Ball Balancing Table

Presentations :

The Ball Balancing Table didactic platform allows students to approach the mains concepts of enslavement.

It is realized A ball is positioned on a touch table. It is stabilized by a two degrees of freedom mechanism associated with a control command.

Open Source applications allow students to create, modify and test their own algorithms.

Technical solutions discussed :

Table with two degrees of freedom mounted on a central cardan shaft

Two analogue servomotors 4.8V and torque 0.5 Nm

Two connecting rod / crank mechanisms with ball joints coupled to the two servomotors and to the table.

A 17-inch 4-wire resistive touch table with vertical and horizontal grids

An electronic interface board between the operating part and the control boards (myRIO, Arduino and Raspberry)

Fully compatible with LabVIEW and MATLAB Simulink

Open Source software structure to customise the desired applications

Rectangular and circular trajectory complements are integrated into the software.

Pedagogical activities :

Functional and structural study of the "Ball Balancing Table" platform:

• The mechanism has one ball-and-socket joint and two connecting rod/crank joints.
• Servomotors
• The touch table and sensors
• The electronic interface card
• The myRIO, Arduino or Raspberry control/command card.

Study of pulse width modulation (PWM) :

• PWM signal theory
• Generating PWM signals with a myRIO card
• Controlling actuators with PWM signals

System modeling :

• Lagrangian Method
• Newton's Law on Movements
• Servomotor model
• Obtaining the transfer function

Study of the feedback loop in systems :

• Reading the position of the whale from the 'touch screen'.
• Derivative filtering

Performance measurement :

• Characteristics in the time domain
• Steady-state response and steady-state error
• Derivative filtering

Design of servo correctors :

• Design of linear correctors
• PID Corrector
• Fuzzy Logic Corrector
• Comparison of simulation and real system responses for different types of correctors

Verification of control systems :

• Frequency response analysis
• Experimental bode diagram
• Determination of the cut-off frequency

ISS / CPGE pedagogical activities :

TP discovery :

• Setting in situation of the 5G and maze
• Carry out simple tests: point, rectangle, circle, path, ...
• Analyse the structure and describe the control system and the kinematic chain

TP initialisation :

• Showing interest in the horizontality of the table
• Understanding the realisation

TP Performance: Time identification (point function)
Step input response in X then Y

• Show the different behaviours in X and Y (different lever arms for the rest identical) for the same proportional coefficient.
• Adjust the proportional coefficients for behaviours close to the two axes, interest
• Qualify: speed, precision, stability based on measurements
• Optimiser avec coefficient proportionnel
• Propose a model and refine by minimising the gap

TP Performance: Time identification (rectangle function)
Response Step input in X and Y combined

• Not enslaving one of the axes: consequences
• Send one rung diagonally, establish the associated performance (different from the performance of each axis), conclude

TP Performances: Time identification (circle function)
Analysis and preparation of frequency studies

• Carry out the tests
• Compare set and measured trajectories
• Analyse the influence of proportional coefficients
• Present the notion of gain (not in dB) and phase with circles and angles.

TP Performance: Frequency identification (closed-loop bode tracing)
Single-axis frequency survey" function

• Define gain (in dB) and phase
• To show the different behaviours in X and Y for the same proportional coefficient.
• Adjust the proportional coefficients for the neighbouring behaviours of the two axes, the interest and compare with the temporal study.
• Propose a model and refine by minimizing the gap, compare with temporal study
• Conclude

TP Performance: Frequency identification (closed-loop bode tracing)
Circle function

• Establish the associated performances (different from the performances of each axis)
• Conclude

TP Performance: Frequency identification (open-loop bode tracing)
Identification and stability

TP Performances PID Tuning: PID Corrector Optimisation

• Influence of the Derivative, remove: instability
• Influence of the
• Performance and optimisation

TP Movement transmission study (circle function)
Geometrical laws transmission motor movement - table

• Measuring and plotting the motor geometric law - table
• Establishing the theoretical law (Matlab model)
• Compare, conclude
• Establish the conditions for linearisation

TP Movement transmission study (circle function)
Geometrical laws of the ball table

• Measuring and plotting the geometrical law ball - table
• Establishing the theoretical law (Matlab model)
• Compare, conclude

TP Movement transmission study (circle function)
Motor-ball law

• Establishing the theoretical law (Matlab model)
• Compare measured and theoretical ball trajectories
• Assumptions on the dynamic effects of the motor rotor, table connecting rods, balls

This list of assignments is subject to change.

Strong points :

Ball Balancing Table" tutorial table to learn the basics of enslavement.

User-selectable control part with programming under LabVIEW, MATLAB Simulink, Python.

Open source programs for creating your own control interfaces

Implementation of advanced numerical control/command techniques

References :

AO03 : Ball Balacing Table without control command

AO01 : Control command with MyRIO

AO02 : Control command with Arduino Mega

AC//RPi3 : Command control with Raspberry Pi 3

Video :