A Stateflow® chart is a graphical representation of a finite state machine consisting of states, transitions, and data. You can create a Stateflow chart to define how a MATLAB® algorithm or a Simulink® model reacts to external input signals, events, and time-based conditions. For more information, see Model Finite State Machines.
For instance, this Stateflow chart presents the logic underlying a half-wave rectifier. The chart contains two
Off. In the
state, the chart output signal
y is equal to the input
Off state, the output signal is set to zero. When the input signal
crosses some threshold
t0, the chart transitions between these states. The
actions in each state update the value of
y at each time step of the
This example shows how to create this Stateflow chart for simulation in Simulink and execution in MATLAB.
The Stateflow Editor is a graphical environment for designing state transition diagrams, flow charts, state transition tables, and truth tables. Before opening the Stateflow Editor, decide on the chart execution mode that best meets your needs.
To model conditional, event-based, and time-based logic for periodic or continuous-time Simulink algorithms, create a Stateflow chart that you can simulate as a block in a Simulink model. At the MATLAB command prompt, enter:
sfnew rectify % create chart for simulation in a Simulink model
Simulink creates a model called
rectify that contains an empty
Chart block. To open the Stateflow Editor, double-click the chart block.
To design reusable state machine and timing logic for MATLAB applications, create a standalone Stateflow chart that you can execute as a MATLAB object. At the MATLAB command prompt, enter:
edit rectify.sfx % create chart for execution as a MATLAB object
If the file
rectify.sfx does not exist, the Stateflow Editor creates an empty chart with the name
The main components of the Stateflow Editor are the object palette, the chart canvas, and the Symbols pane.
The chart canvas is a drawing area where you create a chart by combining states, transitions, and other graphical elements.
On the left side of the canvas, the object palette displays a set of tools for adding graphical elements to your chart.
On the right side of the canvas, in the Symbols pane, you add new data to the chart and resolve any undefined or unused symbols.
After you construct your Stateflow chart, you can copy its contents to another chart with a different execution mode. For example, you can construct a chart for execution in MATLAB and copy its contents into a chart for simulation in Simulink.
From the object palette, click the State icon
and move the pointer to the chart canvas. A state with
its default transition appears. To place the state, click a location on the canvas. At
the text prompt, enter the state name
On and the state action
y = x.
Add another state. Right-click and drag the
On state. Blue
graphical cues help you to align your states horizontally or vertically. The name of the
new state changes to
Off. Double-click the state and modify the state
y = 0.
Realign the two states and pause on the space between the two states. Blue transition cues indicate several ways in which you can connect the states. To add transitions, click the appropriate cue.
Alternatively, to draw a transition, click and drag from the edge of one state to the edge of the other state.
Double-click each transition and type the appropriate transition condition
x>=t0. The conditions appear inside
Clean up the chart:
To improve clarity, move each transition label to a convenient location above or below its corresponding transition.
To align and resize the graphical elements of your chart, in the Format tab, click Auto Arrange or press Ctrl+Shift+A.
To resize the chart to fit the canvas, press the space bar or click the Fit To View icon .
Before you can execute your chart, you must define each symbol that you use in the chart and specify its scope (for example, input data, output data, or local data). In the Symbols pane, undefined symbols are marked with a red error badge . The Type column displays the suggested scope for each undefined symbol based on its usage in the chart.
Open the Symbols pane.
If you are building a chart in a Simulink model, in the Modeling tab, under Design Data, select Symbols Pane.
If you are building a standalone chart for execution in MATLAB, in the State Chart tab, select Add Data > Symbols Pane.
In the Symbols pane, click Resolve Undefined Symbols .
If you are building a chart in a Simulink model, the Stateflow Editor resolves the symbols
t0 as input data and
y as output data
If you are building a standalone chart for execution in MATLAB, the Stateflow Editor resolves
y as local data .
Because the threshold
t0 does not change during simulation,
change its scope to constant data. In the Type column, click the
data type icon next to
t0 and select
Set the value for the threshold
t0. In the
Value column, click the blank entry next to
and enter a value of 0.
Save your Stateflow chart.
Your chart is now ready for simulation in Simulink or execution in MATLAB.
To simulate the chart inside a Simulink model, connect the chart block to other blocks in the model through input and output ports. If you want to execute the chart from the MATLAB Command Window, see Execute the Chart as a MATLAB Object.
To return to the Simulink Editor, on the explorer bar at the top of the canvas, click the name of the
rectify. If the explorer bar is
not visible, click the Hide/Show Explorer Bar icon
at the top of the object palette.
Add a source to the model:
From the Simulink Sources library, add a Sine Wave block.
Double-click the Sine Wave block and set the Sample time to 0.2.
Connect the output of the Sine Wave block to the input of the Stateflow chart.
Label the signal as
Add a sink to the model:
From the Simulink Sinks library, add a Scope block with two input ports.
Connect the output of the Sine Wave block to the first input of the Scope block.
Connect the output of the Stateflow chart to the second input of the Scope block.
Label the signal as
Save the Simulink model.
To simulate the model, click Run . During the simulation, the Stateflow Editor highlights active states and transitions through chart animation.
After you simulate the model, double-click the Scope block. The scope displays the graphs of the input and output signals to the charts.
The simulation results show that the rectifier filters out negative input values.
To execute the chart in the MATLAB Command Window, create a chart object and call its
function. If you want to simulate the chart inside a Simulink model, see Simulate the Chart as a Simulink Block.
Create a chart object
r by using the name of the
sfx file that contains the chart definition as a function. Specify
the initial value for the chart data
x as a name-value pair.
r = rectify('x',0);
Initialize input and output data for chart execution. The vector
contains input values from a sine wave. The vector
Y is an empty
T = 0:0.2:10; X = sin(T); Y = ;
Execute the chart object by calling the
step function multiple
times. Pass individual values from the vector
X as chart data
x. Collect the resulting values of
y in the vector
Y. During the execution, the Stateflow Editor highlights active states and transitions through chart
for i = 1:51 step(r,'x',X(i)); Y(i) = r.y; end
Delete the chart object
r from the MATLAB workspace.
Examine the results of the chart execution. For example, you can call the
stairs function to create a stairstep graph that compares the values of
ax1 = subplot(2,1,1); stairs(ax1,T,X,'color','#0072BD') title(ax1,'x') ax2 = subplot(2,1,2); stairs(ax2,T,Y,'color','#D95319') title(ax2,'y')
The execution results show that the rectifier filters out negative input values.