Question

A ramp input applied to a unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are
1. 1 and 20
2. 0 and 20
3. 0 and 1/20
4. 1 and 1/20

Answer 1

Correct Answer - Option 1 : 1 and 20

Calculation:

e_ss = 5% = 0.05

∵ e_ss is finite with ramp input type of the system is 1

\({K_v} = \frac{1}{{0.05}} = 20\) 

Zero – frequency gain of the system = 20

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	∞	∞	\(\frac{1}{{{K_a}}}\)