એક યુનિટી ફીડબેક સિસ્ટમનું ઓપન-લૂપ ટ્રાન્સફર ફંક્શન G(s) = K(s + 2)/s² (s² + 7s + 12) છે. સિસ્ટમનો ટાઇપ કયો છે?
જવાબ અને પગલાવાર ઉકેલ
સિસ્ટમ ટાઇપ એટલે ઓપન-લૂપ ટ્રાન્સફર ફંક્શનમાં શુદ્ધ ઇન્ટિગ્રેટર (ઉદ્ગમ બિંદુ પરના પોલ) ની સંખ્યા. અહીં છેદમાં s² છે, તેથી ઉદ્ગમ બિંદુ પર બે પોલ છે અને સિસ્ટમ ટાઇપ 2 છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
Finite poles such as roots of s²+7s+12=(s+3)(s+4) do not affect system type. Likewise the zero at −2 does not reduce the count unless it exactly cancels a pole at the origin, which it does not. Type determines steady-state error constants for step, ramp and parabolic inputs.
How to Solve It in the Exam
Count uncancelled poles at the origin only.
Important Exam Point
Do not count total denominator order.
Quick Trick
Count uncancelled poles at the origin only.
Common Mistake
Calling it Type 4 because the overall denominator is fourth order.
For a unity feedback system, the open loop transfer function is G(s) = K(s + 2)/s² (s² + 7s + 12). What is the type of system?
Answer & step-by-step solution
System type equals the number of pure integrators (poles at the origin) in the open-loop transfer function G(s)H(s). Here the denominator contains s², so there are two poles at the origin and the system is Type 2.
Concept & Reasoning
Finite poles such as roots of s²+7s+12=(s+3)(s+4) do not affect system type. Likewise the zero at −2 does not reduce the count unless it exactly cancels a pole at the origin, which it does not. Type determines steady-state error constants for step, ramp and parabolic inputs.
How to Solve It in the Exam
Count uncancelled poles at the origin only.
Important Exam Point
Do not count total denominator order.
Quick Trick
Count uncancelled poles at the origin only.
Common Mistake
Calling it Type 4 because the overall denominator is fourth order.
एक यूनिटी फीडबैक सिस्टम का ओपन-लूप ट्रांसफर फंक्शन G(s) = K(s + 2)/s² (s² + 7s + 12) है। सिस्टम का टाइप क्या है?
उत्तर और चरणबद्ध हल
सिस्टम टाइप ओपन-लूप ट्रांसफर फंक्शन में शुद्ध इंटीग्रेटरों (मूल बिंदु पर पोल) की संख्या है। यहाँ हर (denominator) में s² है, अतः मूल बिंदु पर दो पोल हैं और सिस्टम टाइप 2 है।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
Finite poles such as roots of s²+7s+12=(s+3)(s+4) do not affect system type. Likewise the zero at −2 does not reduce the count unless it exactly cancels a pole at the origin, which it does not. Type determines steady-state error constants for step, ramp and parabolic inputs.
How to Solve It in the Exam
Count uncancelled poles at the origin only.
Important Exam Point
Do not count total denominator order.
Quick Trick
Count uncancelled poles at the origin only.
Common Mistake
Calling it Type 4 because the overall denominator is fourth order.
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