Question

Question 2 For the system shown below use the MATLAB to find: X + 0.5s+1.3 s+1.2s+1.6s For the previous system if K-1, and the input is sin(2t) find: 1) 2) 3) 4) Peak amplitude Rise time Settling time Steady state value Question 3 For the system shown below If the input is unit step find: 1) 2) 3) 4) Peak amplitude Rise time Settling time Steady state value

Answer 1

Question 2

Code for the first question :

G = tf([0.5 1.3],[1 1.2 1.6 0]); % transfer function gievn
K = 1; % value of K
sys = feedback(G*K,1);   % close loop system
t = 0:0.01:28;    % defining the time interval and data will be taken with 0.01 interval
u = sin(2*t);     % input function
y = lsim(sys,u,t);
plot(t,y)       % this will plot the data got at each interval
grid;
output = lsiminfo(y,t) % this will give the output

this is the result :

output =

    SettlingTime: 27.9673
             Min: -0.5493
         MinTime: 3.9700
             Max: 0.5712
         MaxTime: 2.0800

0.6 X: 2.1 Y: 0.571 0.4 0.2 X: 3.06 Y:0.005502 -0.2 0.4 -0.6 10 15 20 25 30

From the graph we can find the values : Peak amplitude = 0.571, Rise time = 2.1s(approx), Settling time = 3.06s (Rise time for a sinusoid is the time at the first peak, and settling time is the time at the second zero crossing) and steady state value = not defined, since output is sinusoid

Question 3

fs) 10o S+5 100 S+ 5 1 00 s-10 (S)(s) 100 x (S+1)(S +lo 100 (S.111+20 ) う 7(S) ^

Code for the 2nd problem

G =100*tf([1 12 20],[1 18 187 1110])

step(G); grid on;

Output = stepinfo(G)

Output =

        RiseTime: 0.0154
    SettlingTime: 1.1755
     SettlingMin: 0.3105
     SettlingMax: 6.9785
       Overshoot: 287.3059
      Undershoot: 0
            Peak: 6.9785
        PeakTime: 0.1436

Peak Amplitude: 6.98

Steady state value : 1.81

Step Response System G Time (seconds): 0.144 Amplitude: 6.98 3 System G Time (seconds): 1.59 Amplitude: 1.81 0.2 04 0.6 0.8 Time (seconds) 1.2 1.4 1.6

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