MATLAB求解一阶RC电路和二阶RLC电路

  • 理论知识：
  • 交互界面介绍
    • 一阶RC全相应
      • Multisim仿真：
      • 仿真结果为：
    • 二阶RLC电路
      • Multisim仿真：
      • 仿真结果为：
  • 实现代码：

理论知识：

一阶RC电路全相应：根据节点电压法求出戴维宁等效电路，列写微分方程求得Uc与t之间的关系，并绘图。
二阶RLC电路: 根据节点电压法求出戴维宁等效电路，列写微分方程求得Uc，UL和t之间的关系，并绘图。

交互界面介绍

一阶RC全相应

Multisim仿真：

我们先用仿真软件Multisim绘制出待测电路图以及Uc-t曲线：

易得 t = 5s 时，Uc = 6.541V 。

仿真结果为：


易得 t = 5s 时，Uc = 6.541V 。

二阶RLC电路

Multisim仿真：


易得 t = 5s 时，Uc = 8.707V， UL = 0.3712V 。

仿真结果为：


易得 t = 5s 时，Uc = 9.078V，UL = 0.3711V。

实现代码：

classdef dianlu2 < matlab.apps.AppBase% Properties that correspond to app componentsproperties (Access = public)UIFigure           matlab.ui.FigureTabGroup           matlab.ui.container.TabGroupTab                matlab.ui.container.TabLabel              matlab.ui.control.LabelEditField          matlab.ui.control.NumericEditFieldEditField_2Label   matlab.ui.control.LabelEditField_2        matlab.ui.control.NumericEditFieldLabel_2            matlab.ui.control.LabelEditField_3        matlab.ui.control.NumericEditFieldCaculateButton     matlab.ui.control.StateButtonUIAxes             matlab.ui.control.UIAxesLabel_3            matlab.ui.control.LabelEditField_4        matlab.ui.control.NumericEditFieldLabel_4            matlab.ui.control.LabelEditField_5        matlab.ui.control.NumericEditFieldLabel_5            matlab.ui.control.LabelEditField_6        matlab.ui.control.NumericEditFieldLabel_6            matlab.ui.control.LabelEditField_7        matlab.ui.control.NumericEditFieldTab_2              matlab.ui.container.TabCaculateButton_2   matlab.ui.control.StateButtonUIAxes_2           matlab.ui.control.UIAxesEditField_8Label   matlab.ui.control.LabelEditField_8        matlab.ui.control.NumericEditFieldLabel_7            matlab.ui.control.LabelEditField_9        matlab.ui.control.NumericEditFieldEditField_10Label  matlab.ui.control.LabelEditField_10       matlab.ui.control.NumericEditFieldEditField_11Label  matlab.ui.control.LabelEditField_11       matlab.ui.control.NumericEditFieldEditField_12Label  matlab.ui.control.LabelEditField_12       matlab.ui.control.NumericEditFieldEditField_13Label  matlab.ui.control.LabelEditField_13       matlab.ui.control.NumericEditFieldLabel_8            matlab.ui.control.LabelEditField_14       matlab.ui.control.NumericEditFieldRLCTab             matlab.ui.container.TabCaculateButton_3   matlab.ui.control.StateButtonUIAxes_3           matlab.ui.control.UIAxesEditField_15Label  matlab.ui.control.LabelEditField_15       matlab.ui.control.NumericEditFieldEditField_16Label  matlab.ui.control.LabelEditField_16       matlab.ui.control.NumericEditFieldLabel_12           matlab.ui.control.LabelEditField_17       matlab.ui.control.NumericEditFieldEditField_18Label  matlab.ui.control.LabelEditField_18       matlab.ui.control.NumericEditFieldLabel_9            matlab.ui.control.LabelEditField_19       matlab.ui.control.NumericEditFieldLabel_10           matlab.ui.control.LabelEditField_20       matlab.ui.control.NumericEditFieldLabel_11           matlab.ui.control.LabelEditField_21       matlab.ui.control.NumericEditFieldLabel_13           matlab.ui.control.LabelEditField_22       matlab.ui.control.NumericEditFieldEditField_23Label  matlab.ui.control.LabelEditField_23       matlab.ui.control.NumericEditFieldGLCTab             matlab.ui.container.TabCaculateButton_4   matlab.ui.control.StateButtonUIAxes_4           matlab.ui.control.UIAxesEditField_24Label  matlab.ui.control.LabelEditField_24       matlab.ui.control.NumericEditFieldEditField_25Label  matlab.ui.control.LabelEditField_25       matlab.ui.control.NumericEditFieldEditField_26Label  matlab.ui.control.LabelEditField_26       matlab.ui.control.NumericEditFieldLabel_14           matlab.ui.control.LabelEditField_27       matlab.ui.control.NumericEditFieldEditField_28Label  matlab.ui.control.LabelEditField_28       matlab.ui.control.NumericEditFieldLabel_15           matlab.ui.control.LabelEditField_29       matlab.ui.control.NumericEditFieldLabel_16           matlab.ui.control.LabelEditField_30       matlab.ui.control.NumericEditFieldEditField_31Label  matlab.ui.control.LabelEditField_31       matlab.ui.control.NumericEditFieldEditField_32Label  matlab.ui.control.LabelEditField_32       matlab.ui.control.NumericEditFieldend% Callbacks that handle component eventsmethods (Access = private)% Value changed function: CaculateButtonfunction CaculateButtonValueChanged(app, event)x=(0:0.1:100);R=app.EditField.Value;C=app.EditField_2.Value;U0=app.EditField_3.Value;T=R*C;U1=app.EditField_4.Value;app.EditField_5.Value=T;time=app.EditField_6.Value;app.EditField_7.Value=U1+(U0-U1)*exp(-time/T);y=U1+(U0-U1)*exp(-x/T);plot(app.UIAxes,x,y);end% Value changed function: CaculateButton_2function CaculateButton_2ValueChanged(app, event)x=(0:0.1:100);R=app.EditField_8.Value;L=app.EditField_9.Value;I0=app.EditField_10.Value;T=L/R;U1=app.EditField_11.Value;app.EditField_12.Value=T;time=app.EditField_13.Value;%app.EditField_14.Value=abs(U1-(U1+(U0-U1)*exp(-time/T))*R);%y=U1+(U0-U1)*exp(-x/T);syms ti = dsolve('L*Di + i*R = U1,i(0) = I0','t');ul1=zeros(1,1001);ul= L*diff(i,t);h = 1;for t=0:0.1:100ul1(h)=eval(ul);h=h+1;endt = time;app.EditField_14.Value=abs(eval(ul));plot(app.UIAxes_2,x,ul1);end% Value changed function: CaculateButton_3function CaculateButton_3ValueChanged(app, event)r=app.EditField_15.Value;c=app.EditField_16.Value;l=app.EditField_17.Value;us=app.EditField_18.Value;time=app.EditField_19.Value;u0=app.EditField_22.Value;i0=app.EditField_23.Value;syms uc t uc = dsolve('u+r*c*Du+l*c*D2u=us','u(0) =u0','Du(0) = i0/c','t');i = c*diff(uc,t);ul= l*diff(i,t);uc1=zeros(1,1001);ul1=zeros(1,1001);i1=zeros(1,1001);h=1;for t=0:0.1:100uc1(h)=eval(uc);ul1(h)=eval(ul);i1(h)=eval(i);h=h+1;endt=0:0.1:100;plot(app.UIAxes_3,t,uc1,'r-',t,ul1,'b',t,i1,'g-.');t=app.EditField_19.Value;app.EditField_20.Value=eval(uc);app.EditField_21.Value=eval(ul);end% Value changed function: CaculateButton_4function CaculateButton_4ValueChanged(app, event)r=app.EditField_24.Value;c=app.EditField_25.Value;l=app.EditField_26.Value;is=app.EditField_27.Value;time=app.EditField_28.Value;u0=app.EditField_31.Value;i0=app.EditField_32.Value;g=1/r;syms il til = dsolve('i + l*c*D2i + Di*l*g = is','i(0) = i0,Di(0) = u0/l','t');u= l*diff(il,t);ic= c*diff(u,t);il1=zeros(1,1001);u1=zeros(1,1001);ic1=zeros(1,1001);h=1;for t=0:0.1:100il1(h)=eval(il);u1(h)=eval(u);ic1(h)=eval(ic);h=h+1;endt=0:0.1:100;plot(app.UIAxes_4,t,il1,'r-',t,ic1,'b',t,u1,'g-.');t=time;app.EditField_29.Value=eval(il);app.EditField_30.Value=eval(ic);endend% Component initializationmethods (Access = private)% Create UIFigure and componentsfunction createComponents(app)% Create UIFigure and hide until all components are createdapp.UIFigure = uifigure('Visible', 'off');app.UIFigure.Position = [100 100 698 579];app.UIFigure.Name = 'MATLAB App';% Create TabGroupapp.TabGroup = uitabgroup(app.UIFigure);app.TabGroup.Position = [1 4 700 576];% Create Tabapp.Tab = uitab(app.TabGroup);app.Tab.Title = '电容';% Create Labelapp.Label = uilabel(app.Tab);app.Label.HorizontalAlignment = 'right';app.Label.Position = [65 53 37 22];app.Label.Text = '电阻';% Create EditFieldapp.EditField = uieditfield(app.Tab, 'numeric');app.EditField.Position = [34 87 100 22];% Create EditField_2Labelapp.EditField_2Label = uilabel(app.Tab);app.EditField_2Label.HorizontalAlignment = 'right';app.EditField_2Label.Position = [168 53 29 22];app.EditField_2Label.Text = '电容';% Create EditField_2app.EditField_2 = uieditfield(app.Tab, 'numeric');app.EditField_2.Position = [133 87 100 22];% Create Label_2app.Label_2 = uilabel(app.Tab);app.Label_2.HorizontalAlignment = 'right';app.Label_2.Position = [261 53 41 22];app.Label_2.Text = '初始值';% Create EditField_3app.EditField_3 = uieditfield(app.Tab, 'numeric');app.EditField_3.Position = [232 87 100 22];% Create CaculateButtonapp.CaculateButton = uibutton(app.Tab, 'state');app.CaculateButton.ValueChangedFcn = createCallbackFcn(app, @CaculateButtonValueChanged, true);app.CaculateButton.Text = 'Caculate';app.CaculateButton.Position = [254 10 100 22];% Create UIAxesapp.UIAxes = uiaxes(app.Tab);title(app.UIAxes, '电容电压')xlabel(app.UIAxes, '时间/s')ylabel(app.UIAxes, '电压/V')app.UIAxes.TitleFontWeight = 'bold';app.UIAxes.Position = [34 160 628 379];% Create Label_3app.Label_3 = uilabel(app.Tab);app.Label_3.HorizontalAlignment = 'right';app.Label_3.Position = [360 53 41 22];app.Label_3.Text = '电压源';% Create EditField_4app.EditField_4 = uieditfield(app.Tab, 'numeric');app.EditField_4.Position = [331 87 100 22];% Create Label_4app.Label_4 = uilabel(app.Tab);app.Label_4.HorizontalAlignment = 'right';app.Label_4.Position = [482 120 53 22];app.Label_4.Text = '时间常数';% Create EditField_5app.EditField_5 = uieditfield(app.Tab, 'numeric');app.EditField_5.Position = [550 120 100 22];% Create Label_5app.Label_5 = uilabel(app.Tab);app.Label_5.HorizontalAlignment = 'right';app.Label_5.Position = [506 74 29 22];app.Label_5.Text = '时间';% Create EditField_6app.EditField_6 = uieditfield(app.Tab, 'numeric');app.EditField_6.Position = [550 74 100 22];% Create Label_6app.Label_6 = uilabel(app.Tab);app.Label_6.HorizontalAlignment = 'right';app.Label_6.Position = [494 32 41 22];app.Label_6.Text = '电压值';% Create EditField_7app.EditField_7 = uieditfield(app.Tab, 'numeric');app.EditField_7.Position = [550 32 100 22];% Create Tab_2app.Tab_2 = uitab(app.TabGroup);app.Tab_2.Title = '电感';% Create CaculateButton_2app.CaculateButton_2 = uibutton(app.Tab_2, 'state');app.CaculateButton_2.ValueChangedFcn = createCallbackFcn(app, @CaculateButton_2ValueChanged, true);app.CaculateButton_2.Text = 'Caculate';app.CaculateButton_2.Position = [254 10 100 22];% Create UIAxes_2app.UIAxes_2 = uiaxes(app.Tab_2);title(app.UIAxes_2, '电感电压')xlabel(app.UIAxes_2, '时间/s')ylabel(app.UIAxes_2, '电压/V')app.UIAxes_2.TitleFontWeight = 'bold';app.UIAxes_2.Position = [34 160 628 379];% Create EditField_8Labelapp.EditField_8Label = uilabel(app.Tab_2);app.EditField_8Label.HorizontalAlignment = 'right';app.EditField_8Label.Position = [65 53 37 22];app.EditField_8Label.Text = '电阻';% Create EditField_8app.EditField_8 = uieditfield(app.Tab_2, 'numeric');app.EditField_8.Position = [34 87 100 22];% Create Label_7app.Label_7 = uilabel(app.Tab_2);app.Label_7.HorizontalAlignment = 'right';app.Label_7.Position = [168 53 29 22];app.Label_7.Text = '电感';% Create EditField_9app.EditField_9 = uieditfield(app.Tab_2, 'numeric');app.EditField_9.Position = [133 87 100 22];% Create EditField_10Labelapp.EditField_10Label = uilabel(app.Tab_2);app.EditField_10Label.HorizontalAlignment = 'right';app.EditField_10Label.Position = [261 53 41 22];app.EditField_10Label.Text = '初始值';% Create EditField_10app.EditField_10 = uieditfield(app.Tab_2, 'numeric');app.EditField_10.Position = [232 87 100 22];% Create EditField_11Labelapp.EditField_11Label = uilabel(app.Tab_2);app.EditField_11Label.HorizontalAlignment = 'right';app.EditField_11Label.Position = [360 53 41 22];app.EditField_11Label.Text = '电压源';% Create EditField_11app.EditField_11 = uieditfield(app.Tab_2, 'numeric');app.EditField_11.Position = [331 87 100 22];% Create EditField_12Labelapp.EditField_12Label = uilabel(app.Tab_2);app.EditField_12Label.HorizontalAlignment = 'right';app.EditField_12Label.Position = [482 120 53 22];app.EditField_12Label.Text = '时间常数';% Create EditField_12app.EditField_12 = uieditfield(app.Tab_2, 'numeric');app.EditField_12.Position = [550 120 100 22];% Create EditField_13Labelapp.EditField_13Label = uilabel(app.Tab_2);app.EditField_13Label.HorizontalAlignment = 'right';app.EditField_13Label.Position = [506 74 29 22];app.EditField_13Label.Text = '时间';% Create EditField_13app.EditField_13 = uieditfield(app.Tab_2, 'numeric');app.EditField_13.Position = [550 74 100 22];% Create Label_8app.Label_8 = uilabel(app.Tab_2);app.Label_8.HorizontalAlignment = 'right';app.Label_8.Position = [494 32 41 22];app.Label_8.Text = '电压值';% Create EditField_14app.EditField_14 = uieditfield(app.Tab_2, 'numeric');app.EditField_14.Position = [550 32 100 22];% Create RLCTabapp.RLCTab = uitab(app.TabGroup);app.RLCTab.Title = '二阶RLC';% Create CaculateButton_3app.CaculateButton_3 = uibutton(app.RLCTab, 'state');app.CaculateButton_3.ValueChangedFcn = createCallbackFcn(app, @CaculateButton_3ValueChanged, true);app.CaculateButton_3.Text = 'Caculate';app.CaculateButton_3.Position = [254 10 100 22];% Create UIAxes_3app.UIAxes_3 = uiaxes(app.RLCTab);title(app.UIAxes_3, '')xlabel(app.UIAxes_3, '时间/s')ylabel(app.UIAxes_3, '电压/V')app.UIAxes_3.TitleFontWeight = 'bold';app.UIAxes_3.Position = [34 160 628 379];% Create EditField_15Labelapp.EditField_15Label = uilabel(app.RLCTab);app.EditField_15Label.HorizontalAlignment = 'right';app.EditField_15Label.Position = [65 53 37 22];app.EditField_15Label.Text = '电阻';% Create EditField_15app.EditField_15 = uieditfield(app.RLCTab, 'numeric');app.EditField_15.Position = [34 87 100 22];% Create EditField_16Labelapp.EditField_16Label = uilabel(app.RLCTab);app.EditField_16Label.HorizontalAlignment = 'right';app.EditField_16Label.Position = [168 53 29 22];app.EditField_16Label.Text = '电容';% Create EditField_16app.EditField_16 = uieditfield(app.RLCTab, 'numeric');app.EditField_16.Position = [133 87 100 22];% Create Label_12app.Label_12 = uilabel(app.RLCTab);app.Label_12.HorizontalAlignment = 'right';app.Label_12.Position = [273 53 29 22];app.Label_12.Text = '电感';% Create EditField_17app.EditField_17 = uieditfield(app.RLCTab, 'numeric');app.EditField_17.Position = [232 87 100 22];% Create EditField_18Labelapp.EditField_18Label = uilabel(app.RLCTab);app.EditField_18Label.HorizontalAlignment = 'right';app.EditField_18Label.Position = [360 53 41 22];app.EditField_18Label.Text = '电压源';% Create EditField_18app.EditField_18 = uieditfield(app.RLCTab, 'numeric');app.EditField_18.Position = [331 87 100 22];% Create Label_9app.Label_9 = uilabel(app.RLCTab);app.Label_9.HorizontalAlignment = 'right';app.Label_9.Position = [506 120 29 22];app.Label_9.Text = '时间';% Create EditField_19app.EditField_19 = uieditfield(app.RLCTab, 'numeric');app.EditField_19.Position = [550 120 100 22];% Create Label_10app.Label_10 = uilabel(app.RLCTab);app.Label_10.HorizontalAlignment = 'right';app.Label_10.Position = [482 74 53 22];app.Label_10.Text = '电容电压';% Create EditField_20app.EditField_20 = uieditfield(app.RLCTab, 'numeric');app.EditField_20.Position = [550 74 100 22];% Create Label_11app.Label_11 = uilabel(app.RLCTab);app.Label_11.HorizontalAlignment = 'right';app.Label_11.Position = [482 32 53 22];app.Label_11.Text = '电感电压';% Create EditField_21app.EditField_21 = uieditfield(app.RLCTab, 'numeric');app.EditField_21.Position = [550 32 100 22];% Create Label_13app.Label_13 = uilabel(app.RLCTab);app.Label_13.HorizontalAlignment = 'right';app.Label_13.Position = [138 149 89 22];app.Label_13.Text = '电容电压初始值';% Create EditField_22app.EditField_22 = uieditfield(app.RLCTab, 'numeric');app.EditField_22.Position = [133 120 100 22];% Create EditField_23Labelapp.EditField_23Label = uilabel(app.RLCTab);app.EditField_23Label.HorizontalAlignment = 'right';app.EditField_23Label.Position = [237 149 89 22];app.EditField_23Label.Text = '电感电流初始值';% Create EditField_23app.EditField_23 = uieditfield(app.RLCTab, 'numeric');app.EditField_23.Position = [232 120 100 22];% Create GLCTabapp.GLCTab = uitab(app.TabGroup);app.GLCTab.Title = '二阶GLC';% Create CaculateButton_4app.CaculateButton_4 = uibutton(app.GLCTab, 'state');app.CaculateButton_4.ValueChangedFcn = createCallbackFcn(app, @CaculateButton_4ValueChanged, true);app.CaculateButton_4.Text = 'Caculate';app.CaculateButton_4.Position = [254 10 100 22];% Create UIAxes_4app.UIAxes_4 = uiaxes(app.GLCTab);title(app.UIAxes_4, '')xlabel(app.UIAxes_4, '时间/s')ylabel(app.UIAxes_4, '电流/I')app.UIAxes_4.TitleFontWeight = 'bold';app.UIAxes_4.Position = [34 160 628 379];% Create EditField_24Labelapp.EditField_24Label = uilabel(app.GLCTab);app.EditField_24Label.HorizontalAlignment = 'right';app.EditField_24Label.Position = [65 53 37 22];app.EditField_24Label.Text = '电阻';% Create EditField_24app.EditField_24 = uieditfield(app.GLCTab, 'numeric');app.EditField_24.Position = [34 87 100 22];% Create EditField_25Labelapp.EditField_25Label = uilabel(app.GLCTab);app.EditField_25Label.HorizontalAlignment = 'right';app.EditField_25Label.Position = [168 53 29 22];app.EditField_25Label.Text = '电容';% Create EditField_25app.EditField_25 = uieditfield(app.GLCTab, 'numeric');app.EditField_25.Position = [133 87 100 22];% Create EditField_26Labelapp.EditField_26Label = uilabel(app.GLCTab);app.EditField_26Label.HorizontalAlignment = 'right';app.EditField_26Label.Position = [273 53 29 22];app.EditField_26Label.Text = '电感';% Create EditField_26app.EditField_26 = uieditfield(app.GLCTab, 'numeric');app.EditField_26.Position = [232 87 100 22];% Create Label_14app.Label_14 = uilabel(app.GLCTab);app.Label_14.HorizontalAlignment = 'right';app.Label_14.Position = [360 53 41 22];app.Label_14.Text = '电流源';% Create EditField_27app.EditField_27 = uieditfield(app.GLCTab, 'numeric');app.EditField_27.Position = [331 87 100 22];% Create EditField_28Labelapp.EditField_28Label = uilabel(app.GLCTab);app.EditField_28Label.HorizontalAlignment = 'right';app.EditField_28Label.Position = [506 120 29 22];app.EditField_28Label.Text = '时间';% Create EditField_28app.EditField_28 = uieditfield(app.GLCTab, 'numeric');app.EditField_28.Position = [550 120 100 22];% Create Label_15app.Label_15 = uilabel(app.GLCTab);app.Label_15.HorizontalAlignment = 'right';app.Label_15.Position = [482 74 53 22];app.Label_15.Text = '电容电流';% Create EditField_29app.EditField_29 = uieditfield(app.GLCTab, 'numeric');app.EditField_29.Position = [550 74 100 22];% Create Label_16app.Label_16 = uilabel(app.GLCTab);app.Label_16.HorizontalAlignment = 'right';app.Label_16.Position = [482 32 53 22];app.Label_16.Text = '电感电流';% Create EditField_30app.EditField_30 = uieditfield(app.GLCTab, 'numeric');app.EditField_30.Position = [550 32 100 22];% Create EditField_31Labelapp.EditField_31Label = uilabel(app.GLCTab);app.EditField_31Label.HorizontalAlignment = 'right';app.EditField_31Label.Position = [138 149 89 22];app.EditField_31Label.Text = '电容电压初始值';% Create EditField_31app.EditField_31 = uieditfield(app.GLCTab, 'numeric');app.EditField_31.Position = [133 120 100 22];% Create EditField_32Labelapp.EditField_32Label = uilabel(app.GLCTab);app.EditField_32Label.HorizontalAlignment = 'right';app.EditField_32Label.Position = [237 149 89 22];app.EditField_32Label.Text = '电感电流初始值';% Create EditField_32app.EditField_32 = uieditfield(app.GLCTab, 'numeric');app.EditField_32.Position = [232 120 100 22];% Show the figure after all components are createdapp.UIFigure.Visible = 'on';endend% App creation and deletionmethods (Access = public)% Construct appfunction app = dianlu2% Create UIFigure and componentscreateComponents(app)% Register the app with App DesignerregisterApp(app, app.UIFigure)if nargout == 0clear appendend% Code that executes before app deletionfunction delete(app)% Delete UIFigure when app is deleteddelete(app.UIFigure)endend
end

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