State Transition Diagram for Oral B 5000 Braun Electric Toothbrush

This assignment focuses on developing a state chart diagram for the operation of the Oral B 5000 Braun electric toothbrush. The transition between modes is modeled using input signals from the SmartGuide system. MATLAB is used to model the state diagram.

Name of the Student
Assignment 1
State transition diagram
Name of the Instructor
Date

Introduction:
The objective of this assignment is to develop a state chart diagram for the operation of
Oral B 5000 Braun electric toothbrush. The functionalities of the electric toothbrush is controlled
by installed SmartGuide user interface. Hence, the transition between the modes of the electric
toothbrush is modelled with the input signals from the SmartGuide system which is user
controlled and affected by some external condition like pressure input in the toothbrush. The
state transition diagram is basically an interchangeability of states based on particular input
conditions. In addition to the state diagram all the states of the machine and their functionality is
listed in the later section. The software chosen for modelling the state diagram of the machine is
MATLAB (more specifically Simulink) due to it simple and compact design and visually
attractive graph generation ability. The Oral B Braun electric toothbrush is recommended by
most of the dentists as it takes full care of the brushing operation of mouth and teeth and solves
almost every dental problem if used regularly in the prescribed manner.
Oral B Braun 5000 electric toothbrush Functionality & SmartGuide:
The main functions of the Oral B Braun electric toothbrush are listed below.
 The electric toothbrush is chargeable and charging is very easy as it only requires to the
toothbrush handle of be plugged in into an electric outlet and once get fully charged it can
operate 1 to 2 days without charging.
 The brushing timer can easily be adjusted by the user by the SmartGuide interface. The
user has the option to choose between the professional mode and 2- minute timer mode
and under each mode the brushing time can be increased or decreased using the count up
or count down button by user’s need.

 The brushing feedback in real time is displayed to the user by the Bluetooth capability of
the electric toothbrush and the oral B app which can be installed in the any computer.
 The toothbrush offers a total of 5 brushing modes and one tongue cleaning mode. The
user can switch between the modes after turning on the toothbrush. The brushing modes
are Daily clean mode, Massage mode, Sensitive mode, Whitening mode and Deep clean
mode.
 One pressure sensor is also installed in the toothbrush which senses if pressure is
increased over a predefined value while brushing. This triggers a red bulb in the system
and a warning message is displayed in the SmartScreen. Also, if the brush is operating in
daily clean mode or deep clean mode then if pressure bulb glows then it brushing mode
automatically changes to sensitive mode. However, in other modes and in tongue
cleaning mode the pressure sensor remains deactivated.
Description of the state transition diagram:
Now, the electric toothbrush does not turn on as soon as the ON switch is pressed by the
user. It takes a delay of 2 seconds to activate all the components within the system and after that
the toothbrush is fully operational. After that user can choose any brushing mode and user can
continue with that or change according to their desire.
Hence, this can be modelled in MATLAB by using the states of the machine as described below.
The signal of the user which is converted by the SmartGuide to some specific values of signal u
for state transition is shown below. Also, the state in which the machine is operating is
represented by the signal y. The particular discrete values of u and y corresponds to their
transition condition and current state. Additionally, the signal generated by the pressure sensor
which changes the daily clean mode and deep clean mode to sensitive mode is modelled by the

signal x. If the value of x is 0 that means the pressure in the toothbrush is normal and if the value
of x=1 then the pressure of the toothbrush has been exceeded the specified limit. The toothbrush
also gets OFF while brushing if the power supply from it rechargeable battery falls below the
operating requirement voltage. The state name, transition condition and the operating state for
their corresponding values of signals are shown in the following table.
State Name SmartGuide signal input for
state transition
State of the machine
OFF State u=0 or u<0 y= -1
Wait u>0 (for 2 secs) y= 0
ON state u>0 y= 1
Daily clean mode u=1 y=2
Sensitive mode u=2, x=1 y=3
Massage mode u=3 y=4
Whitening mode u=4 y=5
Deep clean mode u=5 y=6
Tongue Clean mode u=6 y=7

State model:
State transition diagram:
The transition states as build inside Simulink are given as follows.

State transition table:

Testing:
Now, the model is tested with random user input signal modelled by SmartGuide and pressure
signal as given below.
u = [4 5 6 1 2 3 4 3 2 1 4]
at time t=[0,1,2…10] seconds and x=1:
Figure 3
Now, from the above figure it can be seen that machine goes to ON state after 2 secs as specified
in the state table. It can be seen that the delay is slightly more than 2 secs which is known as the
transition delay as it has some constant value of a few milliseconds inbuilt in MATLAB. Now, it

can be seen that all the transitions follow the rule specified in the table, however, it can be seen
that there is a spike at t =9 secs when u = 1 or the daily clean mode signal is given. In this case
as the pressure input signal is high (pressure is over the limit) the output state suddenly change to
y= 3 or sensitive mode.
Video Transcript description:
The final state transition diagram is formed by modifying the state diagram developed in
earlier section. The conditions for state transition can be viewed by double clicking the state
table block in Simulink. Now, inside the state transition table the states are defined in the first
column (States column). The toothbrush modes are modelled as its states which are Daily clean,
sensitive mode, Massage mode, whitening mode, deep clean mode and tongue clean mode. In
addition to these states OFF state, ON state and Wait state is provided in the model. The wait
state is there as the toothbrush takes the sometime (typically of 2 seconds) to initially all its
operations that is to move from OFF to ON state. Now, in the later columns define the state
transition conditions inside if and elseif statements. The state transition conditions are controlled
by the user input signal (u) and the pressure sensor signal(x). Now, if the input signal is too much
low i.e. the less than value to keep the circuit operational then machine goes to off State(u<0) as
in low voltage the circuit operation may be abnormal and can cause abnormal state change. The
value of x which is the random generated pressure signal (equivalent to the pressure signal input
by user modified into signal by SmartGuide interface) has produced 0 value or the pressure is
normal. The user input signal u= [0,1,2,3,4,5,6,5,4,3,2] in time t=[0,1,2…10] seconds is
generated in signal builder block in Simulink from custom signal option. Then finally the state
diagram is simulation with discrete solver option in Simulink for a duration of 11 seconds. Now,
the scope block in Simulink is opened and two graphs of state of machine and user input signal

can be found as given in Figure 3. Similarly, figure 1 and figure can be found when the user
input signal is constant (i.e. the user chooses only a specific toothbrush mode) and x=1 (pressure
applied to toothbrush by the user is always above the pressure limit). As specified in the Oral B
brush manual the daily clean mode and deep clean mode goes to sensitive mode when the
pressure is over limit. Hence, in the state transition table transition condition x=1 is entered in the
rows corresponding to daily clean state and deep clean state. The current states of the machine is
modelled by the signal y and its values are entered inside the individual state cell in the state
transition table.

Conclusion:
Hence, almost all the functionalities of the Oral B toothbrush are listed and successfully
implemented in a state transition table using Simulink (a simulation environment in MATLAB).
The testing of the state transition table shows equivalent results as specified in the manual of
Oral B Braun 5000 electric toothbrush. The input signals are assumed to be fed by SmartGuide
interface which is controlled by the user and external conditions.