Question

Error constants of a system are measure of

• A. Relative stability
• B. Transient state response
• C. Steady state response
• D. Marginal stability

Hint:

Remember: \[ K_p \rightarrow \text{Position Error Constant} \] \[ K_v \rightarrow \text{Velocity Error Constant} \] \[ K_a \rightarrow \text{Acceleration Error Constant} \] All three are used for steady-state error analysis.

Answer 1

The Correct Option is C

Concept: Error constants are used to evaluate the steady-state performance of a control system. The important static error constants are: \[ K_p=\lim_{s\to0}G(s) \] \[ K_v=\lim_{s\to0}sG(s) \] \[ K_a=\lim_{s\to0}s^2G(s) \] These constants help determine the steady-state error for standard test inputs such as step, ramp and parabolic signals.

Step 1: Understand the purpose of error constants.
Error constants do not provide information about transient response parameters such as: \[ t_r,\; t_p,\; t_s,\; M_p \] Instead, they indicate how accurately the system tracks the input after all transients die out.

Step 2: Relate error constants to steady-state error.
For a unity feedback system, \[ e_{ss}=\frac{1}{1+K_p} \] for step input, \[ e_{ss}=\frac{1}{K_v} \] for ramp input, and \[ e_{ss}=\frac{1}{K_a} \] for parabolic input. Thus, error constants directly measure steady-state accuracy.

Step 3: Choose the correct option.
Hence, \[ \boxed{\text{Error constants are measures of steady-state response}} \] Therefore, \[ \boxed{\text{Correct Option (C)}} \]