Error: "Number of variables exceeds number of equations." Probably a mistake in my code, but where?

Hello, i try to program a simple Simscape-Block which calculates a braking moment for an output signal by using an external force and some parameters. When i try to run the model in the test environment, the error-message "Number of variables exceeds number of equations. Check for missing reference node." comes up. I'm pretty sure its a mistake in the code, but where? I already tried not to inlcude v = {0, ...) and across(v, ...), but that didnt change anything. The code is the following:

component Multi_Disc_Brake     

    nodes 
        R = foundation.mechanical.translational.translational; % R:left
        C = foundation.mechanical.translational.translational; % C:right
    end

    parameters
        n = {1, '1'};   % Number of rotating discs
        r_i = {1, 'm'}; % Radii of inner discs
        r_a = {2, 'm'}; % Radii of outer discs
        my = {1, '1'};  % Friction coefficient
    end

    variables
        f = {0, 'N'};
        M_B = {0, 'N*m'};
        r_m = {0, 'm'};
        v = {0, 'm/s'};
    end

    outputs 
        out = {0, 'N*m'}; % M(t):right:top
    end

    function setup
        if n <= 0
            error ('Number of discs must be greater than zero');
        end
        if r_i <= 0
            error ('Inner radii must be greater than zero');
        end
        if r_a <= 0
            error ('Outer radii must be greater than zero');
        end
        if r_i >= r_a
            error ('Inner radii has to be smaller than outer radii');
        end
        through (f, R.f, C.f);
        across (v, R.v, C.v);
    end

    equations
        let
            r_m = (2/3)*((r_a^3 - r_i^3)/(r_a^2 - r_i^2)); % Centre radius
        in
            M_B == my*f*r_m*2*n; % Calculation of the braking moment
        end
        out == M_B;
    end
  end

Thank you in advance for your help!

Matt

Answer 1

[Ryan G]

Sounds like you understand the basics of the error. Without digging to deep I see 4 variables and maybe 2 or 3 equations (I'm not sure how Simscape counts equations in let-in format). So at best you still have 1 more variable than equation.

That being said I don't see v utilized in the equations section nor do I see either of your nodes being used. In other words, right now I believe this would output a constant, which doesn't make sense for a Simscape component.

I might be missing something here, let me know if I'm wrong.

Answer 2

[Matthias]

Hi Ryan! Thanks for your answer. The thing is, even if i remove every line with the velocity, the same error occurs. I included v because i saw this in codes of blocks from the simscape library and assumed it is necessary because the through-variable f (force) should always come with an across-variable v (velocity). In this case the vlocity should just transfer from node R to C. Concerning the equations, i thought variable f comes from node R as input and is thereby defined. M_B is determined in the equation section as well as r_m. That's why i'm confused.I need to get the value of the force f from node R for calculating the moment M_B. I also tried deleting the "let..in"-expression, but nothing changes.

Here is the code without the velocity but with the same error:

component Multi_Disc_Brake     
  nodes 
      R = foundation.mechanical.translational.translational; % R:left
      C = foundation.mechanical.translational.translational; % C:right
  end    
  parameters
      n = {1, '1'};   % Number of rotating discs
      r_i = {1, 'm'}; % Radii of inner discs
      r_a = {2, 'm'}; % Radii of outer discs
      my = {1, '1'};  % Friction coefficient
  end    
  variables
      f = {0, 'N'};
      M_B = {0, 'N*m'};
      r_m = {0, 'm'};
  end    
  outputs 
      out = {0, 'N*m'}; % M(t):right:top
  end    
  function setup
      if n <= 0
          error ('Number of discs must be greater than zero');
      end
      if r_i <= 0
          error ('Inner radii must be greater than zero');
      end
      if r_a <= 0
          error ('Outer radii must be greater than zero');
      end
      if r_i >= r_a
          error ('Inner radii has to be smaller than outer radii');
      end
      through (f, R.f, C.f);
  end    
  equations
      let
          r_m = (2/3)*((r_a^3 - r_i^3)/(r_a^2 - r_i^2)); % Centre radius
      in
          M_B == my*f*r_m*2*n; % Calculation of the braking moment
      end
      out == M_B;
  end
end

Also, Matlab creates a warning when opening the test-environmentmodel without v in the block: "Warning: In instatiating linked block '.../Multi-Dioc-Brake' : Multi-Disc-Brake block (mask) does not have a parameter named 'v_Log' In general\private\openmdl at 13 In general\private\openslx at 9 In open at 159 In uiopen at 196

greetings, Matthias

[Ryan G]

Could you get rid of M_B and instead set out == directly?

[Ryan G]

by the way, I was able to successfully SSC_BUILD the code you pasted above in R2013a.

[Matthias]

Hi Ryan! I'm using the version R2012b (student license), and i could ssc_build the code too, but it didn't work in the test-model. Using 'out == ...' and deleting 'out == B_M' didn't solve the problem either unfortunately. I think it has to do with the way how i handle the variable f. There is no equation concerning f except "through(f, ...)" and i'm not sure if that is enough. I found out that when i insert the line f == 0; in the equations section, the failure is gone but then i have problems with initial conditions. And it would be wrong for my model anyways. However, i think the problem is that don't know how to handle f right. Of course, i could implement the model without nodes with f as a signal (that actually worked), but if i later want to implement a spring which presses the discs apart, i need the counterforce from the discs to the force-input-block. Thats why i somehow have to handle f physically and not as a signal. greetings, Matthias

[Ryan G]

Have you tried working from an example first? It may make more sense to take an example, change it to match your equation (start with constants instead of variables) and build up to your final system with all required variables.

[Matthias]

Yeah, thats a good idea. I wrote a new code now, starting with a similar code to a translational reference block. This code works in the model, but generates a warning:

"Warning: The model 'Lamellenbremse_Testumgebung' does not have continuous states, hence Simulink is using the solver 'VariableStepDiscrete' instead of solver 'ode15s'. You can disable this diagnostic by explicitly specifying a discrete solver in the solver tab of the Configuration Parameters dialog, or by setting the 'Automatic solver parameter selection' diagnostic to 'none' in the Diagnostics tab of the Configuration Parameters dialog"

I will need the solver ode15s, so i'm not sure if this will work in my final model. The code i used is the following:

component Multi_Disc_Brake

    nodes 
        V = foundation.mechanical.translational.translational; % R:left
    end

    parameters
        k = {1, 'm'};   % Number of rotating discs
    end

    variables
        f = {0, 'N'};
        M_B = {0, 'N*m'};
    end

    outputs 
        out = {0, 'N*m'}; % M(t):right:top
    end

    function setup
        through (f, V.f, []);
    end

    equations
        M_B == k*f; % Calculation of the braking moment
        out == M_B;
        V.v == 0;
    end
end

It seems like "V.v == 0" solved the problem, but i have no idea why and what exactly happens in the code.

[Matthias]

I've found another solution, this time with a physical force. It seems that i need to insert a line describing the force f in the equations section by any means. However, if i change the mass for example, there is no change in B_M, because the acceleration R.v_der is zero as i guess. Can anybody tell me why i need this line although nothing changes in the calculation of B_M?

here is the code:

component Multi_Disc_Brake

    nodes 
        R = foundation.mechanical.translational.translational; % R:left
        C = foundation.mechanical.translational.translational; % C:right
    end

    parameters 
        k = {1, 'm'}; 
        m = {1, 'kg'};
    end

    variables
        f = {0, 'N'};
        M_B = {0, 'N*m'};
        v = {0, 'm/s'};
    end

    outputs 
        out = {0, 'N*m'}; % M(t):right:top
    end

    function setup
        through (f, R.f, C.f);
        across (v, R.v, C.v);
    end

    equations
        f == m * R.v.der;
        M_B == k*f; % Calculation of the braking moment
        out == M_B;
    end
end