Professor : Chi-Jo Wang

Student’s name : Nguyen Van Binh

Student ID : MA02B203

Two Wheels Self Balancing Robot

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Southern Taiwan UniversityDepartment of Electrical Engineering

CONTENT

1. Overview of two wheel balancing robot2. Dynamic model3. PID controller4. Implement5. Conclusion

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Overview of two wheel balancing robot Two wheel balancing robot based on inverted pendulum model.

Inverted pendulum model is a complex nonlinear object. In recent

years there have been many projects about the application of inverted

pendulum principle to make two wheel self balancing robot.

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A robot that is capable of balancing upright on its two wheels is

known as a two wheeled balancing robot. The process of balancing is

typically referred to as stability control. The two wheels are situated

below the base and allow the robot chassis to maintain an upright

position by moving in the direction of tilt, either forward or

backward, in an attempt to keep the centre of the mass above the

wheel axles. The wheels also provide the locomotion thus allowing

the robot to transverse across various terrains and environments.

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Overview of two wheel balancing robot

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Overview of two wheel balancing robot Some applications of two wheels balancing robot

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Overview of two wheel balancing robot

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Dynamic model

Two wheels balancing robot based on inverted pendulum dynamic

model. So, research about inverted pendulum dynamic model is

necessary in modeling robot . Consider inverted pendulum dynamic

model as following:

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With

Dynamic model

O-I signals block diagram of model

Inverted pendulum

system

x

Fx

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Suppose (xp; yp) is coordinate of m heavy at the top of the

pendulum, we have:

Applying Newton's II law of motion in the x, we have:

Dynamic model

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Change xp in [2-1] into [2-3], we have:

Applying Newton's II Law for rotation of the pendulum around axis

Dynamic model

Implement calculating from [2-4]

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From [2-1], [2-2], [2-6] we have:

Dynamic model

Implement calculating from [2-7]

From [2-5] and [2-8] easy to have:

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Dynamic model Suppose F = u

Set state-space, we have:

11x

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Balance point at the vertical position:

Linear around at the balance point:

Dynamic model

With:

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Dynamic model

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PID Controller

PID is “Proportional, Integral, and derivative”. PID is the three-

term controller.

PID controller based on a feedback control method.

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Process is a controlled object. The purpose of control is to

make the output y (PV) followed r set point (set point-SP). To

do this, the controller will get the error between output signal

and input signal and then through the stages of control to make

control signals accordingly, to minimize this error.

A proportional controller (Kp) will have the effect of

reducing the rise time and will reduce ,but never eliminate, the

steady-state error. An integral control (Ki) will have the effect of

eliminating the steady-state error, but it may make the transient

response worse. A derivative control (Kd) will have the effect of

increasing the stability of the system, reducing the overshoot,

and improving the transient response

PID Controller

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PID Controller 1. Proportional control

Proportional control generate the changes of output. This

change is proportional to the bias current value. Response of

Proportional control can be adjusted multiplying the difference

signal with Kp.

Pout = Kp.e(t)

with Kp is Gain

e is error = SP-PV

t is current time

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PID Controller

With larger Kp value is easy to adjust error. However, the system

lost stability. Kp is too small then the system will react very slowly

with the input error

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PID Controller 2. Integral control

The value adjusted at Integral control is proportional with bias

in a period of time. It is total of bias. This signal are then

multiplied by the integral gain Ki and taken to adjust output

With Iout is the integral of output

Ki is Gain of the integral

e is error = SP-PV

t is current time

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PID Controller

Integral control in PID controller increase process to output close

SP value and eliminate setting error of proportional control.

However, Integral control added up all bias in stages before, so It is

cause of overshoot.

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PID Controller 3. Derivative control

Derivative control will determine the rate of change of error.

With Dout is the derivative of output

Kd is Gain of the derivative

e is error = SP-PV

t is current time

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PID Controller

Integral control in PID controller increase process to output close

SP value and eliminate setting error of proportional control.

However, Integral control added up all bias in stages before, so It is

cause of overshoot.

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Implement

Left wheel motor

Right wheel motor

L298 PIN 9Vx2

Gyro Accelerometer PIN9V

MicrocontrollerATMEGA32

Source 5V

IR Receiver

Figure 4.1 Block Diagram two wheel balancing robot

This project was successful in achieving its aims to

balance a two-wheeled autonomous robot based on the

inverted pendulum model.

The Kalman filter has been successfully implemented.

The gyroscope drift was effectively eliminated allowing

for an accurate estimate of the tilt angle and its derivative

for the robot.

More research is needed to investigate the effects of

linearising the dynamics of the system mode to improve

the stability and robustness of the robot. An attempt to

control the system using nonlinear methods is highly

recommended for future research24

Conclusions

[1] Anderson, DP, 2007, nBot Balancing Robot, viewed 20 Th March 2008,

<http://www.geology.smu.edu/~dpa www/robo/nbot/>

[2] Andrade-Cetto, J & Sanfeliu, A 2006, Environment Learning for Indoor Mobile

Robots, Springer, New York.

[3] Angeles, J 2007, Fundamentals of Robotic Mechanical Systems, Springer, New York.

[4] Banks, D 2006, Microengineering MEMs and Interfacing, Taylor & Francis, London.

[5] Bates, Hellebuyck, Ibrahim, Jasio, D, Morton, Smith, D, Smith, J & Wilmshurst

2008, PIC Microcontroller, Elsevier Inc, New York.

[6] Bergren, C 2003, Anatomy of a Robot, McGraw-Hill, Sydney.

[7] Bishop, R 2002, The Mechatronics Handbook, CRC Press, London.

[8] Bishop, R 2006, Mechatronics - An Introduction, Taylor & Francis, London.

[9] Bokor, J, Hangos, K & Szederkenyi, G 2004, Analysis & Control of Nonlinear

Process Systems, Springer, New York.

[10] Braunl, T 2006, Embedded Robotics, Springer, Perth.

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References

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Thank you for your attention