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Comment:Saved (quite old) version which integrates IR to give SR
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SHA3-256: e67a236326010ab178cd4951ffceaac07fde748c82b2a0d8e26fe9e402ec2935
User & Date: gawthrop@users.sourceforge.net on 1996-12-05 10:18:52
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Context
1996-12-05
10:38:36
Decided that integrating the IR is a bad idea.
So now explicitly computes the SR using matrix exponential -- much
more accurate. check-in: 5fd8598766 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
10:18:52
Saved (quite old) version which integrates IR to give SR check-in: e67a236326 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
10:17:34
Put in version control history. check-in: 532092897f user: gawthrop@users.sourceforge.net tags: origin/master, trunk
Changes
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Modified mttroot/mtt/bin/trans/m/sm2sr.m from [3cfd117635] to [aedb773097]. 

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function [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% sm2sr - Constrained-state matrix to step response.
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%     %%%%% Model Transformation Tools %%%%%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% Matlab function  sm2sr
% [Y,X] = sm2sr(A,B,C,D,T,u0,x0);
% Constrained-state matrix to impulse response.
% A,B,C,D,E - (constrained) state matrices
% T vector of time points
% u0 input gain vector: u = u0*unit step.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.3  1996/10/27  10:39:04  peterg
% %% Only compute matrix exponential once.
% %%
% %% Revision 1.2  1996/09/10  16:48:21  peter
% %% Changed ar counts in default settings.
% %%
% %% Revision 1.1  1996/08/19 15:34:29  peter
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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if M>N
  T = T';
  N = M;
end;



one = eye(Nx);

Y = zeros(N,Ny);
X = zeros(N,Nx);

dt = T(2)-T(1);% Assumes fixed interval
expAdt = expm(A*dt); % Compute matrix exponential
i = 0;
expAt = one;

for t = T'
  i=i+1;
  if Nx>0
    x = ( A\(expAt-one) )*B*u0 + expAt*x0;
    expAt = expAt+expAdt;
    X(i,:) = x';
    if Ny>0
      y = C*x + D*u0;
      Y(i,:) = y';
    end;
  elseif Ny>0
    y = D*u0;
    Y(i,:) = y';
  end;
end;
% $$$ one = eye(Nx);
% $$$ 
% $$$ Y = zeros(N,Ny);
% $$$ X = zeros(N,Nx);
% $$$ 
% $$$ dt = T(2)-T(1);% Assumes fixed interval
% $$$ expAdt = expm(A*dt); % Compute matrix exponential
% $$$ i = 0;
% $$$ expAt = one;
% $$$ 
% $$$ for t = T'
% $$$   i=i+1;
% $$$   if Nx>0
% $$$     x = ( A\(expAt-one) )*B*u0 + expAt*x0;
% $$$     expAt = expAt+expAdt;
% $$$     X(i,:) = x';
% $$$     if Ny>0
% $$$       y = C*x + D*u0;
% $$$       Y(i,:) = y';
% $$$     end;
% $$$   elseif Ny>0
% $$$     y = D*u0;
% $$$     Y(i,:) = y';
% $$$   end;
% $$$ end;

% Compute the impulse response
[Y,X] = sm2ir(A,B,C,D,T,u0,x0);

% Assume fixed sample interval
dT = T(2)-T(1);

% Do an Euler integration on it
 Y = mtt_euler(Y,dT);
 
 if nargout>1
   X = mtt_euler(X,dT);
 end;

MTT: Model Transformation Tools
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