• System Response and Performance Measures | ACE-Lab
    ACE-CORE · Comprehend · C04

    System Response and Performance Measures

    Learn how the behaviour of a dynamic system is described after a change in reference, and how rise time, overshoot, settling time and steady-state error provide measurable ways of describing that response.

    01

    Why describe the system response?

    Before a control-system requirement can state how fast, accurate or well-damped a response should be, the response itself must be described using consistent measures.

    Learning focus

    From “it looks good” to measurable behaviour

    A controlled system rarely moves instantly from one value to another. Its output changes over time. The shape of that change tells us about speed of response, oscillation, accuracy and whether the system has reached a steady condition.

    ✓Identify the transient and steady-state parts of a response.
    ✓Explain rise time, peak value, overshoot, settling time and steady-state error.
    ✓Calculate simple performance measures from response data.
    ✓Recognise how these measures can later be converted into application requirements.
    02

    Read a step response

    A step response shows how the output changes when the reference is changed suddenly from one constant value to another. Use the buttons to highlight the main performance measures.

    Example response

    Reference changes from 0 to 30 RPM at t = 0 s.

    Annotated step response A speed response rising toward a 30 RPM reference, overshooting, then settling near the reference. Rise time, overshoot, settling time and steady-state error are annotated. Time Output 0 10 20 30 2 4 6 8 Reference = 30 RPM Example settling band Rise time 10% 90% Overshoot Peak above final value Settling time Response remains inside band Steady-state error Difference between reference and final output Transient response Steady-state behaviour

    Rise time

    The time taken for the response to move through a defined portion of the change from its initial value to its final value. A common convention is 10% to 90%.

    Typical notation: tr

    Overshoot

    The amount by which the response exceeds its final or desired value. It is often expressed as a percentage of the final value.

    %OS = (peak − final) / final × 100

    Settling time

    The time after which the response remains within a stated band around its final value. A 2% band is a common convention.

    Typical notation: ts

    Steady-state error

    The remaining difference between the reference and the output once the transient response has died away.

    ess = reference − steady-state output

    Peak value and peak time

    The maximum value reached by the response and the time at which that maximum occurs. These are useful when an overshooting response is present.

    Peak = max output · Peak time = time of peak

    Transient vs steady state

    The transient describes the changing behaviour immediately after the input changes. Steady state describes the behaviour after the transient has substantially disappeared.

    Transient → changing response · Steady state → long-term response
    03

    Worked example: a motor speed response

    Use a simple speed response to calculate the measures before any judgement is made about whether the response is acceptable.

    Measured response

    30 RPM reference

    Suppose a motor is commanded from rest to 30 RPM and the following values are measured from its response.

    Reference30.0 RPM
    10% crossing0.4 s
    90% crossing1.8 s
    Peak output32.4 RPM
    Time response stays in settling band3.6 s
    Steady-state output29.7 RPM
    Rise time 1.4 s

    1.8 − 0.4 = 1.4 s

    Overshoot 8%

    (32.4 − 30) / 30 × 100 = 8%

    Settling time 3.6 s

    The response remains inside the chosen settling band after this point.

    Steady-state error 0.3 RPM

    30.0 − 29.7 = 0.3 RPM

    Important distinction: these values describe the response. They do not yet tell us whether the response is good enough. That judgement requires a requirement or acceptance criterion.
    04

    Check your understanding

    Use the questions below to test whether you can interpret the main response measures before moving on.

    Rise time describes how quickly the response rises, while overshoot describes how far it exceeds the final or desired value.
    Rise time describes the initial speed of the response. Settling time asks when the response has entered a defined band around its final value and remains there.
    The steady-state error is 1 RPM, because 30 − 29 = 1 RPM.
    No. The response measure only describes behaviour. Whether 8% is acceptable depends on the requirement defined for the application.
    05

    Putting the measures together

    Each measure describes a different feature of the response. Together, they provide a simple way to describe how quickly, smoothly and accurately a system behaves.

    Describe first, judge later

    Rise time describes speed of response, overshoot describes how far the output exceeds its final value, settling time describes how long the response takes to become steady, and steady-state error describes the remaining difference from the reference. At this stage, the goal is to understand what each measure means rather than decide what values are acceptable.

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