STUDY PATH/05 — TIME DOMAIN
CHAPTER 05 / TIME DOMAIN

Read a step response

A single target change reveals speed, overshoot, settling and residual error.

01 / THE INTUITION

First, picture it

A fast response is not automatically good. A controller may reach the target quickly, overshoot it, oscillate, and use far more actuator effort than a slightly slower design.

02 / THE IDEA

What the model says

Rise time measures how quickly a response climbs through a stated band; overshoot compares its maximum to the final target; settling time requires it to remain within a tolerance band. Always report the band and observation window. A run that has not settled is 'not settled', not a guessed number. Steady-state error is the remaining difference after transients die out; it may not exist for an unstable response.

RELATION / 관계식M_p=(y_peak-y_target)/|y_target| × 100%

This common overshoot definition requires a meaningful nonzero target and suitable initial condition.

03 / IN PRACTICE

Make it concrete

Compare two motor runs with identical target and load. One may settle earlier but require a larger voltage spike. Inspect both speed and control-input traces.

Compare step responses
BE CAREFUL / 주의

A metric without its definition and conditions can mislead. Saturation may also make the textbook linear step-response formulas inapplicable.

Check your understanding+

Why should a settling-time report state its tolerance band?

A 2% band and a 5% band can yield different times for the same trace.