Question

The block diagram for a control system is shown below: for a unit step change in the set point, \( R(s) \), the steady-state offset in the output \( Y(s) \) is 

• A. 0.2
• B. 0.3
• C. 0.4
• D. 0.5

Hint:

For control systems with a unit step input, use the final value theorem to compute the steady-state error, which depends on the system type and error constants.

Answer 1

The Correct Option is C

- For a unit step input, the steady-state offset can be calculated using the final value theorem and the open-loop transfer function. 
- The system type determines the steady-state error, with type 0 systems having a non-zero error for step inputs. 
- Using the formula \( {Steady-state error} = \frac{1}{1+K_p} \), where \( K_p \) is the system's position error constant, we find that the steady-state error is 0.4. 
Conclusion: The steady-state offset in the output \( Y(s) \) is 0.4, as given by option (C).