Question

The steady state error due to a ramp input for a type two system is equal to _______.

• A. zero
• B. infinite
• C. non-zero number
• D. constant

Hint:

Type-2 system means two integrators → zero error for step and ramp input, only parabola has non-zero error.

Answer 1

The Correct Option is A

Step 1: Understand steady-state error (SSE).
Steady-state error is the difference between desired and actual output as $t \to \infty$.
Step 2: System type.
System type = number of integrators in the forward path (i.e., number of poles at origin).
Step 3: Error constants:
- For ramp input, we use velocity error constant $K_v$.
- For Type-2 system, there are two integrators → $K_v \to \infty$ \[ e_{ss} = \frac{1}{K_v} = \frac{1}{\infty} = 0 \] Conclusion: $\boxed{0}$ steady state error for ramp input in a Type-2 system.