Abd-Elmunem Al-Kilani – Ayman Al-Marashdeh

Prepared by:

DIGITAL INVERTED PENDULUMCONCEPT AND APPLICATIONS

The ConceptAbd-Elmunem

CONCEPT

The inverted pendulum system is a standard problem of control

system. They are often useful to demonstrate concepts in linear

control such as the stabilization of unstable systems. Since the

system is inherently nonlinear, it has also been useful in illustrating

some of the ideas in nonlinear control.

The inverted pendulum system inherently has two equilibriums, one

of which is stable while the other is unstable. The stable equilibrium

corresponds to a state in which the pendulum is pointing

downwards.

CONCEPT

In the absence of any control force, the system will naturally return

to this state. The stable equilibrium requires no control input to be

achieved and, thus, is uninteresting form

a control perspective.

The unstable equilibrium corresponds to

a state in which the pendulum points strictly

upwards And, thus, requires control force

to maintain the unstable equilibrium position.

CONCEPT

In this system, an inverted pendulum is attached to a cart equipped

with a motor that drives it along a horizontal track. The user is able

to dictate the position and velocity of the cart through the motor

and the track restricts the cart to move in the horizontal direction.

Sensors are attached to the cart motor and the pendulum pivoted in

order to measure the cart position and pendulum joint angle,

respectively. Measurements are taken with incremental optical

encoders connected to a data acquisition board.

CONCEPT

MATlab/Simulinkg is used to implement the controller and analyze

data. Two limit switches are installed at the ends of the track, if the

cart touches either of them the controller will shut off the power to

the motor.

The ApplicationsAyman

APPLICATIONS

Inverted pendulum has some applications such as:

Space ShuttlesThe concept is used to balance the shuttle

while it initiates taking off.

Using this technique protects the shuttle from

falling down due to the variety in weight all

over it.

APPLICATIONS

Tower & Crawler CranesThe balance is needed to keep the machine stable

while moving elements around ,crawlers cranes

are basically a vehicle with inverted pendulum,

its called “Crawler” due to its movement across

the construction field.

In tower cranes the concept stays still except

the behavior of balancing which depends on

the moving arm.

APPLICATIONS

Segway (PT)It’s a two-wheeled self-balancing electric vehicle

PT stands for (Personal transporter) which is

a modern vehicle works by the inverted pendulum

concept.

It has 2 servo motors, 2 computers as a control

unit, and 2 tilt sensors to detect the device speed,

it also has 5 gyroscopes to detect the orientation

and angle of the device.

APPLICATIONS

The servo motor rotates the wheels forwards and

Backwards as needed for the balance.

The device is built to stay all the time balanced

in one place, trying to mirror the process of human

walking.

So if a driver is standing on the Segway,

starting in the balanced position, there would be

no change, but if the driver bends forward for

example, it will upset the balance…

APPLICATIONS

Once the balance is upset, the gyroscopes detect this change and

send a signal to the controller, which gives a signal to

The servomotor to move forward to regain

the balance, same operation happens in

the backward moving.

So the side effect of all of this is, as

the Segway tries to regain the balance, it’s

going to move itself in the direction needed

to restore the balance, forward or backward , thus,

the balance and movement are essentially one combined system.

APPLICATIONS

The Segway has many fields to be used in, such

as personal use to go to school or having a nice

trip around, or even at work like police officers,

airports employees or the army.

It comes with safety instruction ,and needs

20 – 30 minutes training before using.

Finally It’s quiet cheap, 2000$ - 6000$

depending on the additional features xD.