Description of idareas

AutotunerPID Toolkit

idareas

PURPOSE

Identification of a FOPDT model using the method of the areas.

SYNOPSIS

function model = idareas(y,As,Ts)

DESCRIPTION

IDAREAS Identification of a FOPDT model using the method of the
   areas.

   MODEL = IDAREAS(Y,As,Ts) returns a structure describing the identified
   FOPDT (First Order Plus Dead Time) model in the form
            M(s) = m*exp(-s*L) / (1+s*T)
   The structure has the following fields MODEL.m, MODEL.L and MODEL.T
   with obvious meaning.
   The function requires the recorded step response Y, the amplitude of
   the step used for identification As and the sample time Ts.

   Author:    William Spinelli ([e-mail])
   Copyright  2004 W.Spinelli
   $Revision: 1.0 $  $Date: 2004/02/27 12:00:00 $

CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

• bodePIDcompare BODEPIDCOMPARE Comparison of Bode Diagrams with different autotuning
• pid_autotuner PID_SUPERV Supervisor of a PID autotuner (implmented as an S-function)
• stepPIDcompare STEPPIDCOMPARE Comparison of step response on setpoint and load

SOURCE CODE

0001 function model = idareas(y,As,Ts)
0002 %IDAREAS Identification of a FOPDT model using the method of the
0003 %   areas.
0004 %
0005 %   MODEL = IDAREAS(Y,As,Ts) returns a structure describing the identified
0006 %   FOPDT (First Order Plus Dead Time) model in the form
0007 %            M(s) = m*exp(-s*L) / (1+s*T)
0008 %   The structure has the following fields MODEL.m, MODEL.L and MODEL.T
0009 %   with obvious meaning.
0010 %   The function requires the recorded step response Y, the amplitude of
0011 %   the step used for identification As and the sample time Ts.
0012 %
0013 %   Author:    William Spinelli ([e-mail])
0014 %   Copyright  2004 W.Spinelli
0015 %   $Revision: 1.0 $  $Date: 2004/02/27 12:00:00 $
0016 
0017 % compute auxiliary parameters
0018 m = (y(end)-y(1))/As;                     % process gain
0019 
0020 % if m<0 reverse the step response
0021 if m<0
0022    y = -y;
0023 end
0024 
0025 % change this setting one can try to robustify the identification process
0026 % with noisy step response
0027 y1 = y(1);
0028 yN = y(end);
0029 
0030 % reverse undershoot and overshoot
0031 y(y<y1) = y1;
0032 y(y>yN) = y(y>yN) - 2*(y(y>yN)-yN);
0033 
0034 A0  = sum(yN-y)*Ts;              % upper area
0035 it0 = fix(A0/abs(m)/Ts);         % compute the index of the vector
0036                                  % (not the value of t0)
0037 A1  = sum(y(1:it0)-y1)*Ts;       % lower area
0038 
0039 % compute model parameters
0040 T = exp(1)*A1/abs(m);
0041 L = max((A0-exp(1)*A1)/abs(m),0);
0042 
0043 model.L = L;
0044 model.T = T;
0045 model.m = m;

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