1. DOUBLE ARM JUGGLING SYSTEM Team 1 Proposal Presentation ECSE-4962 Control Systems Design Trinell Ball John Kua Linda Rivera

2. Introduction Goal: Design and development of a juggling system Pivoted double-ended arm Able to handle two or more ping pong balls Motivation Previous project: Team 7, 2004 Related Research: Dr. D. E. Koditschek / University of Michigan

3. Objectives Develop mechanism to simultaneously juggle two or more balls Execute toss and catch operations quickly Provide feedback on arm’s state Provide feedback on balls’ state Predict Trajectory of the ball Design control system Learn from toss/catch errors Compensate for disturbances in flight path of the balls

4. Specifications Flight Profile: x: 0.75m, t: 1s Flight Profile: x: 0.75m, t: 1s Pan: Range of Motion – ±10° Pan: Range of Motion – ±10° Max Accel: 34.9 rad/s 2 Max Accel: 34.9 rad/s 2 Overshoot: <5% (pos) Overshoot: <5% (pos) Settling Time: <0.1 sec Settling Time: <0.1 sec Steady State Error: ±1° (±6.5mm) Steady State Error: ±1° (±6.5mm) Tilt: Range of Motion – ±30° Tilt: Range of Motion – ±30° Max Accel: 201.79 rad/s 2 Max Accel: 201.79 rad/s 2 Launch (Max) Velocity: 5.4 m/s Launch (Max) Velocity: 5.4 m/s Overshoot: <5% (pos), <1% (vel) Overshoot: <5% (pos), <1% (vel) Settling Time: <0.1 sec Settling Time: <0.1 sec Steady State Error: ±1° (±6.5mm) Steady State Error: ±1° (±6.5mm) Can track 2Hz sinusoidal input Can track 2Hz sinusoidal input

5. Modeling & Simulation System: System: Treat as Decoupled LinksTreat as Decoupled Links Parameters: Motor Torque, Gear Ratios, Inertial Loads, Shaft OscillationsParameters: Motor Torque, Gear Ratios, Inertial Loads, Shaft Oscillations Nonlinearities: Friction, Backlash, NoiseNonlinearities: Friction, Backlash, Noise Linearize Model for Control DesignLinearize Model for Control Design Trajectory: Projectile Motion, Drag Trajectory: Projectile Motion, Drag

6. Control Systems Tilt Axis: LQR state space controller Tilt Axis: LQR state space controller Pan Axis: PID controller or LQR state space controller Pan Axis: PID controller or LQR state space controller ControllerPlant d/dx θ ω θdθd Shaft Dynamics Vision System x,y (z) V

7. Model Development Model Verification Parameter Analysis Build System Develop Camera Subsystem X-Y Tracking Z Tracking Trajectory Prediction Pan/Tilt Control Systems Design Open Loop 1-D Testing Open Loop 2-D Testing Open Loop Two Ball Juggle Closed Loop 2-D Testing Closed Loop Two Ball Juggle Vision Feedback Controller Design PlanofAction