Download - 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
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Objectives
Determination of Plant ModelFast System ResponseWide Command Range (± 90 degrees)High Stability Margin (GM, PM)User-friendly Software InterfaceLow Resonant Frequency Mode with New Arm
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Equipment List
200 MHz Pentium-based computerQuanser 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 velocityPercent Overshoot = 0 %Steady-State Error = ± 2 degrees Phase Margin 70 degrees
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Functional Description
Positioning
Figure 1 - Input/Output Description
Command Input
Small Scale Robotic Arm
Control
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Functional Description
Software InterfacePositioning
Modes of Operation
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Block Diagram
System (Plant)Software
Figure 2 - Block Diagram of Robotic Arm
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System Parameters
System (Plant) Amplifier 5 [V] @ 3 [A] Position Sensor 180 of travel DC motor 5 [V] External Gears 5:1 velocity reduction Internal Gears 14.1:1 velocity reduction Antialiasing Filter first-order low-pass with pole @ 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 ResultsOpen-loop ResultsPlant 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
k=0.025 D/A GpR=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
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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
Plant Gp = k[a/(s+a)2]c(t) = k[1-e-at - at(e-at)]
@ k = 1.0 and t = 2.86 seconds, c = 11.352° Double Pole @ a = -0.76
Pole Identification using Laplace Transform
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System Identification
TypicalOpen-loop
Poles
Figure 6 – Second Order System (Poles = -0.76)
ActualOpen-loop
Double Pole
-0.76
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System Identification
Plant Model Equation:
27e-0.0562s
(s/0.76 + 1) 2
(OPEN-LOOP)
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System Identification
20.48º
Figure 7 - SIMULINK Scope Output for Open-loop System = 20.48º
Plant Model Verification
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System Identification
8.38º
Figure 8 - SIMULINK Scope Output for Closed-loop System = 8.38º
Plant Model Verification
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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 OutputFigure 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 OutputFigure 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
(a) With Friction (b) Without Friction
Figure 22(a-b) – Friction Characteristics for Pendulum System
-B/2J
PENDULUM
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System Limitations
Figure 23 - Closed-loop Time Delay and % Overshoot Calculations for Varying Gain k
Tdavg = 56.2 [ms]
Time Delay Gain k Percent Overshoot Time Delay (Td) 0.01 0.64 % 80 ms 0.015 0.76 % 66 ms 0.02 0.91 % 80 ms 0.025 2.29 % 57 ms 0.03 10.45 % 58 ms 0.035 8.07 % 19 ms 0.04 28.00 % 50 ms 0.045 26.70 % 47 ms 0.05 33.48 % 48 ms
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Conclusion
PI Controller is slowPID Controller does not workSolution 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?