Description of pid_autotuner

AutotunerPID Toolkit

pid_autotuner

PURPOSE

Supervisor of a PID autotuner (implmented as a Matlab S-function).

SYNOPSIS

function [sys,x0,str,ts] = pid_autotuner(t,x,u,flag,Ts,As)

DESCRIPTION

PID_SUPERV Supervisor of a PID autotuner (implmented as an S-function)

   The supervisor, rules out the autotuning process mainly performing the
   identification of a process model and the synthesis of the new
   parameters with various methods. 
   Moreover it is possible to constrain the structure of the regulator to
   be a PI or a PID, or the structure can be automatically selected by the
   supervisor.
   In particular, the autotuner has the following feature:
      - identification of process description:
         * a FOPDT model through the areas method
         * one point of the frequency response through the method of the
           relay 
      - sythesis of the PID parameters using
         * KT method
         * IMC method
         * First and second ZN method
      - it's still a work in progress!! ;-)

   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:

• idareas IDAREAS Identification of a FOPDT model using the method of the
• pid_structure PID_STRUCTURE Structure selection for a ISA PID regulator.
• pid_tuning PID_TUNING Tune the parameters of a ISA-PID regulator with some

This function is called by:

SUBFUNCTIONS

• function [sys,x0,str,ts] = mdlInitializeSizes(Ts)
• function [sys] = mdlOutputs(t,x,u,Ts,As)

SOURCE CODE

0001 function [sys,x0,str,ts] = pid_autotuner(t,x,u,flag,Ts,As)
0002 %PID_SUPERV Supervisor of a PID autotuner (implmented as an S-function)
0003 %
0004 %   The supervisor, rules out the autotuning process mainly performing the
0005 %   identification of a process model and the synthesis of the new
0006 %   parameters with various methods.
0007 %   Moreover it is possible to constrain the structure of the regulator to
0008 %   be a PI or a PID, or the structure can be automatically selected by the
0009 %   supervisor.
0010 %   In particular, the autotuner has the following feature:
0011 %      - identification of process description:
0012 %         * a FOPDT model through the areas method
0013 %         * one point of the frequency response through the method of the
0014 %           relay
0015 %      - sythesis of the PID parameters using
0016 %         * KT method
0017 %         * IMC method
0018 %         * First and second ZN method
0019 %      - it's still a work in progress!! ;-)
0020 %
0021 %   Author:    William Spinelli ([e-mail])
0022 %   Copyright  2004 W.Spinelli
0023 %   $Revision: 1.0 $  $Date: 2004/02/27 12:00:00 $
0024 
0025 switch flag,
0026    % Initialization
0027    case 0,
0028       [sys,x0,str,ts] = mdlInitializeSizes(Ts);
0029       % Outputs
0030    case 3,
0031       [sys] = mdlOutputs(t,x,u,Ts,As);
0032       % Unused flags
0033    case { 1, 2, 4, 9 }
0034       sys = [];
0035    otherwise
0036       error(['Unhandled flag = ',num2str(flag)]);        
0037 end
0038 % end pid_superv
0039 
0040 
0041 %=============================================================================
0042 % mdlInitializeSizes
0043 % Return the sizes, initial conditions, and sample times for the S-function.
0044 %=============================================================================
0045 function [sys,x0,str,ts] = mdlInitializeSizes(Ts)
0046 global Y_AUTOTUNING     % store the step (or relay) response used for tuning
0047 
0048 Y_AUTOTUNING = [];      % initialized to an empty vector
0049 
0050 % set up S-function
0051 sizes = simsizes;
0052 
0053 sizes.NumContStates  = 0;
0054 sizes.NumDiscStates  = 0;
0055 sizes.NumOutputs     = 2;
0056 sizes.NumInputs      = 1;
0057 sizes.DirFeedthrough = 1;
0058 sizes.NumSampleTimes = 1;   % at least one sample time is needed
0059 
0060 sys = simsizes(sizes);
0061 
0062 x0  = [];
0063 str = [];
0064 ts  = [Ts 0];
0065 % end mdlInitializeSizes
0066 
0067 
0068 %=============================================================================
0069 % mdlOutputs
0070 % Return the block outputs.
0071 %=============================================================================
0072 function [sys] = mdlOutputs(t,x,u,Ts,As)
0073 % sys(1)    :    auto/manual switch
0074 % sys(2)    :    autotuning (0 : autotuning in progress; 1 : normal operation)
0075 
0076 % u(1)      :    new sample of the step response
0077 
0078 global PIDPARAMETERS
0079 global IDENTIFICATION_METHOD
0080 global TUNING_STRUCTURE
0081 global TUNING_METHOD
0082 global TUNING_PARAM
0083 global AUTOTUNE
0084 global AUTOMAN
0085 
0086 global Y_AUTOTUNING
0087 
0088 step_steadyThr  = 0.05;    % threshold on derivative to consider the
0089                            % step response to a stedy state
0090 relay_steadyThr = 0.05;    % threshold on peaks percentual difference to
0091                            % consider the relay response to steady state
0092 
0093 if AUTOTUNE
0094    % store the new sample of the step response
0095    Y_AUTOTUNING = [Y_AUTOTUNING; u(1)];
0096    y = Y_AUTOTUNING;
0097    
0098    if strcmp(IDENTIFICATION_METHOD,'STEP')
0099       % check if the step response has reached a steady state (i. e. check if
0100       % the last 10% of the step response is ``flat'' enough)
0101       N  = fix(length(y)/10);   % last 10% of the step response
0102       if N > 15
0103          % the step response must be made at least by 150 samples
0104          deltay = abs(y(end)-y(1));
0105          yw = y(end-N:end);
0106          % mean value of the derivative in the window lower than a fraction
0107          % of the maximum value of the derivative
0108          idok = (max(yw)-min(yw)) < step_steadyThr*(max(y)-min(y));
0109       else
0110          idok = 0;
0111       end
0112       if idok
0113          model = idareas(y,1,Ts);
0114       end
0115    elseif strcmp(IDENTIFICATION_METHOD,'RELAY')
0116       % IDENTIFICATION WITH THE RELAY METHOD
0117       dy = diff(y);
0118       ind = find(dy(1:end-1)>0 & dy(2:end)<0);
0119       
0120       % at least 4 oscillations but no more than 10 oscillations
0121       if length(ind)>=4 & length(ind)<10
0122          ym = mean(y);
0123          % mean value of the difference between the last three peaks is
0124          % less than a fraction of the overall range of the response
0125          idok = mean(abs(diff(y(ind(end-2:end))))) < relay_steadyThr*(max(y)-min(y));
0126          % the last ``period'' must cross the zero
0127          idok = idok & any(abs(y(ind(end-1):ind(end))-ym) < relay_steadyThr/2*abs(max(y)-ym));
0128       elseif length(ind)>=10
0129          % force the stop of the relay identification
0130          idok = 1;
0131       else
0132          idok = 0;
0133       end
0134       
0135       if idok
0136          model.A = max(y)-min(y);
0137          model.T = Ts*(ind(end)-ind(end-1));
0138       end    
0139    end
0140    
0141    % autotuning required
0142    if idok        
0143       % selection of the regulator structure
0144       regStruct = pid_structure(model,TUNING_STRUCTURE);
0145       
0146       % synthesis of the PID parameters
0147       try
0148          [K,Ti,Td,N,b] = pid_tuning(model,TUNING_METHOD,TUNING_PARAM,regStruct,As);
0149          % update PID parameters
0150          PIDPARAMETERS = [K Ti Td N b];
0151       catch
0152          % no change in the parameters
0153       end
0154       
0155       AUTOTUNE = 0;
0156    end
0157    % put the PID in manual mode during autotuning and propagate the
0158    % ``autotuning running'' signal
0159    sys = [AUTOMAN 1];   
0160 else
0161    % empty the step response vector
0162    Y_AUTOTUNING = [];
0163    % put the PID in auto mode during autotuning and propagate the
0164    % ``autotuning not running'' signal
0165    sys = [AUTOMAN 0];
0166 end
0167 % end mdlOutputs

idareas

pid_isatd

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