文章目录
- 1、一阶惯性环节的幅频特性曲线分析及绘制
- 2、二阶系统的幅频特性曲线分析及绘制
- 3、一般的系统
- 4、上位机代码实现
-
- [4.1 一阶惯性系统](#4.1 一阶惯性系统)
- [4.2 二阶系统](#4.2 二阶系统)
- 5、稳定裕度
-
- [5.1 幅值裕度](#5.1 幅值裕度)
- [5.2 相角裕度](#5.2 相角裕度)
- 参考
1、一阶惯性环节的幅频特性曲线分析及绘制
这里的a和b可以根据系统的不同修改,然后在0-50Hz内以1/10000的分辨率取点,可得对数幅频特性曲线(1/0.5s+1):
MATLAB脚本实现传递函数(1/0.5s+1)的伯德图绘制:
matlab
% 0.001 - 10^1.5 10000个点
w = logspace(-3,2,10000);
num = [0 1];
f = [0.5 1];
sys = tf(num,f);
P = bodeoptions;
% 横坐标为Hz
P.FreqUnits = 'Hz';
bode(sys,w,P)
2、二阶系统的幅频特性曲线分析及绘制
MATLAB脚本实现传递函数(2/(0.01s+1)(0.2s+1)的伯德图绘制:
matlab
% 0.001 - 10^1.5 10000个点
w = logspace(-3,2,10000);
num = [0 2];
f1 = [0.01 1];
f2 = [0.2 1];
den = conv(f1,f2);
sys = tf(num,den);
P = bodeoptions;
% 横坐标为Hz
P.FreqUnits = 'Hz';
bode(sys,w,P)
3、一般的系统
4、上位机代码实现
源码及Oxyplot源码下载地址: WPF实现bode图demo源码
4.1 一阶惯性系统
csharp
<Page x:Class="WPF_Demo_V2.View.LogChartPage"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:local="clr-namespace:WPF_Demo_V2.View"
xmlns:oxyplot="http://oxyplot.org/wpf"
mc:Ignorable="d"
d:DesignHeight="450" d:DesignWidth="800"
Title="LogChartPage">
<Grid>
<Grid.RowDefinitions>
<RowDefinition/>
<RowDefinition/>
</Grid.RowDefinitions>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="5*"/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
<oxyplot:PlotView Model="{Binding MyPlotModelUp}"/>
<oxyplot:PlotView Grid.Row="1" Model="{Binding MyPlotModelDown}"/>
<StackPanel Grid.Row="0" Grid.Column="1" Orientation="Vertical">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="0.8*"/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
</Grid.RowDefinitions>
<TextBlock Text="a:" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Column="1" Text="{Binding A}" Margin="2"></TextBox>
<TextBlock Text="b:" Grid.Row="1" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="1" Grid.Column="1" Text="{Binding B}" Margin="2"></TextBox>
<TextBlock Text="X max:" Grid.Row="2" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="2" Grid.Column="1" Text="{Binding X_max}" Margin="2"></TextBox>
<TextBlock Text="factor:" Grid.Row="3" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="3" Grid.Column="1" Text="{Binding Factor}" Margin="2" ToolTip="X_max/factor 为最小分辨率"></TextBox>
<TextBlock Text="Y1 min:" Grid.Row="4" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="4" Grid.Column="1" Text="{Binding Y1_min}" Margin="2"></TextBox>
<TextBlock Text="Y1 max:" Grid.Row="5" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="5" Grid.Column="1" Text="{Binding Y1_max}" Margin="2"></TextBox>
<TextBlock Text="Y2 min:" Grid.Row="6" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="6" Grid.Column="1" Text="{Binding Y2_min}" Margin="2"></TextBox>
<TextBlock Text="Y2 max:" Grid.Row="7" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="7" Grid.Column="1" Text="{Binding Y2_max}" Margin="2"></TextBox>
<Button Grid.Row="8" Grid.ColumnSpan="2" Content="确定" Margin="20,2" Command="{Binding sureCommand}"/>
</Grid>
<Image Source="../Resource/Image/function.png"/>
</StackPanel>
</Grid>
</Page>
csharp
using CommunityToolkit.Mvvm.ComponentModel;
using CommunityToolkit.Mvvm.Input;
using OxyPlot;
using OxyPlot.Axes;
using OxyPlot.Series;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace WPF_Demo_V2.ViewModel
{
partial class LogChartViewModel: ObservableObject
{
#region 全局变量
//UInt32 LEN = 50;
//UInt32 FACT = 10000;
double[] Gain;
double[] Phase;
FunctionSeries upFunctionSeries=new FunctionSeries();
FunctionSeries downFunctionSeries=new FunctionSeries();
#endregion
#region 构造函数
public LogChartViewModel()
{
upFunctionSeries.Title = "Gain";
downFunctionSeries.Title = "Phase";
}
#endregion
#region 属性
[ObservableProperty]
public PlotModel _MyPlotModelUp;
[ObservableProperty]
public PlotModel _MyPlotModelDown;
[ObservableProperty]
public double _A = 0.5;
[ObservableProperty]
public double _B = 1;
[ObservableProperty]
public int _X_max = 50;
[ObservableProperty]
public int _Factor = 10000;
[ObservableProperty]
public double _Y1_max = 0;
[ObservableProperty]
public double _Y1_min = -50;
[ObservableProperty]
public double _Y2_max = 0;
[ObservableProperty]
public double _Y2_min = -90;
#endregion
#region 方法
public PlotModel PlotModelInit(string xtitle,string ytitle,double ymin,double ymax)
{
var plotModel = new PlotModel();
//plotModel.Title = "Log Paper";
var logarithmicAxis1 = new LogarithmicAxis();
logarithmicAxis1.MajorGridlineColor = OxyColor.FromArgb(40, 0, 0, 139);
logarithmicAxis1.MajorGridlineStyle = LineStyle.Solid;
logarithmicAxis1.Maximum = X_max;
logarithmicAxis1.Minimum = 1/ (double)Factor;
logarithmicAxis1.MinorGridlineColor = OxyColor.FromArgb(20, 0, 0, 139);
logarithmicAxis1.MinorGridlineStyle = LineStyle.Solid;
logarithmicAxis1.Position = AxisPosition.Bottom;
if (!string.IsNullOrEmpty(xtitle)) logarithmicAxis1.Title = xtitle;
plotModel.Axes.Add(logarithmicAxis1);
var linearAxis1 = new LinearAxis();
linearAxis1.MajorGridlineStyle = LineStyle.Solid;
linearAxis1.MinorGridlineStyle = LineStyle.Dot;
linearAxis1.Maximum = ymax;
linearAxis1.Minimum = ymin;
linearAxis1.Title = ytitle;
plotModel.Axes.Add(linearAxis1);
return plotModel;
}
[RelayCommand]
private void sure()
{
if(upFunctionSeries.Points.Count>0) upFunctionSeries.Points.Clear();
if (downFunctionSeries.Points.Count > 0)downFunctionSeries.Points.Clear();
if (MyPlotModelUp != null)
{
if (MyPlotModelUp.Series.Count > 0) MyPlotModelUp.Series.Clear();
}
if(MyPlotModelDown != null)
{
if (MyPlotModelDown.Series.Count > 0) MyPlotModelDown.Series.Clear();
}
MyPlotModelUp = PlotModelInit("", "Magnitude[dB]", Y1_min, Y1_max);
MyPlotModelDown = PlotModelInit("Frequency[Hz]", "Phase[deg]", Y2_min, Y2_max);
Gain = new double[X_max * Factor];
Phase = new double[X_max * Factor];
for (int i = 0; i < X_max * Factor; i++)
{
double temp_a = 2 * Math.PI * A * (i / (double)Factor);
double temp_2 = Math.Pow(temp_a, 2) + Math.Pow(B, 2);
double temp_sqrt = 1 / Math.Sqrt(temp_2);
double temp = Math.Abs(temp_sqrt);
Gain[i] = 20 * Math.Log10(temp);
Phase[i] = -Math.Atan(temp_a / (double)B) / Math.PI * 180;
upFunctionSeries.Points.Add(new DataPoint(i / (double)Factor, Gain[i]));
downFunctionSeries.Points.Add(new DataPoint(i / (double)Factor, Phase[i]));
}
MyPlotModelUp.Series.Add(upFunctionSeries);
MyPlotModelDown.Series.Add(downFunctionSeries);
MyPlotModelUp.ResetAllAxes();
MyPlotModelUp.InvalidatePlot(true);
MyPlotModelDown.ResetAllAxes();
MyPlotModelDown.InvalidatePlot(true);
}
#endregion
}
}
4.2 二阶系统
csharp
<Page x:Class="WPF_Demo_V2.View.Log3ChartPage"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:local="clr-namespace:WPF_Demo_V2.View"
xmlns:oxyplot="http://oxyplot.org/wpf"
mc:Ignorable="d"
d:DesignHeight="450" d:DesignWidth="800"
Title="Log3ChartPage">
<Grid>
<Grid.RowDefinitions>
<RowDefinition/>
<RowDefinition/>
</Grid.RowDefinitions>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="5*"/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
<oxyplot:PlotView Model="{Binding MyPlotModelUp}"/>
<oxyplot:PlotView Grid.Row="1" Model="{Binding MyPlotModelDown}"/>
<StackPanel Grid.Row="0" Grid.Column="1" Orientation="Vertical">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="0.8*"/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
</Grid.RowDefinitions>
<TextBlock Text="a:" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Column="1" Text="{Binding A}" Margin="2"></TextBox>
<TextBlock Text="b:" Grid.Row="1" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="1" Grid.Column="1" Text="{Binding B}" Margin="2"></TextBox>
<TextBlock Text="c:" Grid.Row="2" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="2" Grid.Column="1" Text="{Binding C}" Margin="2"></TextBox>
<TextBlock Text="X max:" Grid.Row="3" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="3" Grid.Column="1" Text="{Binding X_max}" Margin="2"></TextBox>
<TextBlock Text="factor:" Grid.Row="4" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="4" Grid.Column="1" Text="{Binding Factor}" Margin="2" ToolTip="X_max/factor 为最小分辨率"></TextBox>
<TextBlock Text="Y1 min:" Grid.Row="5" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="5" Grid.Column="1" Text="{Binding Y1_min}" Margin="2"></TextBox>
<TextBlock Text="Y1 max:" Grid.Row="6" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="6" Grid.Column="1" Text="{Binding Y1_max}" Margin="2"></TextBox>
<TextBlock Text="Y2 min:" Grid.Row="7" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="7" Grid.Column="1" Text="{Binding Y2_min}" Margin="2"></TextBox>
<TextBlock Text="Y2 max:" Grid.Row="8" Foreground="White" HorizontalAlignment="Right"/>
<TextBox Grid.Row="8" Grid.Column="1" Text="{Binding Y2_max}" Margin="2"></TextBox>
<Button Grid.Row="9" Grid.ColumnSpan="2" Content="确定" Margin="20,2" Command="{Binding sureCommand}"/>
</Grid>
<Image Source="../Resource/Image/function.png"/>
</StackPanel>
</Grid>
</Page>
csharp
using CommunityToolkit.Mvvm.ComponentModel;
using CommunityToolkit.Mvvm.Input;
using OxyPlot.Axes;
using OxyPlot.Series;
using OxyPlot;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace WPF_Demo_V2.ViewModel
{
partial class Log3ChartViewModel: ObservableObject
{
#region 全局变量
//UInt32 LEN = 50;
//UInt32 FACT = 10000;
double[] Gain;
double[] Phase;
FunctionSeries upFunctionSeries = new FunctionSeries();
FunctionSeries downFunctionSeries = new FunctionSeries();
#endregion
#region 构造函数
public Log3ChartViewModel()
{
upFunctionSeries.Title = "Gain";
downFunctionSeries.Title = "Phase";
}
#endregion
#region 属性
[ObservableProperty]
public PlotModel _MyPlotModelUp;
[ObservableProperty]
public PlotModel _MyPlotModelDown;
[ObservableProperty]
public double _A = 0.5;
[ObservableProperty]
public double _B = 1;
[ObservableProperty]
public double _C = 1;
[ObservableProperty]
public int _X_max = 50;
[ObservableProperty]
public int _Factor = 10000;
[ObservableProperty]
public double _Y1_max = 0;
[ObservableProperty]
public double _Y1_min = -100;
[ObservableProperty]
public double _Y2_max = 100;
[ObservableProperty]
public double _Y2_min = -100;
#endregion
#region 方法
public PlotModel PlotModelInit(string xtitle, string ytitle, double ymin, double ymax)
{
var plotModel = new PlotModel();
//plotModel.Title = "Log Paper";
var logarithmicAxis1 = new LogarithmicAxis();
logarithmicAxis1.MajorGridlineColor = OxyColor.FromArgb(40, 0, 0, 139);
logarithmicAxis1.MajorGridlineStyle = LineStyle.Solid;
logarithmicAxis1.Maximum = X_max;
logarithmicAxis1.Minimum = 1 / (double)Factor;
logarithmicAxis1.MinorGridlineColor = OxyColor.FromArgb(20, 0, 0, 139);
logarithmicAxis1.MinorGridlineStyle = LineStyle.Solid;
logarithmicAxis1.Position = AxisPosition.Bottom;
if (!string.IsNullOrEmpty(xtitle)) logarithmicAxis1.Title = xtitle;
plotModel.Axes.Add(logarithmicAxis1);
var linearAxis1 = new LinearAxis();
linearAxis1.MajorGridlineStyle = LineStyle.Solid;
linearAxis1.MinorGridlineStyle = LineStyle.Dot;
linearAxis1.Maximum = ymax;
linearAxis1.Minimum = ymin;
linearAxis1.Title = ytitle;
plotModel.Axes.Add(linearAxis1);
//var logarithmicAxis2 = new LogarithmicAxis();
//logarithmicAxis2.MajorGridlineColor = OxyColor.FromArgb(40, 0, 0, 139);
//logarithmicAxis2.MajorGridlineStyle = LineStyle.Solid;
//logarithmicAxis2.Maximum = 180;
//logarithmicAxis2.Minimum = -180;
//logarithmicAxis2.MinorGridlineColor = OxyColor.FromArgb(20, 0, 0, 139);
//logarithmicAxis2.MinorGridlineStyle = LineStyle.Solid;
//logarithmicAxis2.Title = "Y";
//plotModel.Axes.Add(logarithmicAxis2);
return plotModel;
}
[RelayCommand]
private void sure()
{
if (upFunctionSeries.Points.Count > 0) upFunctionSeries.Points.Clear();
if (downFunctionSeries.Points.Count > 0) downFunctionSeries.Points.Clear();
if (MyPlotModelUp != null)
{
if (MyPlotModelUp.Series.Count > 0) MyPlotModelUp.Series.Clear();
}
if (MyPlotModelDown != null)
{
if (MyPlotModelDown.Series.Count > 0) MyPlotModelDown.Series.Clear();
}
MyPlotModelUp = PlotModelInit("", "Magnitude[dB]", Y1_min, Y1_max);
MyPlotModelDown = PlotModelInit("Frequency[Hz]", "Phase[deg]", Y2_min, Y2_max);
Gain = new double[X_max * Factor];
Phase = new double[X_max * Factor];
double previousPhase = 0;
for (int i = 0; i < X_max * Factor; i++)
{
double w = 2 * Math.PI * (i / (double)Factor);
double temp_a = 1 - A*B * Math.Pow(w, 2);
double temp_b = (A+B)*w;
double temp_2 = Math.Pow(temp_a, 2) + Math.Pow(temp_b, 2);
double temp_sqrt = C / Math.Sqrt(temp_2);
double temp = Math.Abs(temp_sqrt);
Gain[i] = 20 * Math.Log10(temp);
double currentPhaseA = Math.Atan(A * w) / Math.PI * 180;
double currentPhaseB = Math.Atan(B * w) / Math.PI * 180;
Phase[i] = 0-(currentPhaseA + currentPhaseB);
upFunctionSeries.Points.Add(new DataPoint(i / (double)Factor, Gain[i]));
downFunctionSeries.Points.Add(new DataPoint(i / (double)Factor, Phase[i]));
}
MyPlotModelUp.Series.Add(upFunctionSeries);
MyPlotModelDown.Series.Add(downFunctionSeries);
MyPlotModelUp.ResetAllAxes();
MyPlotModelUp.InvalidatePlot(true);
MyPlotModelDown.ResetAllAxes();
MyPlotModelDown.InvalidatePlot(true);
}
#endregion
}
}
5、稳定裕度
5.1 幅值裕度
5.2 相角裕度
参考
【1】第五章 线性系统的频域分析法:
https://buckyi.github.io/Note-Automation/经典控制理论/第05章 线性系统的频域分析法.html#33
【2】【自动控制原理】第5章 幅相频率特性曲线(奈氏图)及其绘制:
https://blog.csdn.net/persona5joker/article/details/140055111
【3】相角裕度与幅值裕度:
https://blog.csdn.net/qq_38972634/article/details/119787996
【4】【自动控制原理】第五章 奈奎斯特稳定判据,相角裕度和幅值裕度,对数频率特性及其绘制:
【5】自控理论 第6章 II 相对稳定性、伯德图和闭环频率响应