1. DOUBLE ARM JUGGLING SYSTEM Progress Presentation ECSE-4962 Control Systems Design Group Members: John Kua Trinell Ball Linda Rivera

2. Introduction Where are we? Where are we? Bulk of Design and Build CompleteBulk of Design and Build Complete Testing and Tuning PhaseTesting and Tuning Phase Preliminary Results Preliminary Results Physical DesignPhysical Design Model DevelopmentModel Development Control Systems DevelopmentControl Systems Development Camera DevelopmentCamera Development

3. Physical Design Additions: Camera Mounting Overall System Mounting Other physical modifications Shaft Mounting Cable extensions Challenges: Net Design Material Building Possible solutions: Foil wrapping current nets Replacing nets h Camera Mounting Shaft Mounting System Mounting

4. Model Development Lagrange-Euler Model Lagrange-Euler Model Single Joint Single Joint

5. Simulink Model - Nonlinear

6. DAC to Current Model Digital to Analog Conversion Digital to Analog Conversion Tested voltage over a rangeTested voltage over a range Fit curve to data – found slope, offsetFit curve to data – found slope, offset Voltage to Current Conversion Voltage to Current Conversion Adjusted gain to approximately 0.1A/VAdjusted gain to approximately 0.1A/V Tested current over a rangeTested current over a range Applied load to system for accurate measurementApplied load to system for accurate measurement

7. Friction Identification Identify Viscous and Coulomb Friction Identify Viscous and Coulomb Friction Apply constant torque and measure steady state velocity Apply constant torque and measure steady state velocity Automate with LabVIEW Automate with LabVIEW Process data with MATLAB Process data with MATLAB

8. Other Parameters Inertia/Mass Inertia/Mass Calculated with SolidWorksCalculated with SolidWorks Shaft Spring Constant Shaft Spring Constant Possible cause of oscillationsPossible cause of oscillations Experimentally measuredExperimentally measured Found to be very stiff - k=4600N/mFound to be very stiff - k=4600N/m

9. Model Linearization Discard Coulomb Friction Discard Coulomb Friction State Space Equations State Space Equations Transfer Function Transfer Function

10. Model Verification Compare Friction ID results to simulated “Friction ID” Compare Friction ID results to simulated “Friction ID” Compare simulated controlled output to implemented output Compare simulated controlled output to implemented output Potentially apply “chirp” ID methods Potentially apply “chirp” ID methods

11. Velocity Estimation Finite difference method – 10ms Finite difference method – 10ms Minimum velocity of 0.1534 rad/secMinimum velocity of 0.1534 rad/sec Maximum motor speed of 21 rad/secMaximum motor speed of 21 rad/sec Designed peak velocity of 15 rad/secDesigned peak velocity of 15 rad/sec Overflow problem Overflow problem Seeing large velocity pulse in dataSeeing large velocity pulse in data Limited position to +/- 180 degreesLimited position to +/- 180 degrees Corrected velocity when over limits (153 rad/sec)Corrected velocity when over limits (153 rad/sec)

12. Trajectory Calculation Drag force on the ball Drag force on the ball Trajectory deviates from standard projectile motion equationTrajectory deviates from standard projectile motion equation Differential EquationDifferential Equation Iterative vs. Simulink ODE Solver Iterative vs. Simulink ODE Solver

13. Control Systems Development Two methods for designing controllers used MATLAB rltool (Pole Placement method) 1. Obtain transfer function 2. Import transfer function to rltool 3. Convert continuous model to discrete model (sampling time 10ms) 4. Define design constraints, such as rise time and settling time 5. Place gain constant at the crossings of design constraints 6. Export controller to simulink model of system 7. Run simulation to test PID block MATLAB (simulink) Kp = Proportional Ki = Integral Kd = Derivative

14. Pole Placement Methods Tilt-System Root Locus Closed Loop poles Stable Locate system poles at the intersection of ω n and ς Design Criteria ω n = 62.8 rad/s ς =.7

15. Non-Linear System Step Response To different controllers rltool controller PID controller Overshoot: 28.7% Overshoot: 0% Kp = 800 Ki = 20 Kd = 40

18. Camera Development Vision Module Familiarization: Use of NI Vision Assistant Acquire Preliminary data Carry out a number of tests Image Processing Examples: Projectile motion launch

19. Upward vertical launchUpward vertical launch Processing Challenges: Blurred images of the ball Blurred images of the ball Colored backgrounds similar to ball’s color Colored backgrounds similar to ball’s color Image 9/30 Image 12/30

20. Ball blur Ball blur1.2.3.

21. Background similar to ball color Possible solutions: Blur  Take average of circles Background  Create uniform dark background

22. Data Verification: Verify if height prediction data is valid Run new experiment Compare results If results from script seem reasonable Use Overhead camera only If results form script are unreliable Add Additional camera on the side Next Steps: Running Trajectory Prediction Integration of Vision Development with Control System Continue to validate data

23. Summary of Progress Schedule Schedule On track, only a few items outstandingOn track, only a few items outstanding Costs Costs 10% overbudget, 20% under estimates10% overbudget, 20% under estimates Did not purchase motor, built support structuresDid not purchase motor, built support structures Plan of Action Plan of Action No deviationsNo deviations New Difficulties New Difficulties