Numerical values of system characteristics in time domain¶

This example shows how to obtain numerical values of step response characteristics such as rise time, steady-state time, and overshoot using stepinfo. You can use similar methods with lsim to obtain system response characteristics for arbitrary input data or initial conditions.

Before you begin, connect the ControlSystems.jl.

import Pkg
Pkg.add("ControlSystems")

using ControlSystems
s = tf('s');

H = tf([8, 18, 32],[1, 6, 14, 24]);
data = stepinfo(step(H))

StepInfo:
Initial value:     0.000
Final value:       1.333
Step size:         1.333
Peak:              1.687
Peak time:         0.609 s
Overshoot:         26.54 %
Undershoot:         0.00 %
Settling time:     3.507 s
Rise time:         0.210 s

The output is a structure containing the values of the step response characteristics. To access these values or to use them in other calculations, use a point record. For example, data.overshoot is the overshoot value.

data.overshoot

26.543295948871087

To see how other characteristics are labelled in the structure StepInfo, run the following code box. It will bring up a brief help.

?stepinfo

search: stepinfo StepInfo CompositeException InvalidStateException

stepinfo(res::SimResult; y0 = nothing, yf = nothing, settling_th = 0.02, risetime_th = (0.1, 0.9))

G = tf([1], [1, 1, 1])
res = step(G, 15)
si = stepinfo(res)
plot(si)

Calculate the time required for the step characteristic H to settle within 0.5% of its final value.

data = stepinfo(step(H), settling_th = 0.005)
t05 = data.settlingtime

4.893

By default, stepinfo defines the steady-state time as the time required for the output signal to settle within 2% of its final value. Specifying a more stringent "time tube" value of 0.005 will increase the value of settlingtime.

Conclusion¶

In this demo example, we have looked at a functional for analysing the numerical characteristics of system responses in the time domain.

Numerical values of system characteristics in time domain¶

Аргументы¶

Пример:¶

Conclusion¶