Consider the following statements regarding Steady-State Error:
1. Type of system determines steady-state error for standard inputs.
2. Increasing system gain reduces steady-state error.
3. Integral control eliminates steady-state error for step input.
4. Steady-state error is independent of system type.
Which of the above statements is/are correct?
Answer & step-by-step solution
It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. Integral action increases low-frequency gain and improves steady-state accuracy, but it can also affect transient stability margins. Key relation: Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s) as s→0 for unity feedback.
Exam focus: Type-0/1/2 classification comes from poles at the origin. Common trap: Do not infer stability from system type alone.
Statement-wise Verification
- Statement 1 - Correct.
Type of system determines steady-state error for standard inputs.
It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. - Statement 2 - Correct.
Increasing system gain reduces steady-state error.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 3 - Correct.
Integral control eliminates steady-state error for step input.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 4 - Incorrect.
Steady-state error is independent of system type.
The correct principle is: It determines which standard polynomial inputs can be tracked with zero or finite steady-state error.
Core Concept
In unity-feedback control, system type is the number of pure integrators in the open-loop transfer function. It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. Integral action increases low-frequency gain and improves steady-state accuracy, but it can also affect transient stability margins.
Formula / Key Relationship
Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s) as s→0 for unity feedback.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Type-0/1/2 classification comes from poles at the origin.
Common Mistake
Do not infer stability from system type alone.
Quick Revision
System Type Gain and Integral Action is linked with Steady-State Error, Steady-State Analysis and Control Systems. Type-0/1/2 classification comes from poles at the origin.
स्थायी-अवस्था त्रुटि (Steady-State Error) के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. सिस्टम का टाइप मानक इनपुट के लिए स्थायी-अवस्था त्रुटि निर्धारित करता है।
2. सिस्टम गेन बढ़ाने से स्थायी-अवस्था त्रुटि घटती है।
3. इंटीग्रल कंट्रोल स्टेप इनपुट के लिए स्थायी-अवस्था त्रुटि समाप्त करता है।
4. स्थायी-अवस्था त्रुटि सिस्टम टाइप से स्वतंत्र है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
सिस्टम टाइप तय करता है कि कौन-से मानक बहुपद इनपुट शून्य या परिमित स्थायी-अवस्था त्रुटि से ट्रैक होंगे। इंटीग्रल क्रिया निम्न-आवृत्ति गेन बढ़ाकर स्थायी-अवस्था सटीकता सुधारती है, पर स्थिरता मार्जिन प्रभावित कर सकती है। मुख्य संबंध: यूनिटी फीडबैक में s→0 पर Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s)।
परीक्षा फोकस: टाइप 0/1/2 मूल बिंदु पर पोल से। सामान्य गलती: केवल टाइप से स्थिरता का अनुमान लगाना।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Type of system determines steady-state error for standard inputs.
It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. - Statement 2 - Correct.
Increasing system gain reduces steady-state error.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 3 - Correct.
Integral control eliminates steady-state error for step input.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 4 - Incorrect.
Steady-state error is independent of system type.
The correct principle is: It determines which standard polynomial inputs can be tracked with zero or finite steady-state error.
Core Concept
In unity-feedback control, system type is the number of pure integrators in the open-loop transfer function. It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. Integral action increases low-frequency gain and improves steady-state accuracy, but it can also affect transient stability margins.
Formula / Key Relationship
Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s) as s→0 for unity feedback.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Type-0/1/2 classification comes from poles at the origin.
Common Mistake
Do not infer stability from system type alone.
Quick Revision
System Type Gain and Integral Action is linked with Steady-State Error, Steady-State Analysis and Control Systems. Type-0/1/2 classification comes from poles at the origin.
સ્થાયી-સ્થિતિ ત્રુટિ (Steady-State Error) સંબંધિત નીચેના વિધાનો ધ્યાનમાં લો:
1. સિસ્ટમનો ટાઇપ પ્રમાણભૂત ઇનપુટ માટે સ્થાયી-સ્થિતિ ત્રુટિ નક્કી કરે છે.
2. સિસ્ટમ ગેઇન વધારવાથી સ્થાયી-સ્થિતિ ત્રુટિ ઘટે છે.
3. ઇન્ટિગ્રલ કંટ્રોલ સ્ટેપ ઇનપુટ માટે સ્થાયી-સ્થિતિ ત્રુટિ દૂર કરે છે.
4. સ્થાયી-સ્થિતિ ત્રુટિ સિસ્ટમ ટાઇપથી સ્વતંત્ર છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
સિસ્ટમ ટાઇપ નક્કી કરે છે કે કયા પ્રમાણભૂત બહુપદી ઇનપુટ શૂન્ય કે મર્યાદિત સ્થાયી-સ્થિતિ ત્રુટિ સાથે ટ્રેક થશે. ઇન્ટિગ્રલ ક્રિયા નીચી-આવૃત્તિ ગેઇન વધારી સ્થાયી-સ્થિતિ ચોકસાઈ સુધારે છે, પરંતુ સ્થિરતા માર્જિનને અસર કરી શકે. મુખ્ય સંબંધ: યુનિટી ફીડબેકમાં s→0 પર Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s).
પરીક્ષા મુદ્દો: ટાઇપ 0/1/2 ઉદ્ગમ બિંદુ પરના પોલથી. સામાન્ય ભૂલ: ફક્ત ટાઇપ પરથી સ્થિરતાનું અનુમાન કરવું.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Type of system determines steady-state error for standard inputs.
It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. - Statement 2 - Correct.
Increasing system gain reduces steady-state error.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 3 - Correct.
Integral control eliminates steady-state error for step input.
Integral action increases low-frequency gain and improves steady-state accuracy - Statement 4 - Incorrect.
Steady-state error is independent of system type.
The correct principle is: It determines which standard polynomial inputs can be tracked with zero or finite steady-state error.
Core Concept
In unity-feedback control, system type is the number of pure integrators in the open-loop transfer function. It determines which standard polynomial inputs can be tracked with zero or finite steady-state error. Integral action increases low-frequency gain and improves steady-state accuracy, but it can also affect transient stability margins.
Formula / Key Relationship
Kp=lim G(s), Kv=lim sG(s), Ka=lim s²G(s) as s→0 for unity feedback.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Type-0/1/2 classification comes from poles at the origin.
Common Mistake
Do not infer stability from system type alone.
Quick Revision
System Type Gain and Integral Action is linked with Steady-State Error, Steady-State Analysis and Control Systems. Type-0/1/2 classification comes from poles at the origin.
More Steady-State Error questions