State derivatives returned by S-function 'file.m' in 'file/S-Function' during flag=1 call must be a real vector of length 3

I am trying to simulate the response of my state space system but during the runtime in Simulink I get an error stating "State derivatives returned by S-function 'file.m' in 'file/S-Function' during flag=1 call must be a real vector of length 3". I have narrowed it down to 2 of my state equations which are causing this error as when I commented them out and ran the simulation using only the third equation, the simulation compiled and ran without error. I have searched this error and visited the relevant MathWorks forums but none of them have a solution that works for my case.

% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts]=mdlInitializeSizes()

sizes = simsizes;
sizes.NumContStates  = 3;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 3;
sizes.NumInputs      = 1;
sizes.DirFeedthrough = 0;
sizes.NumSampleTimes = 1;

sys = simsizes(sizes);
x0  = zeros(3,1);
str = [];
ts  = [0 0];

% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(t,x,u)
%% Place system here 

%change of variables
%states
x_1 = x(1);
x_2 = x(2);
x_3 = x(3);
%inputs
u_1 = u(1);

%system states sys is your state derivatives
sys(1)= x_2^2 + 16*x_2 - 12*u_1 + x_1 - 9*x_3 + x_1*x_3 - 8;

sys(2)= 2*u_1^2 - 7*u_1 + x_1 + 2*x_2*x_3 + 10;

sys(3)= 2*u_1^2 + 8*x_3 + x_1*x_3;

% end mdlDerivatives
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(t,x,u)
C=eye(3);
sys = C*x;

% end mdlOutputs

The above is a snippet of the code that I am using which is an edited csfunc for a nonlinear system. The equations which are causing the errors are 'sys(1)' and 'sys(2)'.

Any assistance is appreciated.

[Walter Roberson]

Remember that inside Simulink you need to preallocate variables in most cases.

sys = zeros(3,1);

With your current code, when you assign to sys(1) that is the first assignment to the variable and locks it in as having only one element.

[Nicholas Bissessar]

Are you stating that I need to include that line of code in my csfunc? I have x0 = zeros(3,1).

[Walter Roberson]

mdlDerivatives does not preallocate sys

The fact that you initialize x0 in the model initialization function does not mean that you have initialized sys in mdlDerivatives

[Nicholas Bissessar]

Even after initializing sys in mdlDerivatives I am still getting the error. I am at lost on how to solve it but I am sure that the error is being caused by sys(1) and sys(2).

[Walter Roberson]

One potential risk would be if the input u were purely imaginary. Your third output uses u_1^2 which under that hypothesis would become real-valued. Your other two sys use u_1 not square and those would remain imaginary.

[Nicholas Bissessar]

Is it possible to set the initial state of the system to the equilibrium points to resolve this error?

[Walter Roberson]

Do you know the equilibrium points? Is there a way to calculate them?

I would suggest that you use the simulink debugger to look at the output of the assignment to sys(1) and sys(2) to determine whether the results are complex valued.

[Nicholas Bissessar]

I already calculated the equilibrium points but I don't know how to set the initial state of the system to the equilibrium points.

[Walter Roberson]

Right after the line

x0  = zeros(3,1);

assign the appropriate values to x0(1), x0(2), x0(3)