劳斯稳定方法-RouthMethod

最新推荐文章于 2024-11-09 16:47:38 发布

weixin_30348519

最新推荐文章于 2024-11-09 16:47:38 发布

阅读量157

点赞数

CC 4.0 BY-SA版权

文章标签： javascript xhtml ViewUI

原文链接：http://www.cnblogs.com/fengmk2/archive/2007/04/26/RouthMethod.html

本文介绍了一种基于Routh稳定性判据的JavaScript实现方法，该方法用于判断线性控制系统中多项式的稳定性，并通过实例展示了如何使用该工具进行计算。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

今天上<线性控制系统工程>课时, 讲到系统稳定性的一种判定方法: Routh's Method
见今晚没别的事做, 就用来练习了一下JavaScript.

具体算法请见:
Module.9. Routh method,root locus_magnitude and phase equations.rar

测试网址:
Routh Method

JavaScript源代码:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" >
<head>
 <title>Routh's Method</title>
 <style type="text/css">
 table td {
 border: 1px solid;
 padding: 5px;
 }
 </style>
 <script type="text/javascript" language="javascript">
//跨浏览器的event辅助工具
var EventUtil = new Object;
//添加事件监听者
EventUtil.addEventHandler = function (oTarget, sEventType, fnHandler) {
 if(oTarget.addEventListener) {
 oTarget.addEventListener(sEventType, fnHandler, false);
 }
 else if (oTarget.attachEvent) {
 oTarget.attachEvent("on" + sEventType, fnHandler);
 }
 else {
 oTarget["on" + sEventType] = fnHandler;
 }
}

var RouthArray = function(params) {
 this._params = params;
 this._count = this._params.length;
 this._datas = [];
 this._onImaginaryAxis = 0;
 var index = 0;
 for(var row = 0; row < 2; row++) {
 this._datas[row] = [];
 var count = Math.ceil(this._count/2);
 for(var col = 0; col<count; col++) {
 this._datas[row][col] = {};
 this._datas[row][col].value = (this._params[index]!=null)?window.parseFloat(this._params[index]) : 0;
 index += 2;
 }
 index = 1;
 }

 for(var row = 2; row < this._count; row++) {
 this._datas[row] = [];
 var zeroCount = 0;
 for(var col = 0; this._datas[row-2][col+1]!=null && this._datas[row-2][col+1].value!=0; col++) {
 if(this._datas[row-1][col+1]==null) {
 this._datas[row-1][col+1] = {};
 this._datas[row-1][col+1].value = 0;
 }
 this._datas[row][col] = {};
 this._datas[row][col].value = (this._datas[row-1][0].value*this._datas[row-2][col+1].value
 - this._datas[row-2][0].value*this._datas[row-1][col+1].value) / this._datas[row-1][0].value;
 if(this._datas[row][col].value == 0) {
 zeroCount++;
 this._datas[row][col].isZero = true;
 }
 }
 if(zeroCount == (Math.floor((this._count-row-1)/2)+1)) { //全为0
 this._onImaginaryAxis++; //增加一对纯虚根, 即在虚轴上
 var n = this._count-row;
 var ct = Math.floor(n/2);
 var r = row-1;
 for(var c = 0; c<ct; c++) {
 this._datas[row][c].value = this._datas[r][c].value*(n-2*c); //求导
 }
 }
 else if(this._datas[row][0].value == 0 && (this._datas[row][1] != null && this._datas[row][1].value != 0)) { //第一列为0
 this._datas[row][0].value = 0.00000001;
 }
 }
 this.show();
}

RouthArray.prototype = {
 show: function() {
 var belowZero = this._datas[0][0].value > 0;
 var signCngCount = 0;
 var container = document.getElementById("container");
 if(container) {
 container.innerHTML = "";
 }
 else {
 container = document.createElement("div");
 container.id = "container";
 document.body.appendChild(container);
 }
 var table = document.createElement("table");
 container.appendChild(table);
 for(var row=0; row<this._count; row++) {
// var tr = document.createElement("tr"); //IE不支持此方式
// table.appendChild(tr);
 var tr = table.insertRow(-1);
 var td = document.createElement("td");
 td.innerHTML = "s"+(this._count-row-1)+":";
 tr.appendChild(td);
 for(var col=0; col<this._datas[row].length; col++) {
 var td = document.createElement("td");
 td.innerHTML = this._datas[row][col].value + (this._datas[row][col].isZero? "(0)" : "");
 tr.appendChild(td);

 }
 if(belowZero) {
 if(this._datas[row][0].value < 0) {
 belowZero =!belowZero;
 signCngCount++;
 }
 }
 else {
 if(this._datas[row][0].value > 0) {
 belowZero =!belowZero;
 signCngCount++;
 }
 }
 }

 var p = document.createElement("p");
 if(this._onImaginaryAxis!=0) {
 p.innerHTML = "虽然首列符号没有变化, 但在虚轴有"+this._onImaginaryAxis
 +"对关于原点对称的根, 所以系统是不稳定的.";
 }
 else if(signCngCount == 0) {
 p.innerHTML = "Since there are no sign changes in the first column, there are no closed-loop poles to the"+
 " right of the imaginary axis, and the System is stable. ";
 p.innerHTML += "由于首列符号没有变化, 则虚轴的右侧没有闭环极点, 所以系统是稳定的.";
 }
 else {
 p.innerHTML = "Since there are "+signCngCount
 +" sign changes in the first column, there are "
 +signCngCount+" closed-loop poles to the"+
 " right of the imaginary axis, and the System is not stable. ";
 p.innerHTML += "由于首列符号变化了"+signCngCount
 +"次, 则虚轴的右侧有"+signCngCount
 +"对闭环极点, 所以系统是不稳定的.";
 }
 container.appendChild(p);
 }
}
EventUtil.addEventHandler(window,"load", function() {
EventUtil.addEventHandler(document.getElementById("btnSubmit"),"click", function() {
 new RouthArray(document.getElementById("inputParams").value.split(","));
});
});

</script>
</head>
<body>
 Test values: 
 (1)s^4 + 2*s^3 + 3*s^2 + 2*s + 12 = 0 :
 1,2,3,2,12 
 (1)s^6 + 4*s^5 + 8*s^4 + 10*s^3 + 8*s^2 + 4*s + 1 = 0 :
 1,4,8,10,8,4,1 
 (3)s^4 + 3*s^3 + 4*s^2 + 12*s + 16 = 0 :
 1,3,4,12,16 
 (4)s^5 + s^4 + 2*s^3 + 2*s^2 + 3*s + 5 = 0 :
 1,1,2,2,3,5 
 (5)s^5 + 3*s^4 + 3*s^3 + 9*s^2 - 4*s - 12= 0 :
 1,3,3,9,-4,-12 
 (6)s^6 + 2*s^5 + 8*s^4 + 12*s^3 + 20*s^2 + 16*s + 16= 0 :
 1,2,8,12,20,16,16 
 <input id="inputParams" type="text" style="width: 367px" />
 <input id="btnSubmit" type="button" value="Excute" />
 <hr />
</body>
</html>

转载于:https://www.cnblogs.com/fengmk2/archive/2007/04/26/RouthMethod.html