# steady state responce of LTI system

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Answered: Star Strider on 10 Sep 2021
clc
clear all
A=[-0.0295 0.0478 0 -9.81;-0.1777 -1.4411 120 0;0.0005 -0.033 -1.5345 0;0 0 1 0]
B=[0;-12.81;-6.59;0]
C=[0 0 0 1]
D=[0]
[num ,dem]=ss2tf(A,B,C,D)
[z,p,k]=tf2zp(num,dem)
t=linspace(0,100,100)
% i have this LTI system and i want to find out the steady state responce
% in magnitude and phase at w=0.1 rad/s
sys=tf(num,dem)
% is there is any commad that can do it in matlab as i am new in matlab so

Star Strider on 10 Sep 2021
Try this —
A=[-0.0295 0.0478 0 -9.81;-0.1777 -1.4411 120 0;0.0005 -0.033 -1.5345 0;0 0 1 0]
A = 4×4
-0.0295 0.0478 0 -9.8100 -0.1777 -1.4411 120.0000 0 0.0005 -0.0330 -1.5345 0 0 0 1.0000 0
B=[0;-12.81;-6.59;0]
B = 4×1
0 -12.8100 -6.5900 0
C=[0 0 0 1]
C = 1×4
0 0 0 1
D=[0]
D = 0
sys = ss(A,B,C,D)
sys = A = x1 x2 x3 x4 x1 -0.0295 0.0478 0 -9.81 x2 -0.1777 -1.441 120 0 x3 0.0005 -0.033 -1.534 0 x4 0 0 1 0 B = u1 x1 0 x2 -12.81 x3 -6.59 x4 0 C = x1 x2 x3 x4 y1 0 0 0 1 D = u1 y1 0 Continuous-time state-space model.
figure
stepplot(sys)
[y,tOut] = step(sys);
yFinal = y(end)
yFinal = -4.9676
tFinal = tOut(end)
tFinal = 423.9577
S = stepinfo(sys)
S = struct with fields:
RiseTime: 2.5467 SettlingTime: 301.8693 SettlingMin: -16.4422 SettlingMax: 2.5391 Overshoot: 227.8385 Undershoot: 50.6273 Peak: 16.4422 PeakTime: 18.4329
Experiment to get different results.
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