1. Control of a Ball & Plate System Andrew Percy Academic Supervisor – James Welsh

2. Summary Introduction to the Ball & Plate System Introduction to the Ball & Plate System Background & Project Motivation Background & Project Motivation System Modeling System Modeling Actuator Design & Modeling Actuator Design & Modeling Sensor Design & Integration Sensor Design & Integration Control System Design Control System Design Remaining Work Remaining Work

3. The Ball & Plate System Objective Objective Balance a Ball on a Moveable Plate Balance a Ball on a Moveable Plate Control Characteristics Control Characteristics Unstable Unstable Non-Linear Non-Linear Examples Examples x y xx yy Ball Plate

4. Project Motivation Applications Applications Control Research Control Research Stabilized Platforms Stabilized Platforms Rolling Contact Manipulation Rolling Contact Manipulation Existing Apparatus Existing Apparatus Actuator Backlash Actuator Backlash Measurement Errors Measurement Errors Rolling with Slipping Rolling with Slipping

5. System Model A Plate Fixed Reference Frame A Plate Fixed Reference Frame Plate Angular Velocity Plate Angular Velocity

6. System Model Modeling Assumptions Modeling Assumptions The Ball is a Perfect Sphere The Ball is a Perfect Sphere Rolling Without Slipping Rolling Without Slipping Neglect Plate Potential Energy Neglect Plate Potential Energy Small Plate Angles Small Plate Angles Lagrange's Equation Lagrange's Equation

7. System Model Complete & Coupled Non-Linear Model Complete & Coupled Non-Linear Model Decoupled Linear Approximation Decoupled Linear Approximation System Transfer Functions System Transfer Functions

8. Actuation Actuator Selection Actuator Selection Servo Motor Servo Motor Stepper Motor Stepper Motor Linear Solenoid Linear Solenoid Linear Induction Motor Linear Induction Motor Magnetic Force Magnetic Force

9. Sensors Plate Angle Plate Angle Potentiometers Potentiometers Tilt Sensor Tilt Sensor Ball Position Ball Position Image Processing Image Processing Pressure Sensitive Plate Pressure Sensitive Plate Sensor Grid Sensor Grid Solenoid Current Solenoid Current Current Sense Resistor Current Sense Resistor rxrx ryry Plate Ball Camera Buffer Sync Separation Sample & Hold Micro Controller + - Coil Current Sense Out I I

10. Control Design Ball Position Control Ball Position Control State Feedback State Feedback Cascade Control Cascade Control Ball Position Controller Plate Angle Controller Plate Dynamics Ball Dynamics Plate Angle Sensor Ball Position Sensor Desired Ball Position Actual Ball Position - + - +

11. Remaining Work Continue Development of Solenoid Actuator Continue Development of Solenoid Actuator Rebuild the Existing Ball & Plate Apparatus Rebuild the Existing Ball & Plate Apparatus Design Sensor Interface & Control Circuits Design Sensor Interface & Control Circuits Continue Development of System Models Continue Development of System Models Design & Simulation of Controllers Design & Simulation of Controllers Develop Control Software Develop Control Software Implement & Test Control System Implement & Test Control System