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Observer-Based Robot Arm Control System Nick Vogel, Ron Gayles, Alex Certa

Observer-Based Robot Arm Control System Nick Vogel, Ron Gayles, Alex Certa Advised by: Dr. Gary Dempsey. Outline. Project Overview Project Goals Functional Description Technical Background Information Functional Requirements Work Completed Conclusions. Project Overview.

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Observer-Based Robot Arm Control System Nick Vogel, Ron Gayles, Alex Certa

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  1. Observer-Based Robot Arm Control System Nick Vogel, Ron Gayles, Alex Certa Advised by: Dr. Gary Dempsey

  2. Outline • Project Overview • Project Goals • Functional Description • Technical Background Information • Functional Requirements • Work Completed • Conclusions

  3. Project Overview • Control of robot arms • Pendulum & 2 DOF arms • Load Changes • Observer-based • Ellis's method

  4. Pendulum Arm Configuration

  5. 2-DOF Arm Configuration

  6. Project Goals • Learn the Quanser software package • Model the pendulum and horizontal arm • Design controllers using classical control • Design controllers using observer-based control • Evaluate the relative performance of observers to classical controllers

  7. Equipment Used • PC with Matlab, Simulink, and Real Time Workshop • Motor with Quanser Control System • Linear Power Amplifier • Robot arm with Gripper • SRV-02 Rotary Servo Plant

  8. Overall Block Diagram

  9. Ellis's Observer-Based Controller

  10. Situational Description • Command of +-90 degrees • Meet specifications for a load of up to 75 grams • Be able to pass a load back and forth between two systems • Work with existing arm, sensor, and converters

  11. Technical Background Information • % Overshoot – Amount the system advances past the target position • Settling Time – Time it takes for the system to complete its response • Steady-State Error – Error of system after completely settling

  12. Technical Background Information • Gain Margin – How much gain can be added without instability • Phase Margin – how much phase lag can be added to the system without instability • PM=180-|system phase lag|

  13. Product Specifications for 2-DOF Arm • The overshoot of the arm shall be less than or equal to 15% • The settling time of the arm shall be less than or equal to 2s • The phase margin shall be at least 50 deg • The gain margin shall be at least 3.5 dB • The steady state error of the system shall be at most 5 degrees

  14. Product Specifications For Pendulum Arm • The overshoot of the arm shall be less than or equal to 15% • The settling time of the arm shall be less than or equal to 2s • The phase margin shall be at least 50 deg • The gain margin shall be at least 3.5 dB • The steady state error of the system shall be at most 1 degree

  15. Work Completed: Pendulum Arm • Arm Modeling • Traditional Arm Control • Non-Linear Arm Modeling • Load Testing • Observer Design

  16. Modified Estimated DC gain vs Voltage

  17. 2nd Order Pole Locations and Model • System assumed to be as shown to right • Poles at -11, -2.6 • Model results System results

  18. Frequency Response

  19. Proportional Control • Used control toolbox to find initial gain value • Tuned gain: 0.14 • For 20 degree input • % O.S.=15% • ess= 2.5 degrees • tr=0.12 s • ts= 0.41 s

  20. PID controller • Form: kp(0.09s+1)(0.4s+1)/[s(s/p1+1)] • Exact 2nd order • Higher pole is faster • D/A Converter saturates • Rate limitation needed

  21. PID Controller Continued

  22. PID Results • 45 deg input • % OS=3.3% • Ts=0.4 s

  23. Non-Linear Modeling

  24. Loaded Testing • Tested Loaded DC gain: approximately 27 degrees/volt (compared to 50 for unloaded model) • Performed Frequency Response and compared to original model with adjusted DC gain

  25. Observer Controller Design

  26. Observer • Feedback Controller used: Parallel PI controller • Linear System Model Used

  27. Controller • Used PID Controller with disturbance rejection

  28. Unloaded Results

  29. Loaded Results

  30. Disturbance Rejection Observer Specifications • Phase Margin = 50 degrees • Gain Margin = 3.5 • Steady state error < 1 degree • Rise Time = 1.17 s • % Overshoot = 3%

  31. How the Others Fail • All: good rise time and overshoot • Proportional controller: bad steady state error • Observer and PID: insufficient phase margin

  32. Work Completed: 2-DOF Arm • Base Modeling • Spring Modeling • Sample Rate • Controller Design

  33. Base Modeling • Model of arm without effect of springs • Ts=4/(ζωn) • ζωn is the real part of poles • Gp=1500/(s2+10s)

  34. Spring Modeling • Reran test and plotted arm displacement • Frequency of oscillation is imaginary part • Settling time is real part • GD=GDdcs/(s2+8s+289)

  35. Spring Modeling • Spring effect is instantaneous • Springs have no steady state effect • Behaves like differentiator • GD=0.42s/(s2+8s+289)

  36. Spring and Arm Together • Modeled as a minor loop disturbance • Positive feedback because of increasing overshoot and settling time Base transfer function remains unchanged Spring Displacement depends on base movement Actual Arm Position

  37. Model and Plant Comparison Arm Model

  38. Model and Plant Comparison • PlantModel • %os=41.7% %os=37.4% • Ts=1.12s Ts=1.21s

  39. System Root Locus

  40. New Sample Rate • For smooth operation of motor, ωs ≥ 6ωc • ωc =10.7rad/s : Tc= 0.587s • Tsam max≈0.0978s • Tsam chosen to be 0.1s • Largest sample time spreads out root locus • Complex poles and zeros don’t affect response

  41. New Plant Root Locus

  42. Proportional Control • KP = 0.024 Unloaded • 0.27% OS • ζ= 0.88 • Ts= 1.1s • KG = 0.0099 • PM = 70.5 deg • GM = 20.5dB Loaded • 3.91% OS • ζ= 0.72 • Ts= 1.9s • KG = 0.074 • PM= 72 deg • GM= 21dB

  43. PID Control

  44. PID Control • KP = 0.023 • KI = 0.01 • KD = 0.01 Unloaded • 0% OS • ζ= 1 • Ts= 1.1s • PM≈ 75 deg Loaded • 3.3% OS • ζ= 0.74 • Ts= 1.8s • PM≈ 75 deg

  45. Lead Network • Pole-zero cancellation • Lead pole chosen to be at zero for fastest settling time

  46. Lead Network • Gain of 0.06 should give Ts of 0.72s with 15%OS

  47. Lead Network • KP = 0.09 • Gc=z-0.458/z Unloaded • %OS = 0% • ζ=1.0 • Ts= 0.9s • PM = 75 deg • GM =21.3 dB Loaded • %OS = 0% • ζ=1.0 • Ts= 1.1s • PM = 76 deg • GM = 22.2 dB

  48. Minor Loop With PI Control Diagram Position Velocity PI Control

  49. Minor Loop With PI Control • KP = 6.0 • KI = 0.05 Unloaded • %OS = 7.0% • Ts= 1.0s • PM = 50 deg Loaded • %OS = 10% • Ts= 1.0s • PM ≈ 61 deg

  50. Classical Control Conclusions • Proportional and PID control did not handle loads very well • Minor Loop Performed well but is close to instability • Lead Network was the best choice by far

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