MATLAB (7)

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TF&state-space

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syms Y s y(t) t
 
laplace(10*diff(diff(y(t)))+0.4*diff(y(t))+4*y(t))
Y1=s*Y;
Y2=s*Y1;
sol=solve(10*Y2+0.4*Y1+4*Y-1,Y);
pretty(sol)
 
num=[1];
den=[10 0.4 4];
h=tf(num, den);
[A,B,C,D]=tf2ss(num, den)

실행결과

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>> Untitled
 
ans =
 
(2*s*laplace(y(t), t, s))/5 - (2*y(0))/5 - 10*s*y(0) + 10*s^2*laplace(y(t), t, s) - 10*subs(diff(y(t), t), t, 0) + 4*laplace(y(t), t, s)
 
       1
---------------
    2   2 s
10 s  + --- + 4
         5
 
 
A =
 
   -0.0400   -0.4000
    1.0000         0
 
 
B =
 
     1
     0
 
 
C =
 
         0    0.1000
 
 
D =
 
     0

rand, polyfit

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xran=rand(11,1);
plot(xran)
xlabel('Time[s]')
ylabel('Mag.[mm]')
x=0:10;
p=polyfit(x',xran,3);
v=diff(p)
a=diff(v)

실행결과

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v =
 
   -0.1215    0.6093   -0.5209
 
 
a =
 
    0.7309   -1.1302

Constant

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x=[1:1:4];
y=[2 3 2 1];
plot(y)
xlabel('Time[s]')
ylabel('Mag.[mm]')
p=polyfit(x,y,3);
v=diff(p)
a=diff(v)

실행결과

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v =
 
   -3.3333   10.6667  -10.6667
 
 
a =
 
   14.0000  -21.3333

Simulink

State-space equation, Scope