Construct and Run a Stateflow Chart
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 instance, this Stateflow chart presents the logic underlying a half-wave rectifier. The chart
contains two states labeled
Off. In the
On state, the chart output signal
equal to the input
x. In the
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.
Construct the Stateflow Chart
Open the Stateflow Editor
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, use the
sfnewfunction to 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
rectifythat contains an empty Stateflow Chart block. To open the Stateflow Editor, double-click the chart block.
To design reusable state machine and timing logic for MATLAB applications, use the
editfunction to 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.sfxdoes not exist, the Stateflow Editor creates an empty chart with the name
The main components of the Stateflow Editor are the chart canvas, the object palette, 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, events, and messages 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.
Add States and Transitions
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
Onand the state action
y = x.
Add another state. Right-click and drag the
Onstate. 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 action to
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 square brackets.
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 .
Resolve Undefined Symbols
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
t0as input data and
yas output data .
If you are building a standalone chart for execution in MATLAB, the Stateflow Editor resolves
yas local data .
Because the threshold
t0does not change during simulation, change its scope to constant data. In the Type column, click the data type icon next to
Set the value for the threshold
t0. In the Value column, click the blank entry next to
t0and enter a value of 0.
Save your Stateflow chart.
Your chart is now ready for simulation in Simulink or execution in MATLAB.
Simulate the Chart as a Simulink Block
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 Simulink model:
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 (Simulink) 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 (Simulink) 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.
Execute the Chart as a MATLAB Object
To execute the chart in the MATLAB Command Window, create a chart object and call its
step function. If you want to simulate the chart inside a
Simulink model, see Simulate the Chart as a Simulink Block.
Create a chart object
rby using the name of the
sfxfile that contains the chart definition as a function. Specify the initial value for the chart data
xas a name-value pair.
r = rectify(x=0);
Initialize input and output data for chart execution. The vector
Xcontains input values from a sine wave. The vector
Yis an empty accumulator.
T = 0:0.2:10; X = sin(T); Y = ;
Execute the chart object by calling the
stepfunction multiple times. Pass individual values from the vector
Xas chart data
x. Collect the resulting values of
yin the vector
Y. During the execution, the Stateflow Editor highlights active states and transitions through chart animation.
for i = 1:51 step(r,x=X(i)); Y(i) = r.y; end
Delete the chart object
rfrom the MATLAB workspace.
Examine the results of the chart execution. For example, you can call the
stairsfunction 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.