initialplot
Plot initial condition response of dynamic system
Description
The initialplot function plots the initial condition response
of a dynamic system
model and returns an
InitialPlot chart object. To customize the plot, modify the properties of
the chart object using dot notation. For more information, see Customize Linear Analysis Plots at Command Line.
To obtain initial condition response data, use the initial function.
Creation
Syntax
Description
ip = initialplot(sys,IC)sys and
returns the corresponding chart object.
If sys is a multi-input, multi-output (MIMO) model, then the
initialplot function creates a grid of plots with each plot
displaying the initial condition response of one input-output pair.
If sys is a model with
complex coefficients, then the plot shows both the real and imaginary components of the
response on a single axes and indicates the imaginary component with a diamond marker.
You can also view the response using magnitude-phase and complex-plane plots. (since R2025a)
ip = initialplot(___,t)t. You can
use t with any of the input argument combinations in previous
syntaxes. To define the time steps, you can specify:
The final simulation time using a scalar value.
The initial and final simulation times using a two-element vector. (since R2023b)
All the time steps using a vector.
ip = initialplot(___,plotoptions)plotoptions. Settings you specify in
plotoptions override the plotting preferences for the current
MATLAB® session. This syntax is useful when you want to write a script to generate
multiple plots that look the same regardless of the local preferences.
ip = initialplot(parent,___)Figure or TiledChartLayout, and sets the
Parent property. Use this syntax when you want to create a plot
in a specified open figure or when creating apps in App Designer.
Input Arguments
Properties
Object Functions
addResponse | Add dynamic system response to existing response plot |
Examples
Generate a random state-space model with 5 states and create the initial condition response plot chart object ip.
rng("default")
sys = rss(5);
x0 = [1,2,3,4,5];
ip = initialplot(sys,x0);
Change the time units to minutes and turn on the grid. To do so, edit properties of chart object.
ip.TimeUnit = "minutes"; grid on
The plot automatically updates when you modify the properties of the chart object.
Consider the following two-input, two-output dynamic system.
Convert the sys to state-space form since initial condition plots are supported only for state-space models.
sys = ss([0, tf([3 0],[1 1 10]) ; tf([1 1],[1 5]), tf(2,[1 6])]); size(sys)
State-space model with 2 outputs, 2 inputs, and 4 states.
The resultant state-space model has four states. Hence, provide an initial condition vector with four elements.
x0 = [0.3,0.25,1,4];
Plot the initial condition response. Turn on the grid and change the plot title.
ip = initialplot(sys,x0); title("Initial Condition Plot of MIMO System sys(s)") grid on
For this example, consider a MIMO state-space model with 3 inputs, 3 outputs and 3 states. Create an initial condition plot with red colored grid lines.
Create the MIMO state-space model sys_mimo.
J = [8 -3 -3; -3 8 -3; -3 -3 8]; F = 0.2*eye(3); A = -J\F; B = inv(J); C = eye(3); D = 0; sys_mimo = ss(A,B,C,D); size(sys_mimo)
State-space model with 3 outputs, 3 inputs, and 3 states.
Create an initial condition plot with chart object ip and display the grid.
x0 = [0.35,0.1,4];
ip = initialplot(sys_mimo,x0);
grid on
Set the grid color to red.
ip.AxesStyle.GridColor = [1 0 0];
The plot automatically updates when you modify the chart object. For MIMO models, initialplot produces a grid of plots, each plot displaying the initial condition response of one I/O pair.
For this example, examine the initial condition response of the following zero-pole-gain model and limit the plot to tFinal = 15 s. Use 15-point blue text for the title.
First, convert the zpk model to an ss model since initialplot only supports state-space models.
sys = ss(zpk(-1,[-0.2+3j,-0.2-3j],1)*tf([1 1],[1 0.05])); tFinal = 15; x0 = [4,2,3];
Create the initial conditions response plot and set the title properties of the chart object.
ip = initialplot(sys,x0,tFinal); ip.Title.FontSize = 15; ip.Title.Color = [0 0 1];
For this example, plot the initial condition responses of three dynamic systems and use the plot handle to enable the grid.
First, create the three models and provide the initial conditions.
rng('default');
sys1 = rss(4);
sys2 = rss(4);
sys3 = rss(4);
x0 = [1,1,1,1];Plot the initial condition responses of the three models.
t = 0:0.1:5; ip = initialplot(sys1,'r--',sys2,'b',sys3,'g-.',x0,t); legend('sys1','sys2','sys3'); grid on
Since R2025a
Create a state-space model with complex coefficients.
A = [-2-2i -2;1 0]; B = [2;0]; C = [0 0.5+2.5i]; D = 0; sys = ss(A,B,C,D);
Plot the initial-condition response of the system to an arbitrary starting state.
ic = [1 2]; ip = initialplot(sys,ic);
By default, the plot shows the real and imaginary components of the response on a single axes, indicating the imaginary component using a diamond marker.
You can also view the complex response using either a magnitude-phase plot or a complex-plane plot. For example, to view the magnitude and phase of the response, right-click the plot area and select Complex View >Magnitude-Phase.
Alternatively, you can set the ComplexViewType parameter of the corresponding chart object.
ip.ComplexViewType = "magnitudephase";
The plot shows the magnitude and phase of the response on a single axes, indicating the phase plot using a diamond marker.
You can view response characteristics in the plot. For example, to view the peak response, right-click the plot and select Characteristics > Peak Response.
Alternatively, you can enable the Visible property of the corresponding characteristic parameter of the chart object.
ip.Characteristics.PeakResponse.Visible = "on";
Tips
Plots created using
initialplotdo not support multiline titles or labels specified as string arrays or cell arrays of character vectors. To specify multiline titles and labels, use a single string with anewlinecharacter.initialplot(sys) title("first line" + newline + "second line");
