Observer-Based Robot Arm Control System

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

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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

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Overall Block Diagram
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Ellis's Observer-Based Controller
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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
• PM180-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

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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

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Work Completed Pendulum Arm

• Arm Modeling
• Traditional Arm Control
• Non-Linear Arm Modeling
• Load Testing
• Observer Design

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Modified Estimated DC gain vs Voltage
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2nd Order Pole Locations and Model

• System assumed to
• be as shown to right
• Poles at -11, -2.6
• Model results System results

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Frequency Response
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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
• tr0.12 s
• ts 0.41 s

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PID controller

• Form kp(0.09s1)(0.4s1)/s(s/p11)
• Exact 2nd order
• Higher pole is faster
• D/A Converter saturates
• Rate limitation needed

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PID Controller Continued
Pole Location Gain Value Overshoot Settling Time Rate Limitation Rate Limited Settling Time
-40 0.75 14.9 0.20 155 1.16
-80 1.5 15 0.10 148 1.20
-60 1.1 14.9 0.14 151 1.18
Rad/s s deg/s
1 deg input 180 deg input
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PID Results

• 45 deg input
• OS3.3
• Ts0.4 s

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Non-Linear Modeling
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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

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Observer Controller Design
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Observer

• Feedback Controller used Parallel PI controller
• Linear System Model Used

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Controller

• Used PID Controller with disturbance rejection

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Unloaded Results
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Loaded Results
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Disturbance Rejection Observer Specifications

• Phase Margin 50 degrees
• Gain Margin 3.5
• Steady state error lt 1 degree
• Rise Time 1.17 s
• Overshoot 3

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How the Others Fail

• All good rise time and overshoot
• Proportional controller bad steady state error
• Observer and PID insufficient phase margin

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Work Completed 2-DOF Arm

• Base Modeling
• Spring Modeling
• Sample Rate
• Controller Design

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Base Modeling

• Model of arm without effect of springs
• Ts4/(??n)
• ??n is the real part of poles
• Gp1500/(s210s)

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Spring Modeling

• Reran test and plotted arm displacement
• Frequency of oscillation is imaginary part
• Settling time is real part
• GDGDdcs/(s28s289)

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Spring Modeling

• Spring effect is instantaneous
• Springs have no steady state effect
• Behaves like differentiator
• GD0.42s/(s28s289)

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Spring and Arm Together

• Modeled as a minor loop disturbance
• Positive feedback because of increasing overshoot
  and settling time

Base transfer function remains unchanged
Actual Arm Position
Spring Displacement depends on base movement
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Model and Plant Comparison
Arm Model
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Model and Plant Comparison

• Plant Model
• os41.7 os37.4
• Ts1.12s Ts1.21s

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System Root Locus
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New Sample Rate

• For smooth operation of motor, ?s 6?c
• ?c 10.7rad/s Tc 0.587s
• Tsam max0.0978s
• Tsam chosen to be 0.1s
• Largest sample time spreads out root locus
• Complex poles and zeros dont affect response

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New Plant Root Locus
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Proportional Control

• KP 0.024
• Unloaded
• 0.27 OS
• ? 0.88
• Ts 1.1s
• KG 0.0099
• PM 70.5 deg
• GM 20.5dB
• Loaded
• 3.91 OS
• ? 0.72
• Ts 1.9s
• KG 0.074
• PM 72 deg
• GM 21dB

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PID Control
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PID Control

• KP 0.023
• KI 0.01
• KD 0.01
• Unloaded
• 0 OS
• ? 1
• Ts 1.1s
• PM 75 deg
• Loaded
• 3.3 OS
• ? 0.74
• Ts 1.8s
• PM 75 deg

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Lead Network

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

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Lead Network

• Gain of 0.06 should give Ts of 0.72s with 15OS

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Lead Network

• KP 0.09
• Gcz-0.458/z
• Unloaded
• OS 0
• ?1.0
• Ts 0.9s
• PM 75 deg
• GM 21.3 dB
• Loaded
• OS 0
• ?1.0
• Ts 1.1s
• PM 76 deg
• GM 22.2 dB

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Minor Loop With PI Control Diagram
Position
Velocity
PI Control
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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

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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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Observer Controller

• GC(s) Our Lead Network (0.2)(z - 0.458)/z
• GPEst(s) Plant Estimator (3.127z 2.246)/(z2
  - 1.368z 0.3679)
• GCO(s) Observer Compensator (Lead-Network
  Controller) (0.06)(z 0.4)/z

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Estimator Output
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• The Observer gave us no overshoot and a settling
  time of 0.9 seconds.

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Observer Controller With Disturbance Rejection
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Observer With Disturbance Rejection

• KDD 2
• GCO (z-0.4)/z
• No Load
• OS 9
• Ts 1.2s
• PM 63 deg
• Loaded
• OS 12
• Ts 1.4s
• PM 55 deg

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Comparison Of No Load Results
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Comparison Of Loaded Results
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Spring Inaccuracy
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Results
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2-DOF Arm Conclusions

• Observer works best if there is no need for
  disturbance rejection
• With disturbance rejection, observer was not
  better than classical controller methods
• Lead Network Controller proved to be the most
  effective overall for both loaded and unloaded
  conditions

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Inverted Arm Conclusions

• Encoder used was very accurate
• Results mildly are improved
• Useful if computational complexity is cheap

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Questions
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Root Locus with Graphical KProportional control
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Lead Network Root Locus
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Minor Loop Graphical Gain
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Minor Loop Bode Plot
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2-DOF Arm Configuration
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Inverted Arm Configuration
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2nd Order Step Response

• Proportional gain of 0.45
• O.S.46
• Ts0.58 s
• Tr0.06 s
• Tp0.14 s

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Q8 Acquisition Board Specs

• 14 bit A/D converter -10V
• - 1.22 mV resolution
• - Maximum conversion time 5.2µs
• - Maximum Sample Frequency 192kHz

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Q8 Acquisition Board Specs

• 12 bit D/A converter - 5V
• - 2.44 mV resolution
• - Slew rate 2.5V/µs
• - Max voltage change is from -5 to 5, or 10V
• - Max conversion time 4µs
• - Max sample frequency 250kHz