Could't get right result laplace,ilaplace,PD

hi friends,

I am trying to plot laplace with PD ,the plot I have got is wrong according to book ,where am I making mistake.Automatic Control Systems(Benjamin C. Kuo)

syms Kp Kd s t

K = 181.17;

Ku = 5;

Tu = 0.5;

Kp = 1;

Kd = 0.002;

Ki = 0;

%Fs=sym(((1.5E7*K)/(s^3 + 3408.3*s^2 + 1213086*s + 1.5E7*K))*(Kp + Kd*s));

Fs=sym( ((1.5E7*K)*(Kp + Kd*s )) / ((s+3293.3)*(s+57.49+j*906.6)*(s+57.49-j*906.6)) )

ft=ilaplace(Fs,s,t);

t = 0:0.001:0.3;

f = subs(ft);

plot(t,f)

Answer 1

[Star Strider]

I have no idea what the plot is supposed to look like. However depending on your MATLAB release/version, you may have to use the expand function first, then the partfrac function, before you call ilaplace:

Fs=sym( ((1.5E7*K)*(Kp + Kd*s )) / ((s+3293.3)*(s+57.49+j*906.6)*(s+57.49-j*906.6)) )
Fs = expand(Fs)
Fspf = partfrac(Fs)
ft=ilaplace(Fspf,s,t);
t = 0:0.001:0.3;
f = subs(ft);
plot(t,f)

See if that does what you want.

The partial fraction expansion is:

and the time domain expression is:

[Star Strider]

Emrah Duatepe’s Answer moved here:

That was what I need ,but thank you to help

a=1

Kp = 0.11112;

Kd = 0.00034198;

Ki = 4.3789;

t0=0.3;

ts=0.0001;

t=[0:ts:t0];

s = tf('s');

Fs = (2.718E9/(s*(s+400.26)*(s+3008)))*(Kp + Kd*(s/(a*s+1)) + Ki/s)

H = 1;

FB = feedback(Fs,H,-1);

%Giriş sinyali oluşturuluyor(Kare dalga)

u0 = t>= 0;

ut03 = (t-t0/3) >= 0;

u2t03 = (t - 2*t0/3) >= 0;

m1 = u0 - ut03;

m2 = -2*(ut03 - u2t03);

m = m1 + m2;

noise = 0.1*randn(1,length(t));

u=u0 + noise;

lsim(FB,u,t)

[Star Strider]

My pleasure.

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