Topic: Control Systems
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
- A. 1 and 20
- B. 0 and 20
- C. 0 and 1/20
- D. 1 and 1/20
Answer: A. 1 and 20
Explanation: A finite, non-zero steady-state error for a ramp input implies the system is Type 1.
The steady-state error for a Type 1 system with a ramp input is $e_{ss} = \frac{1}{K_v}$.
Given $e_{ss} = 5\% = 0.05$, we have $0.05 = \frac{1}{K_v} \Rightarrow K_v = \frac{1}{0.05} = 20$.
The velocity error constant $K_v$ corresponds to the gain of the system.