MATLAB: Strange result in ilaplace()

ilaplacesymbolic transform

Hi! I'm trying to make inverse laplace transform, but clearly the result is wrong because the expression don't even has the time variable. Could someone help me?

syms Kp Ki Kd s time
plant = 1/(s^3 + 9*s^2 + 23*s + 15);
controler = Kp + Kd*s + Ki/s;
system_laplace = simplify((plant * controler)/(1 + plant * controler));
system_time = ilaplace(system_laplace, s, time)

Best Answer

It’s not strange. It’s just that you have a transfer function that’s not possible to invert. Just before the ilaplace call, I added:

system_laplace = partfrac(system_laplace, s, 'FactorMode', 'full')

since that can allow inversion in situations where ilaplace otherwise fails. It didn’t work with your system.

You probably need to do your analysis in the Control System Toolbox. See the documentation for the tf function, since it will allow you to enter your equations as you have entered them here:

s = tf('s') to specify a TF model using a rational function in the Laplace variable, s.

Related Solutions

MATLAB: I want to find the determinant for 5.5 matrix

>> syms s1 s2 s3 s4 s5 s6 s7 s8 s9 s10
>> M = [0 -s1 -s2 -s3 -s4; s1 0 -s5 -s6 -s4; s2 s5 0 -s8 -s9; s3 s6 s8 0 -s10; s4 s7 s9 s10 0];
>> det(M)
ans =
s1*s4^2*s8^2 - s1*s4*s7*s8^2 - s2*s4^2*s6*s8 + s3*s4^2*s5*s8 - s3^2*s4*s5*s9 - s2^2*s4*s6*s10 + s3^2*s5*s7*s9 + s2^2*s6*s7*s10 + s2*s3*s4*s5*s10 + s2*s3*s4*s6*s9 + s1*s2*s4*s8*s10 - s1*s3*s4*s8*s9 - s2*s3*s5*s7*s10 - s2*s3*s6*s7*s9 + s2*s4*s6*s7*s8 - s3*s4*s5*s7*s8 - s1*s2*s7*s8*s10 + s1*s3*s7*s8*s9
>> simplify(ans)
ans =
(s4 - s7)*(s3*s5 - s2*s6 + s1*s8)*(s2*s10 - s3*s9 + s4*s8)

MATLAB: Solving system of equations with parameters

Like sir Walter says I think you should be using ode solvers to solve the problem because it clearly is a system of odes:

tspan=[0 1];  % time span 
ic=[0;1;0;0;0;0;0;0;0;0;0;0]; % initial conditions
[t,x]=ode45(@myod,tspan,ic);  % function call
plot(t,x(:,1)) % likewise another 11 solutions can be plotted
function dSdt = myod(t,x)  % function definition
 S0=x(1);
 S1=x(2);
 S2=x(3);
 S3=x(4);
 S4=x(5);
 S5=x(6);
 S6=x(7);
 S7=x(8);
 S8=x(9);
 S9=x(10);
 S10=x(11);
 S11=x(12);
Ca_sr_conc  = 1.3e-3;
MgATP_conc  = 5e-3;  
MgADP_conc  = 36e-6; 
Pi_conc     = 1e-3;  
Ca=1e-3;  % change it to your value
Ca_cyt_conc = 140e-9; 
k_S0_S1   = 4e7;   
k_S1_S0   = 450;   
k_S1_S2   = 120;   
k_S2_S1   = 25;    
k_S2_S3   = 1e8;   
k_S3_S2   = 16;    
k_S3_S4   = 2e7;  
k_S4_S3   = 40;   
k_S4_S5   = 135;   
k_S5_S4   = 765;   
k_S5_S6   = 15;    
k_S6_S5   = 7.5e4;
k_S6_S7   = 1.5; k_S7_S6   = 2.0;
k_S7_S8   = 350; 
k_S8_S7   = 1.2e5;
k_S8_S9   = 160;   
k_S9_S8   = 250;   
k_S9_S10  = 300;
k_S10_S9  = 9e4;   
k_S10_S11 = 60;    
k_S11_S10 = 60;    
k_S11_S0  = 250;   
k_S0_S11  = 2.7e5; 
dSdt  = [ ((k_S11_S0 * S11) + (k_S1_S0 * S1)) - ((Ca_cyt_conc* k_S0_S1 + Pi_conc * k_S0_S11) * S0);
((Ca_cyt_conc* k_S0_S1 * S0) + (k_S2_S1 * S2)) - ((k_S1_S0 + k_S1_S2) * S1);
((k_S1_S2 * S1) + (k_S3_S2 * S3)) - ((k_S2_S1 + Ca* k_S2_S3) * S2);
((Ca_cyt_conc* k_S2_S3 * S2) + (k_S4_S3 * S4)) - ((k_S3_S2 + MgATP_conc * k_S3_S4) * S3);
((MgATP_conc * k_S3_S4 * S3) + (k_S5_S4 * S5)) - ((k_S4_S3 + k_S4_S5) * S4);
((k_S4_S5 * S4) + (k_S6_S5 * MgADP_conc * S6)) - ((k_S5_S4 + k_S5_S6) * S5);
((k_S5_S6 * S5) + (k_S7_S6 * S7)) - ((k_S6_S5 * MgADP_conc + k_S6_S7) * S6);
((k_S6_S7 * S6) + (Ca_sr_conc * k_S8_S7 * S8)) - ((k_S7_S6 * MgADP_conc + k_S7_S8) * S7);
((k_S7_S8 * S7) + (k_S9_S8 * S9)) - ((Ca_sr_conc * k_S8_S7 + k_S8_S9) * S8);
((k_S8_S9 * S9) + (Ca_sr_conc * k_S10_S9 * S10)) - ((k_S9_S8 + k_S9_S10) * S9);
((k_S9_S10 * S9) + (k_S11_S10 * S11)) - ((k_S10_S11 + Ca_sr_conc * k_S10_S9) * S10);
((k_S10_S11 * S10) + (Pi_conc * k_S0_S11 * S0)) - ((k_S11_S0 + k_S11_S10) * S11)];
end

Best Answer

Related Solutions

MATLAB: I want to find the determinant for 5.5 matrix

MATLAB: Solving system of equations with parameters

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