7. MATHEMATICAL MODELLING
TRANSFER FUNCTION OF MOTOR,CART AND
PENDULUM
HARDWARE INTERFACING OF CART WITH P.C
COMPENSATOR DESIGN
8.
9. MATHEMATICAL MODELING
Define the angle of the rod from
the vertical line as tetha. Define
also the
(x, y) coordinates of the center of
gravity of the pendulum rod as
(XG,YG ).Then
The rotational motion of the
pendulum rod about its center of
gravity.
The horizontal motion and vertical of
center of gravity of pendulum rod is
given by
Since we must keep the inverted pendulum
vertical, we can assume that u(t) and are
small quantities such that sin u u, cos u=1,
10. Consider the inverted pendulum system. since in this system
the mass is concentrated at the top of the rod, the center of the
gravity is the center of the pendulum ball for this case the
moment of inertia of the pendulum about its center of gravity is
small, and we assume I=0. So the finally equation becomes:
Then finally if we modified the
above two equation we get the
transfer function of the system
20. • Analog to Digital (ADC) circuit is used to read the
analog values provided by rotary (Free turn)
potentiometer. Rotary potentiometer is used for
sensing the pendulum position.
• Use ADC0804 I.C
• Parallel Port
•Arduino mega 2560
21. ADC0804
Easy to with all microprocessors or operates
as a stand alone device.
Differential analogs voltage inputs
On chip clock generator
22. PARALLEL PORT
A parallel port is a type of
interface found on computers
(personal and otherwise) for
connecting peripherals.
23.
24. o Modern Control Theory By Katsushiko
Ogata
o Control System Design
csd.newcastle.edu.au/control/simulations/pendulum.html
o True Digital Control of an Inverted Pendulum System - R. Dixon
www.es.lancs.ac.uk/cres/staff/rdixon/pendulum.html
