ECE 496 Pendubot Design Group A

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ECE 496Pendubot DesignGroup A
David Barron, Todd Parfitt, John Robbins, John
Rose, and Luke Walters
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The Creature

• Mechatronic System
• 2 Links, DC Motor, PC, Encoders, Interface Board
• Inverted Pendulum
• Control Feedback Loop
• Angular Position
• Output Torque

3
Overview

• Specifications and System
• John Rose
• Mechanical Design / Fabrication
• David Barron
• Mathematical Model
• John Robbins
• Software
• Luke Walters
• Conclusion
• Todd Parfitt

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Specifications

• DC Motor
• Linear Amp Provided
• Mechanical Links
• 18 in. in Length
• Golf Ball Mounted On Link 2
• Sensors
• Measure Position
• No Manufactured Pos. Control Devices

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System

• Mechanical Links
• Link 1
• Link 2
• Encoders
• Rotary Optical Encoders (Gurley Precision)
• DC Motor
• Dayton -1hp, 24V
• Linear Amp
• Server to Go
• Interface Hardware
• QMotor
• Control Program

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Grainger Motor

• Motor Type Permanent Magnet DC
• HP 1
• RPM 1800
• Voltage (DC) 24
• Full Load Amps 39.0
• Rotation CW/CCW

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Amplifier Power Output
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ENCODERSGurley PrecisionInstruments

• Motion Type Rotary
• Usage Grade Light Industrial
• Output Incremental
• Max Resolution 1,800 counts/rev.

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Aluminum Links
Link 2
Link 1

• 1 x 5/8 in Aluminum Bar Stoke
• Milled Slots

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Properties of the Links

• Link 1 with Encoder
• Dimensions (mm) X 495.300
  Y 25.4000 Z
  15.8000
• Centroid (mm)
• X 278.666 Y 12.7000
  Z 10.4693
• Mass (kg)
• 0.3944

• Link 2 with Ball
• Dimensions X 469.900
  Y 25.4000 Z 15.8000
• Centroid X 331.628
  Y 12.7000 Z 7.90000
• Mass (kg)
• 0.3374

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Mathematical Overview

• The math provided for this system is as follows
• This equation is in the Euler-Lagrange format.

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Math continued

• After some manipulation the form is changed to a
  state oriented equation
• The output of this system may be defined as
• y Cx Du

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Math continued

• Another perspective
• Dynamics equations for a two link / two motor
  system.

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How do we find the solution?

• The solution can be found via matrix
  manipulation. The equations required are
  outlined in the 409 control text.
• Mat Lab has a command called Linear Quadratic
  Regulator that can automate the solution process.

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The abbreviated version

• If we let
• And we define

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The abbreviated version

• Such that
• The solution is found via the Algebraic Racacati
  Equation

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Ultimately
This K represents the gain values for the
controller.
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SOFTWARE DEVELOPMENT

• Swing Up
• Open Loop
• Prototype 1
• Based on mathematical model
• Prototype 2
• Altered code to assist catch characteristics
• Prototype 3
• Case based sign adjustment

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Swing Up

• Control
• Output swing back torque to motor
• Hold torque until swing back time limit
• Apply forward swing up torque
• Zero out torque when angle limit reached

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Prototype 1
Control Loop Output 5V on Channel 1 to power
encoders Read Link1 and Link2 encoders
Convert encoder values to radians Calculate
angular velocity of Link1 and Link2 Filter
velocities to eliminate high freq noise
continued
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Multiply Link 12 positions and velocities by
separate gains Sum the
products and multiply by tunable scalar Output
the calculated value to amplifier i.e. Vout
scalar ( k1q1 k2q2 k3V1 k4V2)
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Observations of Prototype 1

• Pendubot would not catch and return to zero
• After using Matlab k-values and exhaustive
  tweaking, no success

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Prototype 2
Control Loop Output 5V on Channel 1 to power
encoders Read Link1 and Link2 encoders
Convert encoder values to radians Calculate
angular velocity of Link1 and Link2 Filter
velocities to eliminate high frequency noise
Sum Link 1 and Link 2 Positions MPY Link 12
positions, velocities, sum by gains Sum the
products and multiply by tunable scalar Output
the calculated value to amplifier i.e.
Vout scalar ( k1q1 k2q2 k3V1 k4V2
k5angSum)
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Reasoning
Observe
T1 gt 0 T2 lt 0 T2 gt T1 Therefore T2 T1 lt
0 Torque is negative Vout .k5Sum)
L2
T2
T1
L1
Torque
MOTOR
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Reasoning
Observe
T1 gt 0 T2 gt 0 Therefore T2 T1 gt 0 Torque is
positive Vout k5Sum)
T2
T1
L2
L1
Torque
MOTOR
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Observations of Prototype 2

• Somewhat smoother control
• Helped to catch but not return to home
• Conflicted with mathematical model

T2
L2
T1
L1
T1 T2 0
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Prototype 3
Control Loop Output 5V on Channel 1 to power
encoders Read Link1 and Link2 encoders
Convert encoder values to radians Calculate
angular velocity of Link1 and Link2 Filter
velocities to eliminate high frequency noise
Sum Link 1 and Link 2 Positions If (sign of sum
is opposite that of Link1 Position) then flip
sign of Link1 Position i.e. Vout scalar(
-k1q1 k2q2 k3V1 K4V2 ) Sum the
products and multiply by tunable scalar Output
the calculated value to amplifier i.e.
Vout scalar ( k1q1 k2q2 k3V1
k4V2)
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Observations of Prototype 3

• Very unstable, too fudged
• Still could not find a set of gains that worked

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What did we learn?

• Adapting to the unfamiliar
• Interfacing devices
• Encoder use
• Motor reactions

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What would we do differently?

• Bearings at joint of links
• Flame harden joint hole
• Parts made by manufacturer
• High voltage, low current motor