Final Ball and beamFTYYTT PowerPoint.pdf

EEE

1. BALL AND BEAM
SYSTEM
Feedback systems

2. NAME MATRICULE
MBUNGAI GOERGE BERINYUY FE21A234
CHINEPOH DIVINE-FAVOUR FE21A159
FONGANG KELUAM PAUL DIEUDONNE FE21A193
NGWASIRI RYAN TANIFORM ONGA FE21A266
NTUI RAOUL NTUI NJOCK FE21A288
DERRICK FORCHA FE21A166
NGOUNG TASSA ALAIN FE21A262
CHE KASSINA KUM FE21A158
NYUYSEVER BORIS DINNYUY
YOUNKWE CHAMCHA BEBE
FE21A295
FE21A432
BALL AND BEAM SYSTEM

3. Content
•Introduction
•Definition of terms
•Controller design
•Stability analysis
•Discussion of results
•Frequency Analysis
•Comparison: P, PI & PID CONTROLLERS
•Summary 
Ball and Beam system

4. The ball and beam system is a
fundamental example in control
theory. It involves a ball on a tilting
beam, controlled by sensors and a
motor. Engineers use it to study
unstable systems and develop
control strategies. It demonstrates
the art of controlling machines
effectively.
Ball and Beam system 4

5. A stable system
is a dynamic
system with a
bounded
response to a
bounded input.
A system that,
when given a
finite input, does
not escalate
indefinitely or
return to zero.
A feedback
control loop that
corrects for
error between a
setpoint and an
actual value.
Is a control loop
feedback mechanism
used in industrial
control systems and
other applications
that require
continuously
modulated control.
Ball and Beam system 5

6. statements that
describe the
goals and
objectives of a
control.
The process of
transforming a
nonlinear system
into a linear and
controllable one.
an unwanted
signal that
enters the
system.
A compensator
used in feedback
control systems
to enhance
stability and
transient
response. I
the behavior of a system during the time
it takes to reach a stable state after a disturbance​
Ball and Beam system

7. From Newtons 2nd law and the Lagrange approach,
we deduce the transfer function from the gear angle
to the ball position which results with the equation
belo w:

8. The stability of the system can be
analysed from the behaviour of it’s step
responce graph and values such as
settling time and overshoot can be
obtained easily from them

9. The transfer function can be gotten
from the Matlab code with the
provided parameters
The transfer function can be gotten
from the Matlab code with the
provided parameters

10. Matlab code to generate the transfer
function model with respect to the given
parameters
Simulation of the transfer function in
Matlab
From the plot, we see an unstable open-loop system that allows the ball
to roll out. To get control over results, we need to add required
controller(s) to the system
10

11. Settling time, less than 3 seconds
Overshoot time, less than 5%
Stability can be attained if the system is design as a
close loop system with unit feedback which can be
represented as such
For this system we used PID controllersm, due it’s realibility and
perfromance.

12. 12
For this system we used PID controllers, due it’s
reliability and performance.
Recall that the closed loop transfer function for PID
controller is as given below
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13. 13
The closed-loop transfer function for proportional control with a proportional gain (Kp)
equal to 100, with a step input of 0.25m, is model as seen below
system remains marginally stablePresentation Title

14. Using a PID controller we regulate the proportional gain of the system Kp and
the deferential gain of the system Kd control values
Using values: Kd = 10 and Kp = 10
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15. the system becomes stable but the
overshoot is too high and the settling time
needs to go down a bit”
For PID controllers, reducing Kd lowers the overshoot
and decreases the settling time slightly
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16. :
Kp = 15
Kd = 40
The plot can be see in the
image on the left.
We have meet the our control objective with a settling time
considered achieved when response is less than 2% of it s final value
Presentation Title

17. Frequency analysis involves the behaviour
of the following graphs

18. Presentation Title
This the bode plot of the
system at settling time less
than 3s and overshoot less
than 5%.

20. Parameter P - Controller PI - Controller PD - Controller
Rise time  longer shorter shorter
Overshoot significant moderate reduced
Settling time longer shorter shorter
Steady state error exist reduced exists
Ball and Beam system 20
The choice between P, PI, and PD controllers depends on the specific control objectives
and system dynamics, with the P controller offering simplicity and fast response, the PI
controller eliminating steady-state errors, and the PD controller providing improved
disturbance rejection and faster response.

21. The ball and beam system is widely applied in
industrial automation, robotics, motion control,
education, and research. It enables precise positioning,
control algorithm testing, and serves as an
educational tool. Overall, it is a versatile and valuable
system in engineering and technology fields.
21Presentation Title

22. Thank you
….