calculate/pich up x-value from step function

How I can easiest calculate/pick up x value for r63 and r98 prosent av full scale?

clc; clear all; close all;

% 1 order step respons

Gain=0.999*5;

np = tf([5*0.999], [0.000999, 1])

t = linspace(0, 0.1, 1000);

r63= 5*Gain*0.632;% 63prosent of final value

r98=5*Gain*0.98; % 98 prosent of final value

figure(1)

step(np,'k')

hold on

% 63 and 98 % of full scale

yline( r63,'r-',' 63%', 'LabelHorizontalAlignment','left'); hold on

yline( r98,'r-','98%', 'LabelHorizontalAlignment','left'); hold on

xlim([0, 0.01])

ylim([0.7, 5.5])

grid on

hold off

[Oguz Kaan Hancioglu]

You can use stepinfo command to find time response of the given system. https://www.mathworks.com/help/ident/ref/lti.stepinfo.html

Answer 1

[Sam Chak]

Hi @Olga Rakvag

% 1st-order step response
Gain = 0.999*5;
np   = tf(Gain, [0.000999, 1])

np =
 
      4.995
  --------------
  0.000999 s + 1
 
Continuous-time transfer function.

r63 = Gain*0.632    % 63 percent of the final value

r63 = 3.1568

r98 = Gain*0.98     % 98 percent of the final value 

r98 = 4.8951

figure(1)
t = linspace(0, 0.1, 1001);
y = step(np, t);    % generate the output values for y
plot(t, y)          % make a plot of the step response
% step(np,'k')      % or put at this line also can
hold on

% 63 and 98 % of full scale
yline(r63, 'r-', ' 63%', 'LabelHorizontalAlignment', 'left'); 
yline(r98, 'r-', ' 98%', 'LabelHorizontalAlignment', 'left'); 
xlim([0, 0.01])
ylim([0, 5.5])
grid on
hold off

% Time it takes to go from 0 to r63
idx1 = find(y > 0.99*r63 & y < 1.01*r63)

idx1 = 11

y(idx1)         % y value closest to r63 = 3.1568

ans = 3.1593

T63 = t(idx1)   % around 0.001 sec

T63 = 1.0000e-03

% Time it takes to go from 0 to r98
idx2 = find(y > 0.999*r98 & y < 1.001*r98)

idx2 = 40

y(idx2)         % y value closest to r98 = 4.8951

ans = 4.8943

T98 = t(idx2)   % around 0.039 sec

T98 = 0.0039

Note that the computation of the Step Response Characteristics changes in version R2021b.

Make that you understand before using stepinfo()

stepinfo(np)

ans = struct with fields:
         RiseTime: 0.0022
    TransientTime: 0.0039
     SettlingTime: 0.0039
      SettlingMin: 4.4955
      SettlingMax: 4.9949
        Overshoot: 0
       Undershoot: 0
             Peak: 4.9949
         PeakTime: 0.0105