How to get 2% and 5% settling time from simulink?

Hello,

I am simulating a simple open loop control system, as part of it I need to output the 2% and 5% settling time from simulink to check against my matlab and hand calc results. Can anyone help me with outputting the 2% and 5% settling time on simulink?

Answer 1

[Sam Chak]

Hi @Daniel

Below, you'll find the calculation for the settling time based on the 5% criterion:

%% System
zeta= 1/2;
wn  = 1;
sys = tf(1, [1 2*zeta*wn wn^2])

sys =
 
       1
  -----------
  s^2 + s + 1
 
Continuous-time transfer function.

%% Assume that response data {Time t, Output y} is sent to Workspace
[y, t]  = step(sys);

%% Settling time (5% criterion)
yfinal  = 1;    % steady-state response value
S       = stepinfo(y, t, yfinal, 'SettlingTimeThreshold', 5/100);
Ts      = S.SettlingTime

Ts = 5.2895

%% Plot result
plot(t, y), grid on
xline(Ts,   '--', 'Settling time', 'LabelVerticalAlignment', 'bottom'), 
yline(1.05, '--', '+5% threshold')
xlabel t, ylabel y(t)

Update: Demo using Simulink model

%% ----- This part can be skipped ----
load("responseData.mat");
G   = tf(1, [1 8.52 5.3 26]);
step(G), grid on

% ------------------------------------

%% Computation of settling times based on 2% and 5% criteria
yfinal  = 1/26;     % steady-state response value

S2      = stepinfo(out.out, out.t, yfinal);
Ts2     = S2.SettlingTime   % 2% criterion

Ts2 = 28.8686

S5      = stepinfo(out.out, out.t, yfinal, 'SettlingTimeThreshold', 5/100);
Ts5     = S5.SettlingTime   % 5% criterion

Ts5 = 21.7743

[Daniel]

Hello,

Thankyou for the input however this is not quite what I am after since the infomation you have put above is regarding matlab.

[Sam Chak]

Hi @Daniel

You're already familiar with how to send the logged data to the Workspace, as demonstrated in your Simulink model. The same syntax can be utilized to calculate the settling time based on the 5% criterion (the default is 2%).

%% Settling time (5% criterion)
yfinal  = 1/26;     % steady-state response value
S       = stepinfo(out.out, out.t, yfinal, 'SettlingTimeThreshold', 5/100);
Ts      = S.SettlingTime

[Sam Chak]

Hi @Daniel

To illustrate the computation of the settling time, I need to generate some step response data in the MATLAB online platform. However, when using Simulink, you can skip the following section of the code.

%% System
zeta= 1/2;
wn  = 1;
sys = tf(1, [1 2*zeta*wn wn^2])

%% Assume that response data {Time t, Output y} is sent to Workspace
[y, t]  = step(sys);

[Daniel]

Hello,

Thankyou for the help, your code didnt entirely work so I adapted it slightly as shown below.

Not sure why your code did not entirely work on my matlab but thankyou for the help.

[Sam Chak]

Ah, I see, @Daniel. It seems the reason for the discrepancy is that I sent the logged data to the Workspace as an Array, while yours are likely in the form of a Structure. However, as long as you specify the data type correctly, the syntax should work just fine. I'm glad to hear that it's working out for you. 👍

[Daniel]

Thanks for the help. I dont suppose you know how to find the damping ratio from simulink? I cant seem to find how to do it.

[Sam Chak]

Hi @Daniel

If you have already determined the system's transfer function, you can directly calculate the damping ratio using the 'damp()' command in MATLAB. Do you find the demonstrations for getting the settling time and the damping ratio helpful?

G   = tf(1, [1 8.52 5.3 26])

G =
 
               1
  ---------------------------
  s^3 + 8.52 s^2 + 5.3 s + 26
 
Continuous-time transfer function.

damp(G)

                                                                       
         Pole              Damping       Frequency      Time Constant  
                                       (rad/seconds)      (seconds)    
                                                                       
 -1.30e-01 + 1.77e+00i     7.34e-02       1.77e+00         7.68e+00    
 -1.30e-01 - 1.77e+00i     7.34e-02       1.77e+00         7.68e+00    
 -8.26e+00                 1.00e+00       8.26e+00         1.21e-01    

Answer 2

[Paul]

Hi Daniel,

I'm interpreting your question to mean that you have a Simulink model of the system and in Simulink you stimulate the system with a step input and wish to compute the settling time of the output, which is logged by a To Worspace block or something similar.

Once you the the output in the base workspace, you can use stepinfo to compute its settling time.

[Daniel]

Hello,

Yes I have a simulink model of the system, you can see the system in the picture below.

I have done stepinfo however it only provides one settling value, I need to find the values for 2% and 5% settling times.

Hope this makes sense.