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幅频特性曲线分析及使用WPF绘制

news 来源：原创 2024/9/20 0:41:07

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
    • 4.2 二阶系统
  • 5、稳定裕度
    • 5.1 幅值裕度
    • 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

在这里插入图片描述
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）：
在这里插入图片描述
MATLAB脚本实现传递函数（1/0.5s+1）的伯德图绘制：

% 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)

在这里插入图片描述

2、二阶系统的幅频特性曲线分析及绘制

在这里插入图片描述
在这里插入图片描述
在这里插入图片描述
MATLAB脚本实现传递函数（2/(0.01s+1)(0.2s+1)的伯德图绘制：

% 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)

在这里插入图片描述

3、一般的系统

在这里插入图片描述

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

<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>
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

<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>
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

在这里插入图片描述

5.1 幅值裕度

在这里插入图片描述

5.2 相角裕度

在这里插入图片描述

参考

【1】第五章 线性系统的频域分析法：
https://buckyi.github.io/Note-Automation/%E7%BB%8F%E5%85%B8%E6%8E%A7%E5%88%B6%E7%90%86%E8%AE%BA/%E7%AC%AC05%E7%AB%A0%20%E7%BA%BF%E6%80%A7%E7%B3%BB%E7%BB%9F%E7%9A%84%E9%A2%91%E5%9F%9F%E5%88%86%E6%9E%90%E6%B3%95.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：
https://blog.csdn.net/persona5joker/article/details/140059710?utm_medium=distribute.pc_relevant.none-task-blog-2defaultbaidujs_baidulandingword~default-4-140059710-blog-119787996.235v43pc_blog_bottom_relevance_base8&spm=1001.2101.3001.4242.3&utm_relevant_index=7
【5】自控理论 第6章 II 相对稳定性、伯德图和闭环频率响应
https://www.cnblogs.com/harold-lu/p/15740368.html

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