Question
Download Solution PDFएक भौतिक प्रणाली के अवकल समीकरण मॉडल दिया होने पर निम्न प्रणाली का समय स्थिरांक निर्धारित करें।
\(40 \frac{dx}{dt}+2x=f(t)\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
समय स्थिरांक \(\tau = \frac{{ - 1}}{{{\rm{real\ part\ of\ Dominant\ pole}}}}\)
गणना:
\(40\frac{{dx}}{{dt}} + 2x = f\left( t \right)\)
लाप्लास रूपांतर लेने पर हम प्राप्त करते हैं
40 s X(s) + 2X(s) = 12(s)
\(\frac{{X\left( s \right)}}{{F\left( s \right)}} = \frac{1}{{40s + 2}}\)
\( = \frac{1}{{40\left( {s + \frac{1}{{20}}} \right)}}\)
ध्रुव -1/20 पर होगा।
समय स्थिरांक \( = \frac{1}{{pole}} = 20\)
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