PID control with proportional (Kp), integral (Ki) and differential (Kd) coefficient is stated as:
PID controler equation provides the input to the H-bridge. The realisation schematics of the above equation is shown in the following figure:
In .js file, we should add PID control algorithm variables:
// PID Algorithm variables
var Kp = 0.55; // proportional factor
var Ki = 0.008; // integral factor
var Kd = 0.15; // differential factor
var pwm = 0;
var pwmLimit = 254;
var err = 0; // variable for second pid implementation
var errSum = 0; // sum of errors
var dErr = 0; // difference of error
var lastErr = 0; // to keep the value of previous error
The function controlAlgorithm () is written as:
function controlAlgorithm () {
err = desiredValue - actualValue; // error as difference between desired and actual val.
errSum += err; // sum of errors | like integral
dErr = err - lastErr; // difference of error
pwm = Kp*err+Ki*errSum+Kd*dErr; // PID expression
lastErr = err; // save the value of error for next cycle to estimate the derivative
if(pwm > pwmLimit) {pwm = pwmLimit}; // to limit the value for pwm / positive
if(pwm < -pwmLimit) {pwm = -pwmLimit}; // to limit the value for pwm / negative
if (pwm > 0) {board.digitalWrite(2,1); board.digitalWrite(4,0);}; // determine direction if > 0
if (pwm < 0) {board.digitalWrite(2,0); board.digitalWrite(4,1);}; // determine direction if < 0
board.analogWrite(3, Math.abs(pwm));
};
This time PID control tends to reach the desired value. The response depends on Kp, Ki and Kd parameters. Example of the response is shown in the following figure:
In the function startControlAlgorithm
the values are reset to 0:
function startControlAlgorithm () {
if (controlAlgorithmStartedFlag == 0) {
// reset parameters
pwm = 0; // Reset Pulse Width Modulation value
err = 0; // Reset error
errSum = 0; // Reset sum of errors as integral
dErr = 0; // Reset difference of error
lastErr = 0; // Reset value whih keeps the value of previous error to estimate derivative
controlAlgorithmStartedFlag = 1;
intervalCtrl = setInterval(function(){controlAlgorithm();}, 30); // call the alg. on 30ms
console.log("Control algorithm has been started.");
}
};
We should now try to sense the working of the PID. First, we should put desired and actual value to equal in upright position. Then, one should gently (very gently) hold the blue axle and change the desired pot to 15% left or right. If you gently (very gently) try to hold the position upright you will notice, how the motor will struggle to reach the desired value. This corresponds to the last column in the log part - pwm. The control algorithm will push the power to the motor to maximum 255 if needed, just to reach the desired value.
var http = require("http").createServer(handler); // on req - hand
var fs = require("fs"); // variable for file system for providing html
var firmata = require("firmata");
const WebSocket = require('ws'); // for permanent connection between server and client
const wss = new WebSocket.Server({port: 8888}); // websocket port is 8888
wss.broadcast = function broadcast(data) {
wss.clients.forEach(function each(client) {
if (client.readyState === WebSocket.OPEN) {
client.send(data);
}
});
};
var messageJSON;
var controlAlgorithmStartedFlag = 0; // variable for indicating weather the Alg has benn sta.
var intervalCtrl; // var for setInterval in global scope
console.log("Starting the code");
var board = new firmata.Board("/dev/ttyACM0", function(){
console.log("Connecting to Arduino");
console.log("Enabling analog Pin 0");
board.pinMode(0, board.MODES.ANALOG); // analog pin 0
board.pinMode(1, board.MODES.ANALOG); // analog pin 1
board.pinMode(2, board.MODES.OUTPUT); // direction of DC motor
board.pinMode(3, board.MODES.PWM); // PWM of motor i.e. speed of rotation
board.pinMode(4, board.MODES.OUTPUT); // direction DC motor
});
function handler(req, res) {
fs.readFile(__dirname + "/example15.html",
function (err, data) {
if (err) {
res.writeHead(500, {"Content-Type": "text/plain"});
return res.end("Error loading html page.");
}
res.writeHead(200);
res.end(data);
})
}
var desiredValue = 0; // desired value var
var actualValue = 0; // variable for actual value (output value)
var Kp = 0.55; // proportional factor of PID controller
var Ki = 0.008; // integral factor of PID controller
var Kd = 0.15; // differential factor of PID controller
var factor = 0.3; // proportional factor that determines speed of resonse
var pwm = 0; // set pwm as global variable
var pwmLimit = 254; // to limit value of the pwm that is sent to the motor
var err = 0; // error
var errSum = 0; // sum of errors as integral
var dErr = 0; // difference of error
var lastErr = 0; // to keep the value of previous error to estimate derivative
http.listen(8080); // server will listen on port 8080
board.on("ready", function() {
board.analogRead(0, function(value){
desiredValue = value; // continuous read of analog pin 0
});
board.analogRead(1, function(value) {
actualValue = value; // continuous read of pin A1
});
startControlAlgorithm(); // to start control alg.
wss.on('connection', function (ws, req) { // start of wss code
messageJSON = {"type": "message", "content": "Srv connected, board OK"};
ws.send(JSON.stringify(messageJSON));
setInterval(sendValues, 40); // on 40ms we send message to client
ws.on("message", function (msgString) { // message comes as string -> msgString
var msg = JSON.parse(msgString); // string from ws which comes as a string is put to JSON
switch(msg.type) {
case "startControlAlgorithm":
startControlAlgorithm();
break;
case "stopControlAlgorithm":
stopControlAlgorithm();
break;
}
}); // end of wss.on code
}); // end of sockets.on connection
}); // end of board.on(ready)
function controlAlgorithm () {
err = desiredValue - actualValue; // error as difference between desired and actual val.
errSum += err; // sum of errors | like integral
dErr = err - lastErr; // difference of error
pwm = Kp*err+Ki*errSum+Kd*dErr; // PID expression
lastErr = err; // save the value of error for next cycle to estimate the derivative
if(pwm > pwmLimit) {pwm = pwmLimit}; // to limit the value for pwm / positive
if(pwm < -pwmLimit) {pwm = -pwmLimit}; // to limit the value for pwm / negative
if (pwm > 0) {board.digitalWrite(2,1); board.digitalWrite(4,0);}; // determine direction if > 0
if (pwm < 0) {board.digitalWrite(2,0); board.digitalWrite(4,1);}; // determine direction if < 0
board.analogWrite(3, Math.abs(pwm));
};
function startControlAlgorithm () {
if (controlAlgorithmStartedFlag == 0) {
// reset parameters
pwm = 0; // Reset Pulse Width Modulation value
err = 0; // Reset error
errSum = 0; // Reset sum of errors as integral
dErr = 0; // Reset difference of error
lastErr = 0; // Reset value whih keeps the value of previous error to estimate derivative
controlAlgorithmStartedFlag = 1;
intervalCtrl = setInterval(function(){controlAlgorithm();}, 30); // call the alg. on 30ms
console.log("Control algorithm has been started.");
}
};
function stopControlAlgorithm () {
clearInterval(intervalCtrl); // clear the interval of control algorihtm
board.analogWrite(3, 0);
controlAlgorithmStartedFlag = 0;
console.log("Control algorithm has been stopped.");
};
function sendValues () {
wss.broadcast(JSON.stringify({"type": "clientReadValues", "desiredValue": desiredValue, "actualValue": actualValue, "error": (desiredValue - actualValue), "pwm": (pwm).toFixed(0)}));
};
<!DOCTYPE html>
<meta charset = utf8>
<html>
<head>
<title>Example with potentiometers</title>
</head>
<body onload="load()";>
<div>
<canvas id="canvas1" width ="200" height = "100" style="border: 1px dashed #00c3c3;"></canvas>
</div>
<button id="buttonStartControlAlgorithm" onClick="startControlAlgorithm()">Start Ctrl Alg</button>
<button id="buttonStopControlAlgorithm" onClick="stopControlAlgorithm()">Stop Ctrl Alg</button>
<div id="print1"></div>
<br>
<script type="text/javascript">
"use strict"; // in order to use clasess
var divElement = document.getElementById("print1"); // var for div el.
var numberOfLinesBeforeScroll = 10;
var linesPrintCounter = 0;
var potValue1 = 0; // value of the first potentiometer
var x1 = new Array(); // array for x1
var y1 = new Array(); // array for y1
var potValue2 = 0; // value of second potentiometer
var x2 = new Array(); // array for x2 variable
var y2 = new Array(); // array for y2 variable
var canvas1;
var ctx1;
function log(msg) {
var node=document.createElement("tr"); // we create the variable node as the a table row (tr)
var textnode=document.createTextNode(linesPrintCounter + " | " + msg); // we create element with the text adding the counter
node.appendChild(textnode); // adding text to "node", i.e. table row
divElement.insertBefore(node, divElement.childNodes[0]); // inserting into variable node
if (linesPrintCounter > numberOfLinesBeforeScroll-1) { // if the lines are more than limit -> start with scroll
divElement.removeChild(divElement.childNodes[numberOfLinesBeforeScroll]); // we remove the oldest printout
}
linesPrintCounter++; // increasing the number of printouts
}
let ws = new WebSocket("ws://192.168.254.149:8888"); // create socket - connect to it
var messageJSON;
function load() { // function that is started, when we open the page
canvas1 = document.getElementById("canvas1");
ctx1 = canvas1.getContext("2d");
// initialization of graph with points
ctx1.lineWidth = "1";
ctx1.strokeStyle = "#ff0000";
// initializaction of first time series
for (var i=0; i<200; i++) {
x1[i] = i; // for x values are 0, 1, 2, ...
y1[i] = 0; // for y values are 0
};
// initializaion of second graph
for (var i=0; i<200; i++) {
x2[i] = i; // x2 values are 0, 1, 2, ...
y2[i] = 0; // for y2 values are 0
};
};
ws.onmessage = function(event) {
var msg = JSON.parse(event.data); // string from ws is put to JSON
switch(msg.type) {
case "message":
log(msg.content); // add msg to div
break;
case "clientReadValues":
potValue1 = msg.desiredValue;
potValue2 = msg.actualValue;
// Draw first graph *****************************************
ctx1.clearRect(0, 0, canvas1.width, canvas1.height); // clear the canvas
ctx1.lineWidth = "1";
ctx1.strokeStyle = "#ff0000";
ctx1.beginPath(); // to start drawing new line
y1.splice(0, 1); // on the position 0 in the field y1 we erase one value
y1[199] = potValue1; // new value is added at the end
for (var i=0; i<200; i++) {
ctx1.lineTo(x1[i], (100 - (y1[i] / 1023) * 100)); // 0,0 x,y coordinate is in upper left corner
};
ctx1.stroke(); // to draw the line
// End of draw graph***********************************
// Draw second graph **********************************************
ctx1.lineWidth = "1";
ctx1.strokeStyle = "#00ff00";
ctx1.beginPath(); // to start drawing new line
y2.splice(0, 1); // on the position 0 in the field y2 we erase one value
y2[199] = potValue2; // new value is added at the end
for (i=0; i<200; i++) {
ctx1.lineTo(x2[i], (100 - (y2[i] / 1023) * 100)); // 0,0 x,y coordinate is in upper left corner
};
ctx1.stroke(); // to draw the line
// Draw second graph graph END ************************************
log(potValue1 + "|" + potValue2 + "|" + msg.error + "|" + msg.pwm);
break;
}
};
function startControlAlgorithm () {
messageJSON = {"type": "startControlAlgorithm"};
ws.send(JSON.stringify(messageJSON)); // we have to stringify JSON to send it over websocket
}
function stopControlAlgorithm () {
messageJSON = {"type": "stopControlAlgorithm"};
ws.send(JSON.stringify(messageJSON)); // we have to stringify JSON to send it over websocket
}
</script>
</body>
</html>