Assertion (A) : In control systems, steady state response in the final requirement for calculating the efficiency of the system. Reason (R) : The transient response is also critical for the determination of the steady state response.
Both (A) and (R) are correct and (R) is correct explanation of (A).
Both (A) and (R) are correct and (R) is the correct explanation of (A) — option (A), as recorded in the official key.
The two halves of any time response. For a linear system the total response to an input separates into two parts :
\(c(t)=c_{tr}(t)+c_{ss}(t)\)
| Transient response | Steady-state response | |
|---|---|---|
| Definition | The part that decays to zero as \(t\to\infty\) | What remains as \(t\to\infty\) |
| Governed by | The poles of the closed-loop transfer function | The input and the system type |
| Measured by | Rise time, peak time, overshoot, settling time | Steady-state error |
The assertion is true in the sense the item intends: how well a control system finally performs its job is judged by what it settles to. The steady-state error is the standard figure of merit, obtained from the final value theorem
\(e_{ss}=\lim_{s\to 0}\dfrac{sR(s)}{1+G(s)H(s)}\)
and expressed through the error constants \(K_{p}\), \(K_{v}\) and \(K_{a}\) according to system type.
How the key reads the connection. The steady state is not a separate phenomenon — it is what the transient leaves behind. The response reaches its final value only once the transient has died away, so whether a steady state is attained at all, and how long it takes, is decided entirely by the transient term. Where the transient does not decay — poles on or right of the imaginary axis — the system is unstable and there is no steady state to evaluate. On that reading the transient governs the determination of the steady-state response, and (R) explains (A).
The counter-argument, stated fairly. Strictly, the steady-state value is set by the input and by the system’s low-frequency gain, not by the transient, and the two are evaluated independently — the final value theorem needs no knowledge of the transient at all. On that stricter reading (R) is a separate true statement rather than the cause of (A), giving code (B). The answer stored here follows the official key.
Why both parts are specified in practice. A design that meets its steady-state accuracy but overshoots badly, or takes far too long to settle, is useless — and the two requirements pull against each other, since raising the gain reduces steady-state error while worsening overshoot. Resolving that conflict is precisely what compensator design is for.
Hence, the answer recorded is option (A).
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Important Questions from Time Response Analysis
Which of the following is correct for over-damped and under-damped system, respectively?
What will be the time response expression for a standard first order system having unit step function \(\frac{1}{s}\) as the input
A second order system has natural frequency 3rad/sec and unity damping ratio. Identify its transfer function.
Statement (I): All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.
Statement (II): A large resonance peak in frequency response corresponds to a large overshoot in transient response.
The steady state error of a control system can be minimized by:
