"Derivative of state '1' in block 'PD_Control/Integrator2' at time 0.34 in not finite. There are may be a singularity in the solution..."

Hi, now i configures SIMULINK about robot arm.

But in every time, the error is showed as above.

I wonder the reason why error appears and how to solve it.

I upload my SIMULINK file as zip file.

I use MATLAB 2022a version.

Also I attached dynamic equation what I used.

Thank you.

Answer 1

[Sam Chak]

Hi @Junu Lee

Most likely caused by the division-by-zero from this block. Could be triggered when the robot arm rotates to a certain angular position. Can you check the equations?

[Junu Lee]

Thank you for reply, sir. i'll try.

[Junu Lee]

Is it helpful to you if i send the dynamics equation?

[Sam Chak]

I think you can show it here. Others can help to spot the singularity issue.

[Junu Lee]

I edited the attachments, please check it.

[Sam Chak]

From the dynamics equations, I don't see any term where the divisor (denominator) can potentially become zero, unless the singularity occurs in the double-dot terms.

Can you check if the outputs Dinv3 and qddot if they return the following?

Dinv3 =

Inf Inf Inf

Inf Inf Inf

Inf Inf Inf

and

qddot =

Inf

Inf

Inf

[Junu Lee]

function [qddot, D] = Dinv3(u)

m1 = 30.0; m2 = 17.4;

l1 = 0.35;

th1 = u(1); l2 = u(2); dx = u(3);

d11 = m2*dx^2 + m2*l1^2 + (m2*l2^2)/3 + m2*l2*l1 + (m1*l1^2)/3;

d12 = -m2*dx;

d13 = m2*l1 + (m2*l2)/2;

d21 = d12;

d22 = m2;

d23 = 0;

d31 = d13;

d32 = d23;

d33 = m2;

D = [d11 d12 d13; d21 d22 d23; d31 d32 d33];

% D_det = det(D);

% D_inv = inv(D);

T_h = [u(4); u(5); 0];

qddot = D \ T_h;

end

In robot dynamics, .

, Then we obtain acceleration.

This code is 'Dinv3'.

At 21th row in this code, 'T_h' this term is .

At 22th row in this code, 'qddot = D \ T_h' is .

[Junu Lee]

I found something weird,,,

In D matrix, D(2, 2) and D(3, 3) are 'm2'. m2 is mass of the second link.

So it is 'CONSTANT'.

But before singularity time, It goes to some other constant, for example, 0.

The constant value can not be other constant in this matrix.

[Sam Chak]

Hi @Junu Lee

Thanks for showing your observations.

Yes, the mass is constant in and . I have checked the matrix D is positive definite and cannot become singular. However, based on your observations, I suspect that the Simulink model also draws the values from the Dinv3.m file in the same directory because the mass in that file is exactly 20 kg. Due to the anomalies, then we have reasons to suspect that the matrix D in the SImulink model suddenly becomes singular at 0.348 sec.

[Junu Lee]

Oh, I got it. It is something like a duplication(I'm Korean,,,,).

Even I found other terms, C, G, has something wrong about the input.

Now I return to my home when i come to my lab. i'll check these one.

Thank you for your reply.

I'll check and if i have more issue then can i ask more?

Thank you.

[Sam Chak]

mullon-ijyo, @Junu Lee.

It's also an opportunity for me to learn something new about the 2-link robotic manipulator.

Have a nice Sunday!

[Junu Lee]

Now I check and edited the attachment.