The following symbols are used for explaning the characteristic values in the following help text:

• \(y_i\) : Initial output value at \(t=0^-\) before the step is applied.
• \(y_f\) : Final steady state output value.
• \(y_e\) : Absolute error between output \(y\) and final value \(y_f\)

Inputs

sys

LTI system

property

value

Properties/value pairs changing some default thresholds.

‘RaiseTimeLimits’

Array with two entries with relative values of \(y_f\) between which the rise time is determined. The values have to be between 0 and 1. The default is \([r_L \, r_U] = [0.1 \, 0.9]\) if this property is omitted.

‘SettlingTimeThreshold’

Relative value of the absolute maximum or initial difference to \(y_f\) defining a tolerance range around \(y_f\) for TransientTime or SettlingTime (see below). The default is \(s_T = 0.02\) if this property is omitted.

Outputs

info

Structure (or structure array for MIMO systems) with some characteristics of the step response of system sys. In particular, the fields in info are:

‘RaiseTime’

Time required from \(r_L y_f\) to \(r_U y_f\)

‘TransientTime’

Time after which the absolute error \(y_e\) is not larger than \(s_T \max(|y_f-y|)\)

‘SettlingTime’

Time after which the absolute error \(y_e\) is not larger than \(s_T |y_f-y_i|\)

‘SettlingMin’

The minimum value of \(y\) after it has risen (reached \(r_U y_f\)

‘SettlingMax’

The maximum value of \(y\) after it has risen (reached \(r_U y_f\)

‘Overshoot’

Relative overshoot with respect to the normalized step response \(y_n = (y - y_i)/(y_f - y_i)\)

‘Undershoot’

Relative undershoot with respect to the normalized step response \(y_n = (y - y_i)/(y_f - y_i)\)

‘Peak’

Peak value of the absolute step response with respect to \(y_i\)

‘PeakTime’

Time at which the peak value occurs.

‘FinalValue’

Final value \(y(t\to\infty)\) of the step response, corresponds to the static gain.

‘InitialJump’

Output value \(y(t=0^+)\) immediately after the input step.

See also: step

Source Code: stepinfo