Linear induction motor in simscape

Hello,

based on the examples in the ThreePhaseExamples_lib provided by mathworks, I wanted to customize the model for a linear induction motor. So far I've changed the library code to

component lim_custom
% Linear induction motor
% 

      parameters
          nPolePairs                  =  {1, '1'};                    % Number of pole pairs
          t_p                         =  {0.05, 'm'};                 % pole pitch
          pm_flux_linkage             = {0.03, 'Wb'};                 % Permanent magnet flux linkage
          stator_param                = {1,'1'};                      % Stator parameterization
          Ld                          = {0.00025, 'H'};               % Stator d-axis inductance, Ld
          Lq                          = {0.00019, 'H'};               % Stator q-axis inductance, Lq
          Rs                          = {0.013, 'Ohm'};               % Stator resistance per phase, Rs
      end

    parameters (Access=protected)
        shift_3ph = { [0,-2*pi/3,2*pi/3], 'rad' };
    end

    nodes
        L1 = foundation.electrical.electrical;        % L1:left
        L2 = foundation.electrical.electrical;        % L2:left
        L3 = foundation.electrical.electrical;        % L3:left
        R = foundation.mechanical.translational.translational; % R:right
        C = foundation.mechanical.translational.translational; % C:right
    end

    variables
        % Mechanical
        translational_position = {0, 'm'}; % Rotor angle

        % Stator currents
        i_d = {0, 'A'}; % d-axis current
        i_q = {0, 'A'}; % q-axis current
    end

    variables (Access=protected)
        % Mechanical
        force = {0, 'N' }; % Mechanical torque

        % Stator currents
        i1 = { 0 , 'A' }; % Phase currents
        i2 = { 0 , 'A' }; % Phase currents
        i3 = { 0 , 'A' }; % Phase currents
    end

    branches
        i1      : L1.i    -> *;
        i2      : L2.i    -> *;
        i3      : L3.i    -> *;
        force   : R.f     -> C.f;
    end
    equations
        let
            translational_velocity = R.v - C.v;
            electrical_angle = nPolePairs*translational_position*2*pi/t_p;

            % Set up Park's transform
            abc2dq = 2/3*[...
                cos( electrical_angle + shift_3ph );...
                -sin( electrical_angle + shift_3ph )];

            % Voltages a,b,c -> d,q
            U = [L1.v L2.v L3.v];
            vdq = abc2dq*U';
            vd = vdq(1);
            vq = vdq(2);

            % Flux linkages
            psi_d = i_d*Ld + pm_flux_linkage;
            psi_q = i_q*Lq;
            I = [i1 i2 i3];
        in
            % Electric to mechanical rotation
            translational_velocity == translational_position.der;

            % Electrical equations
            vd == i_d*Rs + i_d.der*Ld - nPolePairs*translational_velocity*2*pi/t_p*psi_q;
            vq == i_q*Rs + i_q.der*Lq + nPolePairs*translational_velocity*2*pi/t_p*psi_d;
            [ i_d; i_q ] == abc2dq*I';
            I(1)+I(2)+I(3) == 0;

            % Mechanical force
            force == -3/2*nPolePairs/2/t_p*(i_q*psi_d - i_d*psi_q);
        end
    end

The error message I receive says

My guess is, that the error is related to the domain change from rotational to translational, but due to limited knowledge to simscape I don't know how to solve this. Does anyone have an advice for me?

Thank you, Tobias

[Rohit Kini]

Hey Tobias!

Were you able to solve the error and generate the model?

Answer 1

[Sabin]

This error can also be a consequence of how the simulation model was built and I suspect is not the custom code the culprit. The given code it is however a PMLSM rather than an induction machine. There are a few inaccuracies in the posted code, but I expect it to simulate when put in a proper simulation model. For example, when we talk about linear machines, we usually consider the polar pitch as parameter rather than number of pole pairs and we can then compute the electrical position constant as Np=pi/polar pitch. This way we can work out the force as force == 3/2*Np*(i_q*psi_d - i_d*psi_q). Similarly, we can write the voltage equations.