Side-by-side comparison
| Parameter | Steady State | Transient Response |
|---|---|---|
| Definition | Behaviour as t → ∞ after input is applied | Behaviour from t=0 until system settles |
| Characterised by | Steady-state error (ess) | Rise time, overshoot, settling time, peak time |
| Depends on | System type, loop gain, input type | Pole locations, damping ratio ζ, ωn |
| For underdamped 2nd-order | ess = 0 for step if Type ≥ 1 | Overshoot = exp(−πζ/√(1−ζ²))×100% |
| Settling time (2% criterion) | Not applicable | ≈ 4/(ζωn) |
| Improved by | Adding integrators or increasing K | Increasing ζ or ωn, adding derivative action |
| Real example (DC motor) | Final RPM = V/Kv constant | Speed rise during first 0.5–2 s after step |
| Exam focus | Error constants Kp, Kv, Ka | Overshoot %, rise time, peak time formulae |
Key differences
Transient response is governed by the closed-loop pole locations — poles far left in the s-plane give fast decay, but poles near the imaginary axis give prolonged ringing. Steady-state response depends on system type: a Type 1 system has zero position error but non-zero velocity error (= 1/Kv) for a ramp. Crucially, improving steady-state accuracy by raising loop gain tends to push poles toward instability, worsening the transient. This trade-off is the core tension in classical control design.
When to use Steady State
Focus on steady-state response when the application demands positional accuracy at rest — a CNC machine tool must hold position within ±5 µm once the move is complete, so steady-state error specification drives the design.
When to use Transient Response
Focus on transient response when dynamic performance during motion matters — a hard disk drive read/write head must settle within 1 ms after seeking, so settling time and overshoot are the binding constraints.
Recommendation
For exams, always address both regions when a step response question is asked. Never compute only overshoot or only steady-state error in isolation — most marking schemes allocate separate marks for each region.
Exam tip: Examiners give a second-order transfer function and ask you to compute rise time, peak time, overshoot, and settling time using the four standard formulae — memorise all four along with their derivation from the pole locations.
Interview tip: Interviewers at instrumentation and automation companies will ask you to explain the trade-off: why increasing loop gain reduces steady-state error but degrades transient stability, and how a PD term compensates.