How and what is the time period of following function

Hi, I am a little bit struggling to find a time period for the folowing code and it's graph.

It is a step response of a RCL circuit and I need to find a time period of it.

R = 1;%Given values

C = 0.01;

L = 0.01;

RC = R*C;

LC = L*C;

sys = tf([1/LC],[1 R/L 1/LC])%upper part and denominator part

subplot(2,1,1)

step(sys)

grid;

subplot(2,1,2)

impulse(sys)

grid;

Answer 1

[Jon]

I think you are looking for a characteristic time duration for your circuit. One common criteria is the settling time following a step command. Here is some code that would calculate that

R = 1;%Given values
C = 0.01;
L = 0.01;
RC = R*C;
LC = L*C;
sys = tf([1/LC],[1 R/L 1/LC])%upper part and denominator part 

% get response data
[yStep,tStep] = step(sys)


% find settling time to step input
% which we define here as the last time it leaves band of  +/-3% of final value
settlingThreshold = 0.03; % could use other value here, depends on you criteria
finalValue = 1; 
idx = find(abs(yStep - finalValue)/finalValue > settlingThreshold,1,'last');
tSettle = tStep(idx)

Answer 2

[Star Strider]

The stepinfo function will give essentially all the relevant information —

R = 1;%Given values
C = 0.01;
L = 0.01;
RC = R*C;
LC = L*C;
sys = tf([1/LC],[1 R/L 1/LC])%upper part and denominator part 

sys =
 
         10000
  -------------------
  s^2 + 100 s + 10000
 
Continuous-time transfer function.

SI = stepinfo(sys)

SI = struct with fields:
         RiseTime: 0.0164
    TransientTime: 0.0808
     SettlingTime: 0.0808
      SettlingMin: 0.9315
      SettlingMax: 1.1629
        Overshoot: 16.2929
       Undershoot: 0
             Peak: 1.1629
         PeakTime: 0.0359

figure
step(sys)
grid

.

[Jon]

Thanks, I didn't know about the stepinfo function, very nice!

I see now that I can find that command immediately by Googling the terms: matlab step response settling, also it is on the list searching with these same terms on the internal documentation.

I'll have to remember to search more before writing code!