Small-Scale Robotic Arm

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Small-Scale Robotic Arm

• Senior Capstone Project
• Ben Boyle and Kitera Hayes
• Project Advisor Dr. Gary Dempsey
• April 29, 2004

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Outline

• Objectives
• Equipment List
• System Specifications
• Functional Description
• Block Diagram
• System Parameters
• System Identification
• Implementation of Controllers
• Flexible Rotary Joint
• System Limitations
• Conclusion
• Completed Tasks
• Questions

3
Objectives

• Determination of Plant Model
• Fast System Response
• Wide Command Range ( 90 degrees)
• High Stability Margin (GM, PM)
• User-friendly Software Interface
• Low Resonant Frequency Mode with New Arm

4
Equipment List

• 200 MHz Pentium-based computer
• Quanser System
• Robotic Arm with Flexible Rotary Joint
• Power Amplifier
• Software
• MATLAB (SIMULINK)
• Borland C

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Lab Workstation
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Robotic Arm
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System Specifications

• Command 90 set points, 40 deg/sec velocity
• Percent Overshoot 0
• Steady-State Error 2 degrees
• Phase Margin ? 70 degrees

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Functional Description
Positioning
Figure 1 - Input/Output Description
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Functional Description
Modes of Operation

• Software Interface
• Positioning

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Block Diagram
System (Plant)
Figure 2 - Block Diagram of Robotic Arm
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System Parameters

• System (Plant)
• Amplifier ? ?5 V _at_ 3 A
• Position Sensor ? ? ?180? of travel
• DC motor ? 5 V
• External Gears ? 51 velocity reduction
• Internal Gears ? 14.11 velocity reduction
• Antialiasing Filter ? first-order low-pass with
  pole _at_ 163 rad/sec
• Software
• 200 MHz PC
• A/D converter ? 12 bit plus sign, ?5 V
• D/A converter ? 12 bit, ?5 V

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System Identification

• Closed-loop Results
• Open-loop Results
• Plant Model Equation
• Plant Model Verification

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System Identification

• Closed-loop Results
• Gain k 0.025 ? Best Fit
• Close to 0 overshoot
• Step input of 20
• DC Gain
• Gp(0) 27/V

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System Identification
Controller Voltage (12)(.025) 0.295 V
DC Gain Gp(0) 8/0.295 V 27/V
Figure 3 DC Gain Calculation of System
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System Identification
Figure 4 - Gain k 0.025, Step input of 20,
Closed-loop (Experimental Results)
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System Identification

• Open-loop Results
• Verify DC gain of plant
• Calculate accurate time delay
• Help to determine plant model

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

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System Identification
Pole Identification using Laplace Transform

• Plant Gp ka/(sa)2
• c(t) k1-e-at - at(e-at)
• _at_ k 1.0 and t 2.86 seconds, c 11.352
• Double Pole _at_ a -0.76

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System Identification
Typical Open-loop Poles
Figure 6 Second Order System (Poles -0.76)
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System Identification

• Plant Model Equation

(OPEN-LOOP)
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System Identification
Plant Model Verification
20.48º
Figure 7 - SIMULINK Scope Output for Open-loop
System 20.48º
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System Identification
Plant Model Verification
8.38º
Figure 8 - SIMULINK Scope Output for Closed-loop
System 8.38º
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P Controller
Figure 9 - Theoretical P Controller Output
Figure 10 - P Controller System Output
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PI Controller
Figure 12 - PI Controller System Output
Figure 11 - Theoretical PI Controller Output
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PID Controller
Figure 13 - Theoretical PID Controller Output
Figure 14 - PID Controller System Output
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Feed-Forward/PI Controller
Figure 15 - Feed-Forward/PI Controller Block
Diagram
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Feed-Forward/PI Controller
Figure 16 - Theoretical FF/PI Controller Output
Figure 17 - FF/PI Controller System Output
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Controller Comparison
P Controller
FF/PI Controller
Figure 19 - FF/PI Controller System Output
Figure 18 - P Controller System Output
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Flexible Rotary Joint
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Flexible Rotary Joint
Figure 20 - P Controller System Output
Figure 21 - P Controller Flex Joint System Output
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System Limitations

• D/A Converter ? 5 V
• Static Friction
• Just matches the applied force to try and
  prevent motion
• Modeling ? Time delay e-std (linear)
• Kinetic Friction
• Moving friction with respect to speeds
• Inertia
• J (mass)(radius2)
• Gravity

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System Limitations
PENDULUM
-B/2J
(a) With Friction
(b) Without Friction
Figure 22(a-b) Friction Characteristics for
Pendulum System
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System Limitations
Time Delay
Tdavg 56.2 ms
Figure 23 - Closed-loop Time Delay and
Overshoot Calculations for Varying Gain k
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Conclusion

• PI Controller is slow
• PID Controller does not work
• Solution is FF/PI Controller

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Completed Tasks

• Plant Model and Validation
• Proportional, PI, and PID Controllers
• FF Controller with PI
• User-friendly Software Interface
• Future Work
• Plant Model for Flexible Rotary Joint
• Gripper Motor with Varying Loads
• Notch Filter Incorporation

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Questions?