Writing equation in Simscape

Hello All,

I got got while implementing a piece of code in Simscape. Any help would be highly appreciated.

I need to solve following equations: q(phi) = k2*phi - 0.5*(k1 - k2)(phi - delta - phi - delta) W(phi) = dq/d(phi) = k1 if phi < delta k2 if phi > delta

I have tried writing the following piece of code. It builds but when compiling from the Simulink it says the number of differential equation more than the number of variables.

component memristorLC < foundation.electrical.branch

    parameters
        k1 = {-3e4, 'Ohm^-1'};
        k2 = {9e4, 'Ohm^-1'};
        phi_0 = {0, 'V*s'};
        delta = {1e-12, 'V*s'};
        phi = {1e-14, 'V*s'};
    end

    variables
       q = {3, 'A*s'};
       w = {0.4, 'Ohm^-1'};
    end

    function setup
        phi = phi_0;        
        if (phi_0 > delta || phi_0 < -delta)
            error('Initial value of phi must be within the range of [-delta, delta]');
        end
    end

    equations
       q == k2*phi + 0.5*(k1 - k2) * (abs(phi + delta) - abs(phi - delta));
%        
%        if (abs(phi) < delta)
%            q.der == k1*{1, 'V'};
%        else
%            q.der == k2*{1, 'V'};
%        end

       if (abs(phi) < delta)
          w == k1;
       else
           w == k2;
       end

       w == q.der/{1,'V'};
       i == w*v;
    end

end

Answer 1

[Sebastian Castro]

Well, you have 4 total variables: V and i inherited from the branch, and your additional custom variables q and w.

By inheriting from the electrical branch, you have also inherited 1 equation defining the sign convention of V ... it's something like V == P.v - N.v; .

That leaves you with 3 equations to properly define the system, but you seem to have 4 in your component (Assuming that you plan on leaving that one part commented out).

Without knowing much about your model, it seems like both phi and its initial value phi_0 are in the parameters section. It therefore seems like this could be a dynamical state. If you move phi to the variables section, that should round off your number of variables vs. number of equations.

Also, if you are using R2014a or later, all variables will show up in the "Variables" tab of your block, so you could specify the initial phi value directly there without the need to make it an explicit parameter in the .ssc file.

- Sebastian

[Shital]

Hello Sir, Thank you for your response. Yeah I am changing that phi to the variable, but still that is not solving my problem. My system has two equations:

q(phi) = k2*phi - 0.5*(k1 - k2)(phi - delta - phi - delta) ---(1)

W(phi) = dq/d(phi) = k1 if phi < delta and k2 if phi > delta ---(2)

From my second equation, W(phi) = dq/d(phi). I think I have to use

        if (abs(phi) < delta)

            q.der == k1*{1, 'V'};

        else

            q.der == k2*{1, 'V'};

        end
but since that was giving me error, I tried with 
       if (abs(phi) < delta)
          w == k1;
       else
           w == k2;
       end

And finally from the relation between W(phi) and q, I mentioned

w == q.der/{1,'V'};

I have no idea where I am making mistake.

Thanks Shital joshi

[Shital]

Hello Again,

I did as you suggested (i.e. to move phi to variable), then the code runs. But I am not confident about the one thing. If I use:

if (abs(phi) < delta)
   q.der == k1*{1, 'V'};
else
   q.der == k2*{1, 'V'};
end

Then it still shows the number of variables vs equation error. So I used:

       if (abs(phi) < delta)
          w == k1;
       else
           w == k2;
       end

My question is: Are those two piece of codes above the same when I have this relation to satisfy:

W(phi) = dq/d(phi) = k1 if phi < delta and k2 if phi > delta ---(2)

and later do:

w == q.der/{1,'V'};

Thanks Shital Joshi

[Sebastian Castro]

Yes, I think that should be the same.

Simscape doesn't like when multiple equations try to affect the same variable (in your case, q or q.der)... So, making k1 and k2 affect w instead is a way to get around these limitations, since there is another equation that relates w to q anyhow.

[Shital]

Hi,

Still I am not able to get what I am supposed to get. Here "phi" value is never going to negative values, which it should go.

Let me elaborate it a little bit: It is from electrical foundation. So,

q(phi) = k2*phi - 0.5*(k1 - k2)(|phi - delta| - phi - delta) ---(1)

W(phi) = dq/d(phi) = k1 if phi < delta and k2 if phi > delta ---(2)

i = v*w ------(3)

Since this is a memristor design, it satisfy basic equs:

i = dq/dt

and

v = d(phi)/dt

I have no clue what I am doing mistake in coding. Any suggestions will be highly appreciated.