Linearization of non-linear model

Question

Ajai Singh 2020-12-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/687669-linearization-of-non-linear-model

I was trying to linearize a non-linear model of an invterted pendulum and i used the following method :

created a S-function file and then used simulink to construct the model

then used linearize command and got the requuired ABCD matrices

but when i tried the same thing on a different model with more number of states , i am not getting the expected result ,

i'll attach both the simulink and S function files ,

And here is the S function code:.

function [sys,x0,str,ts] = myfunc(t,x,u,flag)
% MYFUNC An example M-file S-function for defining a 
% nonlinear time-varying state space system of the form:
%
%	 dx/dt = f(x,u,t)
%	     y = g(x,u,t)
%   
%   See sfuntmpl.m for a general S-function template.
%   See csfunc.m for a linear system implementation.
%   Edited version of csfunc.m
%   Copyright (c) 1990-97 by The MathWorks, Inc.
%   $Revision: 1.4 $
switch flag
  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0
    [sys,x0,str,ts]=mdlInitializeSizes;
  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1
    sys=mdlDerivatives(x,u,t);
  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3
    sys=mdlOutputs(x,u,t);
  %%%%%%%%%%%%%%%%%%%
  % Unhandled flags %
  %%%%%%%%%%%%%%%%%%%
  case { 2, 4, 9 }
    sys = [];
  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    error(['Unhandled flag = ',num2str(flag)]);
end
% end myfunc
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts]=mdlInitializeSizes
sizes = simsizes;
sizes.NumContStates  = 2; 	% ENTER state dimension 
sizes.NumOutputs     = 1; 	% ENTER output dimension 
sizes.NumInputs      = 1; 	% ENTER input dimension 
sizes.NumDiscStates  = 0;
sizes.DirFeedthrough = 0;   %this will always be zero
sizes.NumSampleTimes = 1;    
sys = simsizes(sizes);
str = [];
ts  = [0 0];
x0  = [0,0];  			% ENTER initial conditions 
% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(x,u,t)
    
%     syms a b c m l k 
    l = 1;
    k = 0.9;
    a = 9.8/l;
    m = 1;
    b = k/m;
    c = 143;
    %c = 1/(m*l^2);
    x1dot = x(2);
    x2dot = -a*sin(x(1)+pi) -b*x(2) + c*u;
    sys = [x1dot,x2dot];
% end mdlDerivatives
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(x,u,t)
    
  sys  = x(1); % ENTER output equation 
% end mdlOutputs

For my second model ,i'll just post the S-fucntion code as the simulink model is the same:

function [sys,x0,str,ts] = magsuspension(t,x,u,flag)
% MYFUNC An example M-file S-function for defining a 
% nonlinear time-varying state space system of the form:
%
%	 dx/dt = f(x,u,t)
%	     y = g(x,u,t)
%   
%   See sfuntmpl.m for a general S-function template.
%   See csfunc.m for a linear system implementation.
%   Edited version of csfunc.m
%   Copyright (c) 1990-97 by The MathWorks, Inc.
%   $Revision: 1.4 $
switch flag
  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0
    [sys,x0,str,ts]=mdlInitializeSizes;
  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1
    sys=mdlDerivatives(x,u,t);
  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3
    sys=mdlOutputs(x,u,t);
  %%%%%%%%%%%%%%%%%%%
  % Unhandled flags %
  %%%%%%%%%%%%%%%%%%%
  case { 2, 4, 9 }
    sys = [];
  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    error(['Unhandled flag = ',num2str(flag)]);
end
% end myfunc
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts]=mdlInitializeSizes
sizes = simsizes;
sizes.NumContStates  = 3; 	% ENTER state dimension 
sizes.NumOutputs     = 1; 	% ENTER output dimension 
sizes.NumInputs      = 1; 	% ENTER input dimension 
sizes.NumDiscStates  = 0;
sizes.DirFeedthrough = 0;   %this will always be zero
sizes.NumSampleTimes = 1;    
sys = simsizes(sizes);
str = [];
ts  = [0 0];
x0  = [0,0,0];  			% ENTER initial conditions 
% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(x,u,t)
    m = 0.1;
    k = 0.001;
    g = 9.81;
    a = 0.05;
    Lo= 0.01;
    L1 = 0.02;
    R = 1;
    x1_dot = x(2);
    x2_dot = g - k*x(2)/m - (Lo*a*x(3)^2)/(2*m*(a+x(1)))^2;
    x3_dot = (-R*x(3) + Lo*a*x(2)*x(3))*(L1 + Lo/(1+x(1)/a));
    sys = [x1_dot,x2_dot,x3_dot];
% end mdlDerivatives
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(x,u,t)
    
  sys  = x(1); % ENTER output equation 
% end mdlOutputs