# calculate/pich up x-value from step function

2 views (last 30 days)
Olga Rakvag on 21 Feb 2023
Answered: Sam Chak on 21 Feb 2023
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 on 21 Feb 2023
You can use stepinfo command to find time response of the given system. https://www.mathworks.com/help/ident/ref/lti.stepinfo.html

Sam Chak on 21 Feb 2023
% 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

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