Now we will find where the curve cross the axis: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 = print(); # input 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 = print(); # input placeholderThe curve cross the Real axis in:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEjcDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input 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 = print(); # input placeholderTherefore, the curve does not cross the imaginary axis.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Now we will find where the curve cross the axis: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 = print(); # input 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 = print(); # input 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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The curve cross the Real axis in: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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEjcDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUYsNiUtSSNtb0dGJDYtUSIsRidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0ZOLyUqc3ltbWV0cmljR0ZOLyUobGFyZ2VvcEdGTi8lLm1vdmFibGVsaW1pdHNHRk4vJSdhY2NlbnRHRk4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GIzYjLUYvNiNRIUYnRkAtRjs2JEZCRj4= = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input 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 = print(); # input placeholderThe curve cross the Imaginary axis in:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbWlHRiQ2JVEjcDJGJy8lJ2l0YWxpY0dGOy9GMFEnaXRhbGljRic= = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Using the Nyquist plots above, Find for which positive gains each of the transfer function is stable in closed loop.JSFH
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>The Nyquist stability equation:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJORidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJwRidGL0YyRjk=z- zeros of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIitGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSRLR0hGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLw== in the nyquistp- poles of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIitGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSRLR0hGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLw== in the nyquistN- clockwise rounds around 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 of the Nyquist curve.For stability, we want LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
<Text-field style="Heading 3" layout="Heading 3">G1</Text-field>For stability we will set, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. Therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=. so LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GUy1JI21uR0YkNiRRIjFGJ0Y5Rjk=.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 3" layout="Heading 3">G2</Text-field>For stability we will set, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. Therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. so LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
Now we will find where the curve cross the axis: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 = print(); # input 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 = print(); # input placeholderThe curve cross the Real axis in: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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpJm9tZWdhOzJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSZzb2x2ZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUklbXN1YkdGJDYmLUYsNiVRInVGJ0YvRjItRiM2Iy1JI21uR0YkNiRRIjFGJ0Y5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1Gam42JEZfb0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEoJm9tZWdhO0YnL0YwRj1GOUY5 = print(); # input placeholderJSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEsTnlxdWlzdFBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSVzeXMxRidGL0YyL0YzUSdub3JtYWxGJw==%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
For stability we will want LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, So for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
In this system we got 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, Hence, the system is stable.
Now, using Nyquist, check the stability of the outer circuit. Find the range of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for which the system is stable.
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>Now, The transfer function has not changed allot, the new transfer function is: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(); # input placeholderSo the nyquist curve will not change \342\207\222LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. \342\207\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(); # input placeholder
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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 the following 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the Nyquist of the system for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5Rjk= and find all the crossing points of the curve with the Real and Imaginary axis.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>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print(); # input placeholderJSFH
Now we will find where the curve cross the axis:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpJm9tZWdhOzFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSZzb2x2ZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUklbXN1YkdGJDYmLUYsNiVRInZGJ0YvRjItRiM2Iy1JI21uR0YkNiRRIjFGJ0Y5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1Gam42JEZfb0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEoJm9tZWdhO0YnL0YwRj1GOUY5 = print(); # input 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 = print(); # input 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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpJm9tZWdhOzJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSZzb2x2ZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUklbXN1YkdGJDYmLUYsNiVRInVGJ0YvRjItRiM2Iy1JI21uR0YkNiRRIjFGJ0Y5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1Gam42JEZfb0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEoJm9tZWdhO0YnL0YwRj1GOUY5 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input 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%;%;JSFHJSFH
The Curve crosses the Real and Imaginary axis in :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print(); # input placeholderJSFH
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=For which values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= the system is stable.
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>For stability we want LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. In our case, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. Therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. JSFH
The values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for which the system is stable: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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Find the maximal value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for which the system is stable for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>For achieving stable system for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= we can see from the range in the previous article that the maximal value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is determine from the cross with the real axis in it's negative part. We want to see for which value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= the cross point will be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv. JSFHWe will check what we get for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=: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print(); # input placeholderJSFH
Now we will find where the curve cross the Imaginary axis: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 = print(); # input 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 = print(); # input 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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjcDJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSVldmFsRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNictSSVtc3ViR0YkNiYtRiw2JVEidkYnRi9GMi1GIzYjLUkjbW5HRiQ2JFEiMUYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEoJm9tZWdhO0YnL0YwRj1GOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GWDYlLUYsNiVRKSZvbWVnYTsyRidGL0YyRmduRl1vRjk= = print(); # input placeholderBecause the curve does not cross the real axis, what we aimed for.
The maximal value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=. JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>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Given the following positive feedback control 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is known that:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInNGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== does not have poles or zeros on ORHP.By entering Heaviside and finding the steady state error we get that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjdGJ0Y5Rjk=. For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= we found above, we have part of the Nyquist curve: 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if the system is stable or not.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will draw the continue of the Nyquist curve (in 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 are no poles or zeros on the ORHP, therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. The feedback is positive, so we check how much curves there are around the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv. We got LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=.
We know, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ6RidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJwRidGL0YyRjk= and therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=.Hence, the system is Unstable.