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AutotunerPID Toolkit

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from AutotunerPID Toolkit by William Spinelli
Interactive simulation of a PID with autotuning.

Description of pid_isatd
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pid_isatd

PURPOSE ^

Discrete time ISA-PID (implemented as a Matlab S-function).

SYNOPSIS ^

function [sys,x0,str,ts] = pid_isatd(t,x,u,flag,Ts,umin,umax,As,hystLevel)

DESCRIPTION ^

PID_ISATD Discrete time ISA-PID (implemented as an S-function)

   The PID closely resemble the structure of a real industrial PID and has
   the following features: 
     - filter on the derivative action
     - set-point weight (but not the weight of the derivative action which
       is fixed to 0)
     - antiwindup on lower and higher saturation limits of the actuator
     - bumpless auto-manual switch

   It also implements the logic to perform the identification experiment:
     - step response identification (with user-defined step amplitude)
     - relay identification (with user-defined relay amplitude and
       hysteresis level)

   Author:    William Spinelli (wspinell@elet.polimi.it)
   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:

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function [sys,x0,str,ts] = pid_isatd(t,x,u,flag,Ts,umin,umax,As,hystLevel)
0002 %PID_ISATD Discrete time ISA-PID (implemented as an S-function)
0003 %
0004 %   The PID closely resemble the structure of a real industrial PID and has
0005 %   the following features:
0006 %     - filter on the derivative action
0007 %     - set-point weight (but not the weight of the derivative action which
0008 %       is fixed to 0)
0009 %     - antiwindup on lower and higher saturation limits of the actuator
0010 %     - bumpless auto-manual switch
0011 %
0012 %   It also implements the logic to perform the identification experiment:
0013 %     - step response identification (with user-defined step amplitude)
0014 %     - relay identification (with user-defined relay amplitude and
0015 %       hysteresis level)
0016 %
0017 %   Author:    William Spinelli (wspinell@elet.polimi.it)
0018 %   Copyright  2004 W.Spinelli
0019 %   $Revision: 1.0 $  $Date: 2004/02/27 12:00:00 $
0020 
0021 persistent stato;           % internal state variable
0022 
0023 CVBlock = 'ManValue';
0024 switch flag,
0025     case 0,
0026         [sys,x0,str,ts,stato] = mdlInitializeSizes(Ts);
0027     case 3,
0028         [sys,stato] = mdlOutputs(t,x,u,stato,Ts,umin,umax,As,hystLevel);
0029     case { 1, 2, 4, 9 }
0030         sys=[];
0031     otherwise
0032         error(['Unhandled flag = ', num2str(flag)]);
0033 end
0034 % end pid_isatd
0035 
0036 
0037 %=============================================================================
0038 % mdlInitializeSizes
0039 % Return the sizes, initial conditions, and sample times for the S-function.
0040 %=============================================================================
0041 function [sys,x0,str,ts,stato] = mdlInitializeSizes(Ts)
0042 % set up S-function
0043 sizes = simsizes;
0044 
0045 sizes.NumContStates  = 0;
0046 sizes.NumDiscStates  = 0;
0047 sizes.NumOutputs     = 1;
0048 sizes.NumInputs      = 4;
0049 sizes.DirFeedthrough = 1;
0050 sizes.NumSampleTimes = 1;   % at least one sample time is needed
0051 
0052 sys = simsizes(sizes);
0053 
0054 x0  = [];
0055 str = [];
0056 ts  = [Ts 0];
0057 stato = [0 0 0 0 0];
0058 % end mdlInitializeSizes
0059 
0060 %=============================================================================
0061 % mdlOutputs
0062 % Return the block outputs.
0063 %=============================================================================
0064 function [sys,stato] = mdlOutputs(t,x,u,stato,Ts,umin,umax,As,hystLevel)
0065 global CVVALUE                  % control variable (used for M/A commutation)
0066 global IDENTIFICATION_METHOD
0067 global TUNING_METHOD
0068 global PIDPARAMETERS
0069 
0070 % measured signals
0071 sp = u(1);                      % setpoint value
0072 pv = u(2);                      % process value
0073 
0074 % control signals
0075 auto     = u(3);                % auto/man switch (MANUAL=0; AUTO=1)
0076 autotune = u(4);                % true when autotuning
0077 
0078 % PID parameters (c=0)
0079 K  = PIDPARAMETERS(1);
0080 Ti = PIDPARAMETERS(2);
0081 Td = PIDPARAMETERS(3);
0082 N  = PIDPARAMETERS(4);
0083 b  = PIDPARAMETERS(5);
0084 
0085 % translation of the vector stato (for simplicity)
0086 % state variable
0087 ui    = stato(1);               % integral action
0088 ud    = stato(2);               % derivative action (filter)
0089 
0090 % auxiliary variable
0091 pvold = stato(3);               % old process value
0092 cvold = stato(4);               % old control variable
0093 atold = stato(5);               % old autotune state (to ensure bumpless switch)
0094 
0095 % PID algorithm
0096 % compute the constants (made each time since PID parameters may change)
0097 if Ti
0098     a1 = K*Ts/Ti;
0099 else
0100     % when Ti = 0 turn off the integral action
0101     a1 = 0;
0102 end
0103 b1 = Td/(Td + N*Ts);
0104 b2 = K*Td*N/(Td + N*Ts);
0105 
0106 % compute control actions
0107 up = K*(b*sp - pv);
0108 
0109 ud = b1*ud - b2*(pv-pvold);
0110 
0111 if ~autotune & atold
0112     % ensure bumpless switch after a change in the regulator parameters
0113     ui = cvold - up - ud;
0114 end
0115 
0116 if autotune
0117     if strcmp(IDENTIFICATION_METHOD,'STEP')
0118         % increment the value of the control variable
0119         cv = CVVALUE+As;
0120     elseif strcmp(IDENTIFICATION_METHOD,'RELAY')
0121         if ~atold
0122             cv = CVVALUE+As;
0123         else
0124             if pv >= sp+hystLevel
0125                 cv = CVVALUE-As;
0126             elseif pv <= sp-hystLevel
0127                 cv = CVVALUE+As;
0128             else
0129                 cv = cvold;
0130             end
0131         end
0132     end
0133 else
0134     if ~auto
0135         % manual mode
0136         cv = CVVALUE;
0137     else
0138         % automatic regulation
0139         cv = up + ui + ud;
0140     end
0141     
0142     if cv > umax
0143         % saturation on maximum value (note that the state of the integrator is
0144         % not updated)
0145         cv = umax;
0146     elseif cv < umin
0147         % saturation on minimum value
0148         cv = umin;
0149     else
0150         % update the state of the integrator
0151         if auto
0152             ui = ui + a1*(sp-pv);
0153         else
0154             ui = cv - up - ud;
0155         end
0156     end
0157     % update control variable value
0158     CVVALUE = cv;
0159 end
0160 
0161 % update internal state vector
0162 stato = [ui ud pv cv autotune];
0163 % generate control variable
0164 sys = cv;
0165 % end mdlOutputs

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