State Space Representation of a Custom Simscape Component

I am trying to create a custom Simscape component whose differential algebraic equation is put into a state space representation.

When I ssc_build the library, I get the following error.

>> ssc_build optHydro
Generating Simulink library 'optHydro_lib' in the current directory 's:\atG_Tasks\Wave_to_Wave_Tuning\JE101 Hydrodynamic Library for Simscape' ...
Failed to generate 'optHydro_lib'

Caused by:
    Error using optHydro.jespring>setup (line 43)
    Provided units 'm/s' and 'm' are not commensurate.

for the custom component file jespring.ssc

component jespring
% Translational Springy
% The block represents an ideal mechanical linear spring mass damper system
%
% Connections R and C are mechanical translational conserving ports. 
% The block positive direction is from port R to port C. This means that
% the force is positive if it acts in the direction from R to C.

% Copyright 2005-2008 The MathWorks, Inc.
nodes
   R=foundation.mechanical.translational.translational; %r:top
   C=foundation.mechanical.translational.translational; %c:bottom 
end

variables
    f = { 0, 'N'}; %force through
    v = { 0, 'm/s'}; %velocity across
    x = { 0, 'm'}; %position across
end

parameters
  spr_rate = { 1000, 'N/m' };  % Spring rate
  mass = { 1, 'kg' }; % Mass
  damper = {20, 'N/(m/s)' }; % Damping
  init_vel = { 0, 'm/s' };       % Initial velocity
  init_def = { 0, 'm' };       % Initial deformation
end

function setup
  if spr_rate <= 0
    pm_error('simscape:GreaterThanZero','Spring rate' )
  end
 if mass <= 0
    pm_error('simscape:GreaterThanZero','Mass' )
    end
 if damper <= 0
    pm_error('simscape:GreaterThanZero','Damping' )
  end
  across(v,R.v,C.v); %velocity variable from node r to c
  through(f,R.f,C.f); %force variable from node r to c
 % x = init_def;
 % v= init_vel;
  z=[init_def; init_vel];
  A=[0 1; -spr_rate/mass -damper/mass];
  B=[0;1];
  C=[0 1];
end

equations
  z.der == A*z+B*f;
  v == C*z;
end

end

As I understand the error, Simscape doesn't like the fact that the state vector, z includes physical variables with different units. Can anyone please suggest a way around this limitation?

Answer 1

[Guy Rouleau]

Interesting... I never tried combining states with different units into a vector.

Since your example is a simple linear spring+damper, it is easy to rearrange the equations. Something like the following should do the job:

v.der == k*x/m + c*v/m;
x.der == v;

I am curious... is it a test for something more complex you are planning to implement?

[James Eder]

Thanks for replying Guy.

Yes, this is a test case for a more complicated case. Eventually, I would like to pass the block the A,B,C matrices as parameters with an arbitrary order.

I may have made some progress on trying to get rid of the unit discrepancy, by multiplying rows and columns of the state space and A,B,C matrices by other united parameters.

However, all is not well yet. Right now, I am still getting the following error

>> ssc_build optHydro

Generating Simulink library 'optHydro_lib' in the current directory 's:\atG_Tasks\Wave_to_Wave_Tuning\JE101 Hydrodynamic Library for Simscape' ...

Failed to generate 'optHydro_lib'

Caused by:

Error using optHydro.jespring>equations (line 53)

Function 'A_mat' is not supported.

when I ssc_build the following revised code:

component jespring

% Translational Springy

% The block represents an ideal mechanical linear spring mass damper system

%

% Connections R and C are mechanical translational conserving ports.

% The block positive direction is from port R to port C. This means that

% the force is positive if it acts in the direction from R to C.

% Copyright 2005-2008 The MathWorks, Inc.

nodes

R=foundation.mechanical.translational.translational; %r:top

C=foundation.mechanical.translational.translational; %c:bottom

end

variables

f = { 0,'N' }; %force through

v = { 0,'m/s' }; %velocity across

x = { 0,'m' }; %position across

z= {0,'m'}; %internal state

end

parameters

spr_rate = { 1000, 'N/m' }; % Spring rate

mass = { 1,'kg' }; % Mass

damper = {20, 'N/(m/s)' }; % Damping

init_vel = { 0,'m/s' }; % Initial velocity

init_def = { 0,'m' }; % Initial deformation

second={1,'s'};

kilogram={1,'kg'};

end

function setup

if spr_rate <= 0

pm_error('simscape:GreaterThanZero','Spring rate' )

end

if mass <= 0

pm_error('simscape:GreaterThanZero','Mass' )

end

if damper <= 0

pm_error('simscape:GreaterThanZero','Damping' )

end

across(v,R.v,C.v); %velocity variable from node r to c

through(f,R.f,C.f); %force variable from node r to c

%x = init_def;

%v= init_vel;

z_state=[init_def; init_vel*second];

A_mat=[0/second 1/second;-spr_rate*second/mass -damper/mass];

B_mat=[0*second/kilogram; second/mass];

C_mat=[0/second 1/second];

end

equations

z.der==A_mat*z + B_mat*f;

v==C_mat*z_state;

end

end

Do you have any suggestions?

One fall back plan I have is to just "hard code" different versions of this component to reflect the different orders of the system. It won't be that clean, but I think I can make it work.

Thanks again for your interest.