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

In this worksheet LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= means gain, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the control system and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the system feedback.

The system has negative feedback as shown in the figure below.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The junctions method:

This method is given in order to find the transfer function of block diagram without using identities manipulations.

The junction method is based on the summation of the inputs and outputs (will be marked as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFNfX2lgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn ) for each junction.

After summing the all diagram junctions all it's left to do is to solve X equations with X variables.

The junction method example:

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F^p-F;6(F=-FC6&FE-FL6#-FO6$$"%5#)F*$"%?7F*FUFZFfnFjn-F]o6%7$$"%qzF*$"%]5F*FdoFio-F[p6#Qc^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F^p-F;6(F=-FC6&FE-FL6#-FO6$$"%!z*F*$"%+<F*FUFZFfnFjn-F]o6%7$$"%]&*F*$"%I:F*FdoFio-F[p6#Qc^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F^pLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The system of equations is:JSFH

Qyg+SSJBRzYiLUknTWF0cml4R0YlNiMvSSQlaWRHRiUiNUEtKSlSVjJXblc9ISIiPkkiQkdGJS0mSSdWZWN0b3JHRiU2I0knY29sdW1uR0YlNiMvRioiNVUuKSlSVjJXblc9Riw+SSJYR0YlLUYwNiMvRioiNWkvKSlSVjJXblc9Riw=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiWEc2IiwmLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGKUkoX3N5c2xpYkdGJDYkSSJBR0YkRiMiIiJJIkJHRiRGMQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

Solving this system..

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

The set of equation about the check points 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 is:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Qyw+SSRlcTFHNiIvJkkiU0dGJTYjIiIiLCYqJiZJIkhHRiVGKUYqJkYoNiMiIiVGKiEiIkkiUkdGJUYqRjI+SSRlcTJHRiUvJkYoNiMiIiMsJiomJkkiR0dGJUYpRipGJ0YqRioqJiZGLkY4RipGL0YqRjJGMj5JJGVxM0dGJS8mRig2IyIiJCwmKiYmRi5GREYqJkYoNiMiIiZGKkYyRjdGKkYyPkkkZXE0R0YlL0YvKiYmRj1GOEYqRkNGKkYyPkkkZXE1R0YlL0ZJKiYmRj1GREYqRi9GKkYy

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Solving 5 equation with 5 variables:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Pkkkc29sRzYiLUkmc29sdmVHRiQ2JDwnSSRlcTFHRiRJJGVxMkdGJEkkZXEzR0YkSSRlcTRHRiRJJGVxNUdGJDwnJkkiU0dGJDYjIiIiJkYwNiMiIiMmRjA2IyIiJCZGMDYjIiIlJkYwNiMiIiY=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig8Jy8mSSJTR0YoNiMiIiIqKEkiUkdGKEYzLCgqKCZJIkdHRig2IyIiI0YzJkY5NiMiIiRGMyZJIkhHRihGPUYzRjMqJkY4RjMmRkBGOkYzRjNGM0YzRjMsKiooJkY5RjJGM0Y4RjMmRkBGMkYzRjNGN0YzRkFGM0YzRjMhIiIvJkYxRjoqKiwmRjdGM0YzRjNGM0Y1RjNGRUYzRkNGRy8mRjFGPSooRjVGM0ZFRjNGQ0ZHLyZGMTYjIiIlKipGOEYzRjVGM0ZFRjNGQ0ZHLyZGMTYjIiImKixGPEYzRjhGM0Y1RjNGRUYzRkNGRzcjRi4=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The value that needed for the transfer function is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFNfXzVgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EnYFNfXzVgRictSSNtb0dGJDYtUSJ+RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRjA2LVEoJmVxdWl2O0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZOLUYsNiVRIkNGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRidGMw== . So the diagram transfer function is:

LUklc3Vic0clKnByb3RlY3RlZEc2JC8mSSJTRzYiNiMiIiZJIkNHRikqJiZJJHNvbEdGKUYqIiIiSSJSR0YpISIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyomSSJSRzYiISIiSSJDR0YlIiIiKiomSSJHR0YlNiMiIiRGKCZGKzYjIiIjRigmRis2I0YoRigsKiooRjFGKEYuRigmSSJIR0YlRjJGKEYoKihGLkYoRipGKCZGNkYsRihGKComRi5GKCZGNkYvRihGKEYoRihGJg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=