From a0eb0d6d8243fc6a9f9c0303078f9892679baccb Mon Sep 17 00:00:00 2001
From: David Forrest <drf5na@gmail.com>
Date: Mon, 22 Nov 2021 13:49:43 -0500
Subject: [PATCH 1/4] Backcalculate per Astrom 1989 and
http://brettbeauregard.com/blog/2011/04/improving-the-beginner%e2%80%99s-pid-reset-windup/#comment-18721
---
PID_v1.cpp | 12 +++++++++---
1 file changed, 9 insertions(+), 3 deletions(-)
diff --git a/PID_v1.cpp b/PID_v1.cpp
index cb6637c..b9aceda 100644
--- a/PID_v1.cpp
+++ b/PID_v1.cpp
@@ -82,9 +82,15 @@ bool PID::Compute()
/*Compute Rest of PID Output*/
output += outputSum - kd * dInput;
- if(output > outMax) output = outMax;
- else if(output < outMin) output = outMin;
- *myOutput = output;
+ if(output > outMax){
+ outputSum -= output - outMax; // backcalculate integral to feasability
+ output = outMax;
+ }
+ else if(output < outMin) {
+ outputSum += outMin - output; // backcalculate integral to feasability
+ output = outMin;
+ }
+ *myOutput = output;
/*Remember some variables for next time*/
lastInput = input;
From 41bc38c879afcc185ad4eee83dc5c6743cd6ce4a Mon Sep 17 00:00:00 2001
From: David Forrest <drf5na@gmail.com>
Date: Wed, 22 Feb 2023 18:29:55 -0500
Subject: [PATCH 2/4] Update README.txt to .md and add Astrom reference
---
README.txt => README.md | 2 ++
1 file changed, 2 insertions(+)
rename README.txt => README.md (76%)
diff --git a/README.txt b/README.md
similarity index 76%
rename from README.txt
rename to README.md
index 3f2fb63..9e1fa37 100644
--- a/README.txt
+++ b/README.md
@@ -9,3 +9,5 @@
http://brettbeauregard.com/blog/2011/04/improving-the-beginners-pid-introduction/
- For function documentation see: http://playground.arduino.cc/Code/PIDLibrary
+
+This fork uses back calculation per [Astrom 1989](http://cse.lab.imtlucca.it/~bemporad/teaching/controllodigitale/pdf/Astrom-ACC89.pdf) to manage integral windup.
From 06804ed13a9549803a31020d89eb69fe5975ec5e Mon Sep 17 00:00:00 2001
From: David Forrest <drf5na@gmail.com>
Date: Fri, 3 Mar 2023 09:49:40 -0500
Subject: [PATCH 3/4] Expose integral to enable user-space hacking
---
PID_v1.h | 5 +++--
1 file changed, 3 insertions(+), 2 deletions(-)
diff --git a/PID_v1.h b/PID_v1.h
index 9cba046..8734108 100644
--- a/PID_v1.h
+++ b/PID_v1.h
@@ -52,6 +52,8 @@ class PID
// the PID calculation is performed. default is 100
+ void Initialize(); // * bumpless update of internal variables.
+ double outputSum; // * internal integrator state for understanding and user-space control
//Display functions ****************************************************************
double GetKp(); // These functions query the pid for interal values.
@@ -61,7 +63,6 @@ class PID
int GetDirection(); //
private:
- void Initialize();
double dispKp; // * we'll hold on to the tuning parameters in user-entered
double dispKi; // format for display purposes
@@ -80,7 +81,7 @@ class PID
// what these values are. with pointers we'll just know.
unsigned long lastTime;
- double outputSum, lastInput;
+ double lastInput;
unsigned long SampleTime;
double outMin, outMax;
From d1860fbc98eb96fc18ab80c4edf1e15b24266346 Mon Sep 17 00:00:00 2001
From: David R Forrest <drf5na@gmail.com>
Date: Sun, 12 Mar 2023 23:27:42 -0400
Subject: [PATCH 4/4] Add example/PID_heater_simulation
---
.../PID_heater_simulation.ino | 132 ++++++++++++++++++
1 file changed, 132 insertions(+)
create mode 100644 examples/PID_heater_simulation/PID_heater_simulation.ino
diff --git a/examples/PID_heater_simulation/PID_heater_simulation.ino b/examples/PID_heater_simulation/PID_heater_simulation.ino
new file mode 100644
index 0000000..8badd51
--- /dev/null
+++ b/examples/PID_heater_simulation/PID_heater_simulation.ino
@@ -0,0 +1,132 @@
+/********************************************************
+ PID Basic simulated heater Example
+ Reading analog input 0 to control analog PWM output 3
+ ********************************************************/
+// This simulates a 20W heater block driven by the PID
+// Vary the setpoint with the Pot, and watch the heater drive the temperature up
+//
+// Simulation at https://wokwi.com/projects/358122536159671297
+//
+// Based on
+// Wokwi https://wokwi.com/projects/357374218559137793
+// Wokwi https://wokwi.com/projects/356437164264235009
+
+#include "PID_v1.h" // https://github.com/br3ttb/Arduino-PID-Library
+// local copy of .h and .cpp are tweaked to expose the integral per
+// https://github.com/br3ttb/Arduino-PID-Library/pull/132#issuecomment-1453839425
+
+//Define Variables we'll be connecting to
+double Setpoint, Input, Output;
+
+//Specify the links and initial tuning parameters
+double Kp = 17, Ki = .1, Kd = 2; // works reasonably with sim heater block
+//double Kp = 255, Ki = .0, Kd = 0; // works reasonably with sim heater block
+//double Kp = 255, Ki = 0.0, Kd = 0.0; // bang-bang
+//double Kp = 2, Ki = 0.0, Kd = 0.0; // P-only
+//double Kp = 2, Ki = 5, Kd = 1; // commonly used defaults
+
+PID myPID(&Input, &Output, &Setpoint, Kp, Ki, Kd, P_ON_E, DIRECT);
+
+const int PWM_PIN = 3; // UNO PWM pin for Output
+const int INPUT_PIN = -1; // Analog pin for Input (set <0 for simulation)
+const int SETPOINT_PIN = A1; // Analog pin for Setpoint Potentiometer
+const int SETPOINT_INDICATOR = 6; // PWM pin for indicating setpoint PWM
+const int INPUT_INDICATOR = 5; // PWM pin for indicating Input PWM
+const int AUTOMATIC_PIN = 8; // Pin for controlling manual/auto mode, NO
+const int OVERRIDE_PIN = 12; // Pin for integral override, NO
+
+void setup()
+{
+ Serial.begin(115200);
+ Serial.println(__FILE__);
+ myPID.SetOutputLimits(-4, 255);
+ pinMode(OVERRIDE_PIN, INPUT_PULLUP);
+ pinMode(AUTOMATIC_PIN, INPUT_PULLUP);
+ if (SETPOINT_INDICATOR >= 0) pinMode(SETPOINT_INDICATOR, OUTPUT);
+ if (INPUT_INDICATOR >= 0) pinMode(INPUT_INDICATOR, OUTPUT);
+ Setpoint = 0;
+ //turn the PID on
+ myPID.SetMode(AUTOMATIC);
+ if(INPUT_PIN>0){
+ Input = analogRead(INPUT_PIN);
+ }else{
+ Input = simPlant(0.0,1.0); // simulate heating
+ }
+ Serial.println("Setpoint Input Output Integral");
+}
+
+void loop()
+{
+ // gather Input from INPUT_PIN or simulated block
+ float heaterWatts = (int)Output * 20.0 / 255; // 20W heater
+ if (INPUT_PIN > 0 ) {
+ Input = analogRead(INPUT_PIN);
+ } else {
+ float blockTemp = simPlant(heaterWatts,Output>0?1.0:1-Output); // simulate heating
+ Input = blockTemp; // read input from simulated heater block
+ }
+
+ if (myPID.Compute())
+ {
+ analogWrite(PWM_PIN, (int)Output);
+
+ Setpoint = analogRead(SETPOINT_PIN) / 4; // Read setpoint from potentiometer
+ if (INPUT_INDICATOR >= 0) analogWrite(INPUT_INDICATOR, Input);
+ if (SETPOINT_INDICATOR >= 0) analogWrite(SETPOINT_INDICATOR, Setpoint);
+ }
+ if(digitalRead(OVERRIDE_PIN)==LOW) mySetIntegral(&myPID,0); // integral override
+ if(digitalRead(AUTOMATIC_PIN)==HIGH != myPID.GetMode()==AUTOMATIC){
+ myPID.SetMode(digitalRead(AUTOMATIC_PIN)==HIGH ? AUTOMATIC :MANUAL);
+
+ }
+
+ report();
+
+
+}
+
+void report(void)
+{
+ static uint32_t last = 0;
+ const int interval = 1000;
+ if (millis() - last > interval) {
+ last += interval;
+ // Serial.print(millis()/1000.0);
+ Serial.print("SP:");Serial.print(Setpoint);
+ Serial.print(" PV:");
+ Serial.print(Input);
+ Serial.print(" CV:");
+ Serial.print(Output);
+ Serial.print(" Int:");
+ Serial.print(myPID.GetIntegral());
+ Serial.print(' ');
+ Serial.println();
+ }
+}
+
+float simPlant(float Q,float hfactor) { // heat input in W (or J/s)
+ // simulate a 1x1x2cm aluminum block with a heater and passive ambient cooling
+ // float C = 237; // W/mK thermal conduction coefficient for Al
+ float h = 5 *hfactor ; // W/m2K thermal convection coefficient for Al passive
+ float Cps = 0.89; // J/g°C
+ float area = 1e-4; // m2 area for convection
+ float mass = 10 ; // g
+ float Tamb = 25; // °C
+ static float T = Tamb; // °C
+ static uint32_t last = 0;
+ uint32_t interval = 100; // ms
+
+ if (millis() - last >= interval) {
+ last += interval;
+ // 0-dimensional heat transfer
+ T = T + Q * interval / 1000 / mass / Cps - (T - Tamb) * area * h;
+ }
+ return T;
+}
+
+void mySetIntegral(PID * ptrPID,double value ){
+ ptrPID->SetMode(MANUAL);
+ Output = value;
+ ptrPID->SetMode(AUTOMATIC);
+}
+