRi4=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQhK1orOyQpRyEiKTcjRi4=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

As we saw in the lecture, the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn range is 30\303\26760 deg. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we need to add in order to reach to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzNUYnRjlGOQ== deg is:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrWis7JFEnISIp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We got a value which is above the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn range, that is why it is not possible to achieve LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzNUYnRjlGOQ== deg for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDEwMEYnRjlGOQ==

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Given the following system:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is Heaviside

Assuming the system is stable, find the the system Type and Order.

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

JSFH

The system order is 2.

Because the feedback is a single feedback and we have no zeros at the origin, then the system is Type 0

The system error in closed loop is 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. Find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

For the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= you found, what is the system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn ?

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We know that 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 and it is given that

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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Therefore,

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoaXNvbGF0ZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiNRKGBlX19zc2BGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1JJm1mcmFjR0YkNigtRiw2I1EnYFJfXzBgRictRiM2JS1JI21uR0YkNiRRIjFGJ0ZBLUY+Ni1RIitGJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGYW8tRiw2I1EnYEtfX3BgRicvJS5saW5ldGhpY2tuZXNzR0Zcby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqby8lKWJldmVsbGVkR0ZFLUY+Ni1RIixGJ0ZBRkMvRkdGMUZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZRLDAuMzMzMzMzM2VtRidGY29GQQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0klS19fcEc2IiQiKisrKyEqKiEiKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E3L0klS19fcEc2IiQiKisrKyEqKiEiKEYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDExMDgyKUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=

So,

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

LyQiKisrKyEqKiEiKCwkSSJLRzYiIyIiIiIiKg==

, isolating LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= we will get,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiS0c2IiQiKysrKzUqKSEiKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E0L0kiS0c2IiQiKysrKzUqKSEiKEYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDExMDkxKUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=

In order to achieve an steady state error LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EoYGVfX3NzYEYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFElMC4wM0YnRjNGMw== we need Gain=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrKysrNSopISIo

JSFH

Finding the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn for this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= value:

First, we need to find the frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEid0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn which maintains 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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EuYEdfX0kmb21lZ2E7YEYnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2JVEmZXZhbGNGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSVzdWJzRidGTUZQLUZTNiQtRiM2Ky1GLDYlUSJzRidGTUZQLUYwNi1RIj1GJ0YzRjZGOUY7Rj1GP0ZBRkNGRUZILUYsNiVRIklGJ0ZNRlAtRjA2LVEnJnNkb3Q7RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRmVvLUYsNiVRKCZvbWVnYTtGJy9GTkY4RjMtRjA2LVEiLEYnRjNGNi9GOkZPRjtGPUY/RkFGQ0Zkby9GSVEsMC4zMzMzMzMzZW1GJy1GLDYlUSJHRidGTUZQRmFvLUYsNiVRIktGJ0ZNRlBGM0Yz

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSxHX19JJm9tZWdhO0dGKCwmKiYsJiokSSZvbWVnYUdGKCIiIyEiIiIiKiIiIkY2LCYqJEYwRjNGNkYxIiNPRjQkIisrKys1KikhIigqKF4jJCErKysrWWAhIidGNkYyRjZGN0Y0RjY3I0Yu

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 \342\207\222 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Therefore,

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EtYCZvbWVnYTtfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrNkInXClIISIp

JSFH

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQiKjVNeTkiISIoNyNGLg==

Design correction system that we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSM0NUYnRjlGOQ==, without changing the steady state error.

<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEkc3lzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEqTmV3U3lzdGVtRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiR0YnRi9GMi1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GaG4tRiw2JVEiS0YnRi9GMkY5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmhuLyUmZGVwdGhHRmVvLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRKUJvZGVQbG90RidGL0YyLUZTNiQtRiM2I0YrRjktRjY2LVEiO0YnRjlGOy9GP0YxRkBGQkZERkZGSEZnbkZNRmBvLUYsNiVRK0dhaW5NYXJnaW5GJ0YvRjJGYHBGZHBGYG8tRiw2JVEsUGhhc2VNYXJnaW5GJ0YvRjJGYHAtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZnbkZpbg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

NyQkIiIiSSp1bmRlZmluZWRHJSpwcm90ZWN0ZWRHRiM=

NyQkIitVaWpgNiEiKSQiKyJbWylwSEYl

The design requirement is that the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSM0NUYnRjlGOQ== deg.

We got

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIqNU15OSIhIig=

therefore,we need to advance the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn by:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShQTV9fbmV3R0YoJCIqIWY7X0whIig3I0Yu

We need to add phase, that is why we will use a lead correction network

. We will always take a bit more than the value we need in order to get to the requirement LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn because the gain curve will get larger when we add the correction network, and the phase will get a bit larger.

Let choose

Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

we can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.JSFH

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiYUc2IiQiK1ZldS5VISIq

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EzL0kiYUc2IiQiK1ZldS5VISIqRicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTEyODkpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

The gain of lead correction network,

Setting

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JJGFic0clKnByb3RlY3RlZEc2I0knR19fc3lzRzYiJCIrJillS3hbISM1

And in db:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19zeXNHRigkISs1WE9PaSEiKjcjRi4=

Searching in the bode plot (Art 1) this gain (in db) we will get the frequency, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EsYHdfXyZwaGk7fmBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRJTQyLjZGJ0YzLUYwNi1RIn5GJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGUkYz. For an Optimal solution, let set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHdfX21gRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EsYHdfXyZwaGk7fmBGJ0Yz.

Using the eq.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

We can find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kkdGF1RzYiJCIrIT03XDkiISM2

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E2L0kkdGF1RzYiJCIrIT03XDkiISM2RicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTEzMDApRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

So, the correction system is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiKzwpPkgiWyEjNiIiIkYpRiksJkYkJCIrIT03XDkiRihGKUYpISIi

JSFH

Building the new Transfer function:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCooLCZJInNHRigiIiIiIiRGMiEiIywmRjEkIis8KT5IIlshIzZGMkYyRjIsJkYxJCIrIT03XDkiRjhGMkYyISIiJCIrKysrNSopISIoNyNGLg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LSUlUExPVEc2KC0lJ0NVUlZFU0c2JDdgcTckJCIiIiEiIyQhMTNIVV1KYTRPISM7NyQkIitsOHJEOCEjNiQhMXBPQiI+KT4meSUhIzs3JCQiK0QxXmQ8ISM2JCExKTNRL2VlUE0nISM7NyQkIioiPSYqSEIhIzUkITExXUZUZSIqNCUpISM7NyQkIisnZlYpKTMkISM2JCEyZFF0KzslKls2IiEjOzckJCIrbF0iXDQlISM2JCEyW3N3NTEnKXpaIiEjOzckJCIrVmFuR2EhIzYkITF6ZVpUYkdmPiEjOjckJCIrTW4mbz4oISM2JCExVzlieC1BKGYjISM6NyQkIitvWiY0YSohIzYkITE3YCJ6OU9FVyQhIzo3JCQiKzxfJltFIiEjNSQhMSJSZyZlPXJpWCEjOjckJCIrUEgkb24iISM1JCExWnZ2T24oZi8nISM6NyQkIiskWycqSEEjISM1JCExJEh5cC1tJjMhKSEjOjckJCIrRHphZkQhIzUkITFOIlxmel1fQCohIzo3JCQiKy48MFpIISM1JCEyInopNDJQZywxIiEjOjckJCIrcjxBJFIkISM1JCEyb3RmQSplSz43ISM6NyQkIitRKlJwIVIhIzUkITJlREYpKSpHKj1TIiEjOjckJCIqbkslKVwlISIqJCEyJ1JWd2ZxLzY7ISM6NyQkIipXZHAjWyEiKiQhMiZwIT4oZU5uRTwhIzo3JCQiKm91JXpeISIqJCExJT0scTh4LSY9ISM5NyQkIisqZU94YiYhIzUkITJPIioqSGhaTCMpPiEjOjckJCIrPExpamYhIzUkITI6JmVBWV5MQkAhIzo3JCQiK1BCOipSJyEjNSQhMjJWZ2EqW3h0QSEjOjckJCIrXiUpW21vISM1JCEybVRrPF1gVFYjISM6NyQkIjEsKytpWCZ6TyghIzskITFaIXBCMG5cZyMhIzk3JCQiKzpLLzF6ISM1JCEybltUYlYrbnkjISM6NyQkIisqKSpHTVspISM1JCEyOiVlNHd5Iil6SCEjOjckJCIrKnkiKUg1KiEjNSQhMnkhPiVlal5aPSQhIzo3JCQiKjYieW4oKiEiKiQhMTd1Ikh3KSk9UyQhIzk3JCQiK05KNls1ISIqJCExJDRrPiVlYkpPISM5NyQkIitCeWxDNiEiKiQhMSZbXCgqeSxTKFEhIzk3JCQiK0Q7K2w2ISIqJCEyJXAsXGAobysrJSEjOjckJCIrVUV6MTchIiokITJFO2YsKil5JEhUISM6NyQkIisqeSMzXTchIiokITEvXWUleks+RSUhIzk3JCQiK1dlI1xIIiEiKiQhMCR6JXlVQXhSJSEjODckJCIrNnZQVDghIiokITIlKlx3aFZJbmAlISM6NyQkIisnXCZcKlEiISIqJCExUistNCZIKnlZISM5NyQkIit0JlIkUjkhIiokITFlJT1iciJHQ1shIzk3JCQiK2Y7KDRcIiEiKiQhMWNOZycpeXRzXCEjOTckJCIrJiplWFc6ISIqJCEybTpFSS9QVTcmISM6NyQkIitAKGUpKmYiISIqJCExPFJEWWVxeV8hIzk3JCQiK2kqW3NsIiEiKiQhMVgxKUg4ZWdWJiEjOTckJCIrNHpwOzwhIiokITBGeitdJT4nZiYhIzg3JCQiKzcleiN5PCEiKiQhMS1oWSoqPitmZCEjOTckJCIrcipwPyU9ISIqJCExVScpKWUiUk5DZiEjOTckJCIqJClbIjM+ISIpJCEyTngwTmw0QDQnISM6NyQkIit1ISlmdz4hIiokITE+TCo+dTlARSchIzk3JCQiK01GXVo/ISIqJCExVDVsJCk0P01rISM5NyQkIioqMyY0NyMhIikkITFoLiFScyc9M20hIzk3JCQiKyV5THE+IyEiKiQhMSo9OC5HeFF5JyEjOTckJCIrSGYlZUYjISIqJCExRUNlKlxsNSdwISM5NyQkIitHX1tkQiEiKiQhMVlmSXdDYFJyISM5NyQkIisoNGA/VyMhIiokITFiTCRlVFshPnQhIzk3JCQiKyJmYSdIRCEiKiQhMSJlQE1qdCQqXCghIzk3JCQiK0smKVI/RSEiKiQhMChHUXonZi1vKCEjODckJCIrWHdSOUYhIiokITBtKnAhZl05J3khIzg3JCQiKShvPCJHISIoJCExKHpWKltVb1UhKSEjOTckJCIrZkVqN0ghIiokITFAJm9YI1FwQiMpISM5NyQkIis5WzY8SSEiKiQhMWE9LGsjNFVTKSEjOTckJCIrZlxNREohIiokITF5U3B1KWVSZSkhIzk3JCQiK1p2WFBLISIqJCEwQ05gKjNuaSgpISM4NyQkIitVPWZgTCEiKiQhMWw2JkgwdislKikhIzk3JCQiKzlAKlFaJCEiKiQhMS8qKSpwOi9mNiohIzk3JCQiKzR5XSlmJCEiKiQhMVJRZilmJiopKkcqISM5NyQkIitCUGZGUCEiKiQhMSplZ2Z5I3poJSohIzk3JCQiKypSQikqKlIhIiokITFAbWhlakopeiohIzk3JCQiK2hVJD5IJSEiKiQhMm9lRmVBZkIsIiEjOTckJCIrZSN5YGclISIqJCEyLVMzImU1ZlY1ISM5NyQkIitsTHJUXCEiKiQhMil6aCVRM3dMMiIhIzk3JCQiK1Q4aC1gISIqJCEyRmF0MC0mZSw2ISM5NyQkIitOZycpKm8mISIqJCEyaiYqNGpPNiJHNiEjOTckJCIrKkgtYTUnISIqJCEyUiYpM1Fxckc6IiEjOTckJCIyJioqKioqSGQmR15sISM7JCEyYyQ9SUxhIWU8IiEjOTckJCIrays3VnYhIiokITJQQDBhUGdnQCIhIzk3JCQiK1VQNiZvKSEiKiQhMiM+LFs6aSIpWzchIzk3JCQiKywrKys1ISIpJCEyWCFlZm56SnU3ISM5NyQkIissYVJeNiEiKSQhMCpbaCE+JjMkSCIhIzc3JCQiK3B6VEU6ISIpJCExI3lYRis9UEoiISM4NyQkIipsKmVCPyEiKCQhMlkucCFIRU4+OCEjOTckJCIrKnomcCNvIyEiKSQhMUwyTyNvLTJLIiEjODckJCIrNi5bY04hIikkITIzaGMhcDkxRzghIzk3JCQiK3BqJ1tyJSEiKSQhMkVwKXAjUTcnWzghIzk3JCQiMjArKz8kPmJdaSEjOiQhMnlUdzhnLltRIiEjOTckJCIrUHhVJ0cpISIpJCEyRCRcaS0vQU05ISM5NyQkIitWNmEpNCIhIigkITJZMGhDYFM0XCIhIzk3JCQiK3olW2pYIiEiKCQhMjAnPiVlM2whWzohIzk3JCQiK0p4cEk+ISIoJCExKilITTRMPys7ISM4NyQkIis8emFmRCEiKCQhMktUOTtYZlhrIiEjOTckJCIrInlAS1IkISIoJCExTjpwWTBjIW8iISM4NyQkIitmRVYpXCUhIigkITJpVyZlLkkjKjM8ISM5NyQkIitLTGlqZiEiKCQhMVBUJzNybTN0IiEjODckJCIrIz5WZyF6ISIoJCEyJEclMz5Mand1IiEjOTckJCIrUEo2WzUhIickITIpKnBFMTxTL3ciISM5NyQkIisiXCZcKlEiISInJCEyL1o0ZktDLHgiISM5NyQkIit1KnA/JT0hIickITIkKXA+OEVcdXgiISM5NyQkIispM2A/VyMhIickITIjKVxwLD4kKUh5IiEjOTckJCIqYmR1QiQhIiYkITI4YSpbOzc7KHkiISM5NyQkIitbVSQ+SCUhIickITIoPipSIlxWSiF6IiEjOTckJCIrVGcnKSpvJiEiJyQhMSIpejMiWyRwI3oiISM4NyQkIitUKzdWdiEiJyQhMVwyUSRRKVsleiIhIzg3JCQiJysrNSEiIiQhMl8hUkFFQyVleiIhIzktJSZDT0xPUkc2JiUkUkdCRyQiKUMpZXElISIpJCIiISEiIiQiKCc+IVwmISIpLSUlVklFV0c2JDskIiIiISIjJCInKys1ISIiJShERUZBVUxURy0mJSZfQVhJU0c2IyIiIjYrLSUrX0dSSURMSU5FU0c2IyIjQC0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIiLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lKUxPQ0FUSU9ORzYjISIiLSUmX01PREVHNiMiIiItJSZfTU9ERUc2IyIiIi0lJl9NT0RFRzYjIiIiLSYlJl9BWElTRzYjIiIjNictJStfR1JJRExJTkVTRzYjIiM1LSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiItJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUrQVhFU0xBQkVMU0c2J1EtRnJlcX5bcmFkL3NdNiJRLVBoYXNlfltkZWcuXTYiLSUlRk9OVEc2JSUoREVGQVVMVEclKERFRkFVTFRHIiM1JStIT1JJWk9OVEFMRyUpVkVSVElDQUxHLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkPyghIiItJSlCT1VORFNfWUc2IyQiI3EhIiItJS1CT1VORFNfV0lEVEhHNiMkIiYhPjkhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlP00hIiItJSlDSElMRFJFTkc2Ig==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIiIiSSp1bmRlZmluZWRHJSpwcm90ZWN0ZWRHRiM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIis2O24vWSEiKSQiKyZIK19FJUYl

As we can see, we got the system margins and their frequency:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQiKzY7bi9ZISIpNyNGLg==

JSFH

Therefore, the correction network is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYEdfX2NgRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiKzwpPkgiWyEjNiIiIkYpRiksJkYkJCIrIT03XDkiRihGKUYpISIi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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Given the following system and bode plots:

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Analyze the system stability using only Nyquist for the controller LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSI9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSIxRidGMkYy.

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

Using Nyquist method:

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print(); # input placeholder

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NyI=

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print(); # input placeholder

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print(); # input placeholder

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JSFH

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print(); # input placeholder

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print(); # input placeholder

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print(); # input placeholder

IiIh

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print(); # input placeholder

IiIh

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Now we will find where the curve cross the axis:

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print(); # input placeholder

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print(); # input placeholder

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The curve cross the Real axis in:

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print(); # input placeholder

IyEiIiIiJA==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdvbWVnYTJHRihGKDci

Therefore, the curve does not cross the imaginary axis.

JSFH

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JSFH

Using the Nyquist curve and the fact that we used the Nyquist method while knowing the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, we have to see if we have laps around the point (-1,0).

In this case, we dont have a lap around the point -1. Therefore, the system is stable. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Finding LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY2Ni1RIn5GJ0Y5RjsvRj9GPUZARkJGREZGRkhGSi9GTkZMLUYsNiVRI0dNRidGL0YyRjk= from the given bode above:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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print(); # input placeholder

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print(); # input placeholder

NyQkIisvKDQ4RSQhIikkIitlRm8kXCghIzU=

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print(); # input placeholder

L0kjUE1HNiIkIisvKDQ4RSQhIik=

L0kjR01HNiIkIispM0RDYSohIio=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Design Proportional controller so LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYEtfX3ZgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSMxMEYnRjNGMw==. Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEtfX3BgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

The design demand is

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The system is Type 1. Therefore

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print(); # input placeholder

JSFH

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0klS19fcEc2IiIjNQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EuL0klS19fcEc2IiIjNUYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDExNTg3KUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=

Draw the Nyquist plot for the new system. Explain the changes from the Nyquist you draw in article 1. Does the system is stable in closed loop?

<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>

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print(); # input placeholder

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NyI=

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print(); # input placeholder

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print(); # input placeholder

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JSFH

Point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

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print(); # input placeholder

ISM6

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print(); # input placeholder

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point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

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print(); # input placeholder

IiIh

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print(); # input placeholder

IiIh

Now we will find where the curve cross the axis:

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print(); # input placeholder

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print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNwMUdGKCMhIzUiIiQ3I0Yu

The curve cross the Real axis in:

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

IyEjNSIiJA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdvbWVnYTJHRihGKDci

Therefore, the curve does not cross the imaginary axis.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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Therefore, the system is unstable in closed loop.

JSFHJSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Design correction system that fulfill the following:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYGtfX3ZgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSMxMEYnRjNGMw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUS8mR3JlYXRlckVxdWFsO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEjNTBGJ0Y5Rjk=

Explain each step.

<Text-field style="Heading 2" layout="Heading 2">Art. 4</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS1LR19fSSZvbWVnYTtHRigsJiomLCYqJEkvJm9tZWdhO19fJnBoaTtHRigiIiMiIiJGNEY0ISIiLCZGMUY0IiIlRjRGNSEjZyomXiNGNEY0LCYqKEYyRjVGMEY1RjZGNSEjUyooRjBGNUYyRjRGNkY1IiM/RjRGNDcjRi4=

JSFH

We need to find the frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZvbWVnYTtfXyZwaGk7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==.

We will find it solving the

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkZXExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2I1EvYEtHX19JJm9tZWdhO2BGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjFGJ0Y5

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTFHRigvLCYqJiwmKiRJLyZvbWVnYTtfXyZwaGk7R0YoIiIjIiIiRjVGNSEiIiwmRjJGNSIiJUY1RjYhI2cqJl4jRjVGNSwmKihGM0Y2RjFGNkY3RjYhI1MqKEYxRjZGM0Y1RjdGNiIjP0Y1RjVGNTcjRi4=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS8mb21lZ2E7X18mcGhpO0dGKCQiK1AqSFZDIyEiKjcjRi4=

Entering with this frequency and finding the suitable argument:JSFH

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQTUdGKCQhKl9aeVUjISIoNyNGLg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Therefore,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSkmcGhpO19fbUdGKCQiKl9aeVUoISIoNyNGLg==

As we learned LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSMzMEYnRjktRjY2LVErJmRvdGVxZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZXLUZQNiRRIzYwRidGOUY5 deg. We above this range, therefore we will use lag correction network:

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

In order to find the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= we will use the eq.

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

where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the gain for the frequency which is suitable for the phase: (design demand)-180=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEjNTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSgmbWludXM7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUYsNiRRJDE4MEYnRi8=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

ISRJIg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

From the given bode above, we can see that this frequency is

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1E1YCZvbWVnYTtfXyZwaGk7fnRhZ2BGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFElMC40OEYnRjMtRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkg=

[rad/sec]. For this frequency, the gain is

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEjMjVGJ0Y5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZN

Therefore,

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJhR0YoJCIrX0tUQmMhIzY3I0Yu

From the eq.

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

we can isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoaXNvbGF0ZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJGVxMkYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEmJnRhdTtGJy9GMEZFRkFGQQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kkdGF1RzYiJCIrcihbWnEkISIo

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1E2L0kkdGF1RzYiJCIrcihbWnEkISIoRicvJSthY3Rpb250eXBlR1E8bWFwbGVzb2Z0LmNvbTpsYWJlbChMMTE3MDYpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw==

So the lag correction network is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1ErYEdfX2N+bGFnYEYn

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQiK0xMTCQzIyEiKSIiIkYpRiksJkYkJCIrcihbWnEkISIoRilGKSEiIg==

For this correction network we can find the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn of the whole system, we know

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCosSSJzR0YoISIiLCZGMCIiIkYzRjNGMSwmRjBGMyIiI0YzRjEsJkYwJCIrTExMJDMjISIpRjNGM0YzLCZGMCQiK3IoW1pxJCEiKEYzRjNGMSIjPzcjRi4=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIisjSG5JUiIhIikkIisoNEJgTyIhIio=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQkIismKipINVolISIpJCIrayEqR0FcISM1

We still didnt achieve the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we wanted. we need to take a bit smaller angle, so we now enter to the bode with phase=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEjNjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSgmbWludXM7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUYsNiRRJDE4MEYnRi8=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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and go the whole process again.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field>

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Given the following system:

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Design proportional controller so that the velocity entrance error will be 10% from the entrance error.

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

For this question we assume the system has a single feedback.

Because the system has one zero at the origin, the system is Type 1.JSFH

It is given that 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 , therefore

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print(); # input placeholder

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Using the eq. 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 we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:JSFH

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LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkL0klS19fdkdGJy1JJmxpbWl0R0YkNiQqKEkic0dGJyIiIkkiS0dGJ0YwSSJHR0YnRjAvRi8iIiFGMQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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LUknYXNzaWduRyUqcHJvdGVjdGVkRzYjL0kiS0c2IiQiKysrKys1ISIo

JSFH

For the controller you designed, what are the system stability margins in closed loop?

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

Finding the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY2Ni1RIn5GJ0Y5RjsvRj9GPUZARkJGREZGRkhGSi9GTkZMLUYsNiVRI0dNRidGL0YyRjk= of the system:JSFH

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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In order to find the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjR01GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we need to find the frequency we ask the Imaginary Part to be zero.JSFH

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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PkkjR01HNiItSSZldmFsZkclKnByb3RlY3RlZEc2IywkLSZJJGxvZ0c2JEYnSShfc3lzbGliR0YkNiMiIzU2Iy1JJmV2YWxjR0YtNiMtSSRhYnNHRic2Iy1JJXN1YnNHRic2JC9JJm9tZWdhR0YkSSsmb21lZ2E7X19jR0YkSSxHX19JJm9tZWdhO0dGJCEjPw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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In order to find the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUE1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn we need to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZvbWVnYTtfXyZwaGk7YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== , isolating it from the eq.

PkkkZXExRzYiLUkmZXZhbGNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2Iy8tSSRhYnNHRig2Iy1JJXN1YnNHRig2JC9JJm9tZWdhR0YkSS8mb21lZ2E7X18mcGhpO0dGJEksR19fSSZvbWVnYTtHRiQiIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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PkkvJm9tZWdhO19fJnBoaTtHNiItSSZldmFsZkclKnByb3RlY3RlZEc2IyYtSSZzb2x2ZUc2JEYnSShfc3lzbGliR0YkNiQvLCQqJCwmKiQsJiooRiMhIiIsJiokRiMiIiMiIiIiIipGOkY2LCZGOEY6IiQrIkY6RjYiI0kqKEY3RjZGI0Y6RjxGNkY2RjlGOiomRjchIiNGPEZBIiRwIiNGOkY5JCIrKysrK0khIihGOkYjNiNGOQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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PkkjUE1HNiIsJi1JJmV2YWxmRyUqcHJvdGVjdGVkRzYjLCQqJi1JKWFyZ3VtZW50RzYkRihJKF9zeXNsaWJHRiQ2Iy1JJXN1YnNHRig2JC9JJm9tZWdhR0YkSS8mb21lZ2E7X18mcGhpO0dGJEksR19fSSZvbWVnYTtHRiQiIiJJI1BpR0YoISIiIiQhPUY4RjtGOA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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JSFH

SSNQTUc2Ig==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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JSFHJSFH

Design correction system that fulfill the following:

Velocity entrance error will be 10% from the entrance error.

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>

The design requirement is that the PM \342\211\245 70 deg.

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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ErYCZwaGk7X19tYEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== is greater that the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ErYCZwaGk7X19tYEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== range (was mentioned in previous questions), so we will use lag correction network.

QyQ+SSlHX19jfmxhZ0c2IiomLCYqKEkiYUdGJSIiIkkic0dGJUYqSSR0YXVHRiVGKkYqRipGKkYqLCYqJkYrRipGLEYqRipGKkYqISIiRi8=

In order to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= we use the eq.

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in order to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y4USdub3JtYWxGJ0YrRjo= we will need to find the frequency ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EyYCZvbWVnYTtfXyZwaGk7J2BGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= ) which we get

PkkmcGhhc2VHNiIsJkkpJnBoaTtfX21HRiQiIiIhJCE9Ric=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZwaGFzZUdGKCQhK3MrIVs7IiEiKDcjRi4=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH

PkkwJm9tZWdhO19fJnBoaTsnRzYiJi1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQvLUkkdGFuR0YoNiMsJComSSZwaGFzZUdGJCIiIkkjUGlHRilGMyNGMyIkIT0qJi1JJmV2YWxjR0YoNiMtSSNJbUdGKTYjSSxHX19JJm9tZWdhO0dGJEYzLUY5NiMtSSNSZUdGKUY9ISIiSSZvbWVnYUdGJDYjRjM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+STAmb21lZ2E7X18mcGhpOydHRigkIStCPigqPkYhIik3I0Yu

We got

STAmb21lZ2E7X18mcGhpOydHNiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCErQj4oKj5GISIp

[rad/sec]. Now, using the logarithmic eq. we can find

PkkiQUc2IiwkLSZJJGxvZ0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiM1NiMtSSRhYnNHRio2Iy1JJXN1YnNHRio2JC9JJm9tZWdhR0YkSTAmb21lZ2E7X18mcGhpOydHRiRJLEdfX0kmb21lZ2E7R0YkIiM/

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoJCErbV5YOFAhIik3I0Yu

Now we can find the parameter JSFH

SSJhRzYi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

JCIrYyR5Kio9KCEiKQ==

, so now we can find

PkkkdGF1RzYiLCQqJkkiYUdGJCEiIkkwJm9tZWdhO19fJnBoaTsnR0YkRigiIzU=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR0YXVHRigkIStZInpMNiYhIzc3I0Yu

So, after having LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NjQ7RicvRjBGPUY5Rjk= we can build

SSlHX19jfmxhZ0c2Ig==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYsJkkic0c2IiQhK1ImM2xuJCEjNSIiIkYpRiksJkYkJCErWSJ6TDYmISM3RilGKSEiIg==

PkknR19fbmV3RzYiKiZJIkdHRiQiIiJJKUdfX2N+bGFnR0YkRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdHX19uZXdHRigsJCosSSJzR0YoISIiLCZGMCIiIiIiJEYzRjEsJkYwRjMiIzVGM0YxLCZGMCQhK1ImM2xuJCEjNUYzRjNGMywmRjAkIStZInpMNiYhIzdGM0YzRjFGNDcjRi4=

QyY+SSdOZXdTeXNHNiItSSpOZXdTeXN0ZW1HRiU2I0knR19fbmV3R0YlISIiLUkpQm9kZVBsb3RHRiU2I0YkIiIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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print(); # input placeholder

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LUksUGhhc2VNYXJnaW5HNiI2I0knTmV3U3lzR0Yk

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print(); # input placeholder

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The correction system is:

SSlHX19jfmxhZ0c2Ig==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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JSFH

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