Ball on Beam Balancer System

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Ball on Beam Balancer System

• Armin Ataei-Esfahani
• Project Advisor Dr. M. Mahjoob
• Project Co-Advisor Dr. M. Shariat Panahi

Date July 17, 2004
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Introduction

• The ball on beam balancer system is one of the
  most enduringly popular and important laboratory
  models for teaching control systems engineering.
• Control Job Automatically regulating the
  position of the ball on the beam by changing the
  angle of the beam.
• The open loop is unstable.

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Practical Examples of Unstable Systems

• In chemical process industries the control of
  exothermic chemical reactions.
• In power generation the position control of the
  plasma in the Joint European Tours (JET).
• In aerospace the control of a rocket or aircraft
  during vertical take-off.

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Apparatus Design and Construction

• Base and Leveling Screws
• Motor Pod and Bushes
• Back Pod and Bushes
• Shaft and Shaft Bushes
• Bearing Covers
• Rotating Base
• Runner

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System Modeling

• Ball on Beam Balancer Modeling
• DC Motor Modeling
• Theory
• Experiment

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Ball on Beam Balancer Modeling
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DC Motor Modeling

• The actuator in this system is a DC motor,
  M(s) that is coupled through gearing to the beam
  shaft. The DC motor will be controlled with a
  local feedback loop in which beam angular
  position is measured with the shaft-mounted
  potentiometer (Kp).

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DC Motor Modeling - Circuits

• The voltage of motor mounted potentiometer is
  constantly compared with the desired voltage.
• A 1.6 volt is added to the output voltage to
  eliminate the motor dead zone.

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DC Motor Modeling Curve Fitting

• We fit the equation of the step response of a
  second order system (c (t)) to the plot gained
  from the experiment, to get the parameters that
  give the closest possible curve.
• The settling time is taken equal to the time
  during which the response reaches 80 of the step
  value. Applying Root Mean Squares rule (RMS) we
  composed an M-File checking different values of ?
  in a "For Loop", and found ? and ? which give
  best-fitted curve.

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Experiment Data and the Fitted Curve
Best Fitted Curve Parameters ? 1.0601, ?
0.5168
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System Simulation and Controller Design
Open Loop System
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Effects of Adding Zeros
Effect of Adding One Zero
Effect of Adding Two Zeros
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Designed PD Controller
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Controller Implementation

• Sensing angular and linear positions. A.
  Setting A/D card parameter B. Running data
  acquisition procedures.
• Performing controller computations.
• Sending computed voltage to the circuit through
  an D/A card. A. Setting D/A parameters. B.
  Setting reference voltage.

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Controller Implementation - Notes

• Saturation Problem.
• Linearity of Sensors.
• Motor Dead Zone.
• Non-linearity in Motor Dead Zone.
• Motor Driver Voltage Consumption.

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Motor Driver Circuit
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Angular Sensor Circuit
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Linear Potentiometer Circuit
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Electronic Board Features

• On/Off Switch.
• Three mode switch that enables the user to choose
  from three modes a. using the built in
  circuits. b. controlling the system manually
  c. using an analog controller