1. Small-Scale Robotic Arm Senior Capstone Project Ben Boyle and Kitera Hayes Project Advisor: Dr. Gary Dempsey April 29, 2004

2. Outline zObjectives zEquipment List zSystem Specifications zFunctional Description zBlock Diagram zSystem Parameters zSystem Identification zImplementation of Controllers zFlexible Rotary Joint zSystem Limitations zConclusion zCompleted Tasks zQuestions

3. Objectives zDetermination of Plant Model zFast System Response zWide Command Range (± 90 degrees) zHigh Stability Margin (GM, PM) zUser-friendly Software Interface zLow Resonant Frequency Mode with New Arm

4. Equipment List z200 MHz Pentium-based computer zQuanser System yRobotic Arm with Flexible Rotary Joint yPower Amplifier zSoftware yMATLAB (SIMULINK) yBorland C

5. Lab Workstation

6. Robotic Arm

7. System Specifications zCommand: ± 90 set points, ± 40 deg/sec velocity zPercent Overshoot = 0 % zSteady-State Error = ± 2 degrees zPhase Margin  70 degrees

8. Functional Description Positioning Figure 1 - Input/Output Description Command Input Small Scale Robotic Arm Control

9. Functional Description zSoftware Interface zPositioning Modes of Operation

10. Block Diagram System (Plant) Software Figure 2 - Block Diagram of Robotic Arm

11. System Parameters zSystem (Plant) yAmplifier   5 [V] @ 3 [A] yPosition Sensor    180  of travel yDC motor  5 [V] yExternal Gears  5:1 velocity reduction yInternal Gears  14.1:1 velocity reduction yAntialiasing Filter  first-order low-pass with pole @ 163 [rad/sec] zSoftware y200 [MHz] PC yA/D converter  12 bit plus sign,  5 [V] yD/A converter  12 bit,  5 [V]

12. System Identification zClosed-loop Results zOpen-loop Results zPlant Model Equation zPlant Model Verification

13. System Identification zClosed-loop Results y Gain k = 0.025  Best Fit x Close to 0% overshoot y Step input of ±20° y DC Gain x Gp(0) = 27°/[V]

14. System Identification k=0.025 D/A Gp R=20  E=12  Controller voltage=0.2954 C=8  Controller Voltage = (12°)(.025) = 0.295 [V] DC Gain [Gp(0)] = 8°/0.295 [V] = 27°/[V] Figure 3 – DC Gain Calculation of System

15. System Identification Figure 4 - Gain k = 0.025, Step input of ±20°, Closed-loop (Experimental Results)

16. System Identification zOpen-loop Results yVerify DC gain of plant yCalculate accurate time delay yHelp to determine plant model

17. System Identification Figure 5 - k = 1.0, Step input voltage of 0.74 [V], Open-loop (Experimental Results)

18. System Identification Input Voltage = 20°/(27°/[V]) = 0.74 [V] (Open-loop) Command Degree Calculation: (K)(Command Voltage)(DC Gain) = Command Degrees Theoretical Command Degrees  20° Experimental Command Degrees  17° Percent Error = 17.6%

19. System Identification zPlant Gp = k[a/(s+a) 2 ] zc(t) = k[1-e -at - at(e -at )] y@ k = 1.0 and t = 2.86 seconds, c = 11.352° zDouble Pole @ a = -0.76 Pole Identification using Laplace Transform

20. System Identification Typical Open-loop Poles Figure 6 – Second Order System (Poles = -0.76) Actual Open-loop Double Pole -0.76

21. System Identification zPlant Model Equation: 27e -0.0562s (s/0.76 + 1) 2 (OPEN-LOOP)

22. System Identification 20.48º Figure 7 - SIMULINK Scope Output for Open-loop System = 20.48º Plant Model Verification

23. System Identification 8.38º Figure 8 - SIMULINK Scope Output for Closed-loop System = 8.38º Plant Model Verification

24. P Controller Figure 9 - Theoretical P Controller OutputFigure 10 - P Controller System Output

25. PI Controller Figure 12 - PI Controller System OutputFigure 11 - Theoretical PI Controller Output

26. PID Controller Figure 13 - Theoretical PID Controller OutputFigure 14 - PID Controller System Output

27. Feed-Forward/PI Controller Figure 15 - Feed-Forward/PI Controller Block Diagram

28. Feed-Forward/PI Controller Figure 16 - Theoretical FF/PI Controller OutputFigure 17 - FF/PI Controller System Output

29. Controller Comparison P ControllerFF/PI Controller Figure 19 - FF/PI Controller System OutputFigure 18 - P Controller System Output

30. Flexible Rotary Joint

31. Figure 20 - P Controller System OutputFigure 21 - P Controller Flex Joint System Output

32. System Limitations zD/A Converter  ± 5 [V] zStatic Friction y Just matches the applied force to try and prevent motion y Modeling  Time delay e -std (linear) zKinetic Friction y Moving friction with respect to speeds zInertia y J = (mass)(radius 2 ) zGravity

33. System Limitations (a) With Friction(b) Without Friction Figure 22(a-b) – Friction Characteristics for Pendulum System -B/2J PENDULUM

34. System Limitations Figure 23 - Closed-loop Time Delay and % Overshoot Calculations for Varying Gain k Td avg = 56.2 [ms] Time Delay

35. Conclusion zPI Controller is slow zPID Controller does not work zSolution is FF/PI Controller

36. Completed Tasks zPlant Model and Validation zProportional, PI, and PID Controllers zFF Controller with PI yUser-friendly Software Interface zFuture Work yPlant Model for Flexible Rotary Joint yGripper Motor with Varying Loads yNotch Filter Incorporation

37. Questions?