Error in simscape when computing derivative

I have a Simscape block that takes linPosition (physical signal) as an input and computes rotPosition (another physical signal). If I put it in my model, where linPosition is 0 for 1ms and then starts increasing smoothly, it works (rotPosition and theta are constant for 1ms and then follow the growth of linPosition). The problem arises when I try to add an additional computation: omega == der(theta) (I need it to make more calculation and provide another output). With that additional equation, I get this warning:

Equations (including nonlinear equations) of one or more components may be dependent or inconsistent. This can cause problems in transient initialization.

referred to the first and second equations. Then the simulation stops at 1ms:

An error occurred during simulation and the simulation was stopped

Caused by:

['testCircuit/Solver Configuration']: Transient initialization at time 0.001, solving for consistent states and modes, failed to converge.

Nonlinear solver: Linear Algebra error. Failed to solve using iteration matrix.

all components and nodal across variables involved

Cannot solve for one or more variables, including dynamic variable derivatives:

Time derivative of 'CRIB.CRIB_velocityBased.breaking_part.offsetSliderCrank.theta' (rot angle with respect to horizontal)

'CRIB.CRIB_velocityBased.breaking_part.offsetSliderCrank.omega' (omega)

In my mind, theta and gamma in the equations are computed and then omega follows the value of theta, but I guess that this is not how it works.

component offsetSliderCrank

inputs
    linPosition = {0, 'mm'};
end

outputs
    rotPosition = {0, 'deg'};
end

parameters
    lRod = { 45, 'mm' }; %
    rJunction =  { 10, 'mm' }; %
    xC = { 2, 'mm' }; %
    yC = { 40, 'mm' }; %

end


variables(Access=Protected)
    theta = {value={0,'deg'},imin={-90,'deg'},imax={89,'deg'}}; % rot angle with respect to horizontal
    gamma = {value={0,'deg'},imin={0,'deg'},imax={180,'deg'}}; % angle between lRod and horizontal
    omega = {0,'deg/s'};

end

equations
    lRod*cos(gamma)+xC == rJunction*cos(theta);
    yC-linPosition - rJunction*sin(theta) == lRod*sin(gamma);
    let
        theta0 = asin((yC^2+rJunction^2-lRod^2+xC^2)/(2*rJunction*sqrt(xC^2+yC^2))) - atan(xC/yC) ;
    in
        rotPosition == - (theta- theta0);
    end
    omega == der(theta);
end

end

Answer 1

[Torsten]

Can you compute der(linPosition) ?

If this is the case, you get an algebraic equation for omega = der(theta):

Write the first two equations as

lRod*cos(gamma) = rJunction*cos(theta) - xC
lRod*sin(gamma) = yC - linPosition(t) - rJunction*sin(theta)

Now square both equations and add them:

lRod^2 = (rJunction*cos(theta) - xC)^2 + (yC - linPosition(t) - rJunction*sin(theta))^2
lRod^2 =  -2*xC*rJunction*cos(theta) + xC^2 + (yC - linPosition(t))^2 - 2*(yC - linPosition(t))*rJunction*sin(theta) + rJunction^2
lRod^2 - xC^2 - yC^2 - rJunction^2 = -2*xC*rJunction*cos(theta) - 2*yC*linPosition(t) + linPosition(t)^2 - 2*(yC - linPosition(t))*rJunction*sin(theta)

Now differentiate both sides with respect to t:

0 = 2*xC*rJunction*sin(theta)*der(theta) - 2*yC*der(linPosition) + 2*linPosition*der(linPosition) - 2*yC*rJunction*cos(theta)*der(theta) + 2*linPosition*rJunction*cos(theta)*der(theta) + 2*der(linPosition)*rJunction*sin(theta)

and solve for der(theta):

der(theta) = (2*yC*der(linPosition) - 2*linPosition*der(linPosition) - 2*der(linPosition)*rJunction*sin(theta))/(2*xC*rJunction*sin(theta)+2*yC*rJunction*cos(theta)+2*linPosition*rJunction*cos(theta))

By the way: if gamma and theta are in degrees, is it possible in Simscape to use sin and cos ? In MATLAB, you had to use sind and cosd.