Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
217 views
in Electronics by (95.4k points)
closed by

A second-order position control system has an open-loop transfer function \(G\left( s \right) = \frac{{57.3K}}{{s\left( {s + 10} \right)}}\)

What value of K will result in a steady-state error of 1°, when the input shaft rotates at 10 r.p.m.?
1. 21.74
2. 10.47
3. 5.23
4. 0.523

1 Answer

0 votes
by (95.2k points)
selected by
 
Best answer
Correct Answer - Option 2 : 10.47

Concept:

Ka = position error constant = \(\mathop {\lim }\limits_{s \to 0} G\left( s \right)H\left( s \right)\)

Kv = velocity error constant = \(\mathop {\lim }\limits_{s \to 0} sG\left( s \right)H\left( s \right)\)

K= acceleration error constant = \(\mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)H\left( s \right)\)

Steady state error for different inputs is given by

Input

Type -0

Type - 1

Type -2

Unit step

\(\frac{1}{{1 + {K_p}}}\)

0

0

Unit ramp

\(\frac{1}{{{K_v}}}\)

0

Unit parabolic

\(\frac{1}{{{K_a}}}\)

 

Calculation:

The given input, r(t) = 10 rpm

\(r\left( t \right) = \frac{{2\pi }}{{60}} \times 10 \times \frac{{180}}{\pi }t\)

= 60t degree/sec

\(G\left( s \right) = \frac{{57.3K}}{{s\left( {s + 10} \right)}}\)

Velocity error coefficient is,

\({K_v} = \mathop {\lim }\limits_{s \to 0} sG\left( s \right) = \mathop {\lim }\limits_{s \to 0} s\frac{{57.3K}}{{s\left( {s + 10} \right)}} = 5.73K\)

Steady-state error, \({e_{ss}} = \frac{{60}}{{5.73K}}\)

Given that the steady-state error = 1°

\( \Rightarrow \frac{{60}}{{5.73K}} = 1 \Rightarrow K = 10.47\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...