educational model of control system for robot arm team members : irena karasik sylvain ganter...
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Educational Model of Control System for Robot Arm
Team Members : Irena Karasik Sylvain Ganter Olivier Paultre Jeong Ja KongTA : Wei YangProfessor : Riadh Habash
- April 4th, 2007 -
SYS 5100 - Modern Control Engineering - Winter 2007
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References[1] Kok Kiong Tan and Han Leong Goh, “Development of a Mobile
Spreadsheet-Based PID Control Simulation System”, IEEE Transaction on Education, PP. 199-207, may 2006
[2] Guoguang Zhang and Junji Furusho, “Control of Robot Arms using Joint Torque Sensors”, IEEE Control Systems, pp.48-55, 1998
[3] Gloria Suh, Dae Sung Hyun, Jung Il Park, Ki Dong Lee, Suk Gyu Lee, “Design of a Pole Placement Controller for Reducing Oscillation and Settling Time in a Two-Inertia Motor System”, IECON’01:The 27th Annual Conference of the IEEE Industrial Electronics Society, pp.615-620, 2001
[4] Estico Rijanto, Antonio Moran and Minoru Hayase, “Experimental Positioning Control of Flexible Arm Using Two-Degrees-of-Freedom Controller”, p127
[5] Miomir K. Vukobratovic, Aleksandar D. Rodic, “Control of Manipulation Robots Interacting with Dynamic Environment: Implementation and Experiments”, IEEE Transactions on Industrial Electronics, Vol.42, No.4, August 1995
[6] Textbook : “Modern Control Theory”
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References[1] Development of a Mobile Spreadsheet-Based PID Control
Simulation System
- To control the Temperature of Thermal Chamber
- Mobile PID Tuning Preparatory Exercise - Mobile Spreadsheet Simulator
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References[2] Control of Robot Arms using Joint Torque Sensors
- Two-Inertia System Modeling - With Joint Torque Feedback - Dealt with Pole Assignment & Effect of Disturbance - ½ Bandwidth of resonance
frequency (PD Controller) - Identical Damping Coefficients ( 1 = 2 ) - A wider bandwidth and better
disturbance rejection over conventional PD
control
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[3] Design of a Pole Placement Controller for Reducing Oscillation and Settling Time in a Two-Inertia Motor System
- Identical Real Part settling time
- Comparison among 3 controller
I-P, I-PD, State Feedback control
- Conventional ITAE & Weighted ITAE - Full state feedback control is the best in terms of oscillation & settling
time
References
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References[4] Experimental Positioning Control of Flexible Arm Using Two-
Degrees-of-Freedom Controller Two Methods: * 2) is better
1) Feedback Control (frequency domain)
Based on Model matching
method using the inverse dynamics
of the arm system
2) Feed-forward Control (time domain)
Using the inverse dynamics of the non-minimum phase system of the arm
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References
[5] Control of Manipulation Robots Interacting with Dynamic Environment: Implementation and Experiments
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Our Goals
To design a control system for Robot Arm, To practice the control theories acquired in class, To provide an educational model of control
theories with Robot Arm model, To help the students understand the control
system theory and increase their interest in the subject matter.
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Team & Roles
Irena Karasik (Model Analysis) Sylvain Ganter (Controller Design) Olivier Paultre (SIMULINK) Jeong Ja Kong (Controller Design,
Leader)
Topic Selection
Role Assignment
References Search
Plant Modeling
Controllers Design
MATLAB Simulation
Educational Model
WeeklyMeeting
Start
End
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Actuator + Process(Robot Arm)
Output(Arm Dynamics)
(Controller Gain Adjust)
GUI
Controller
Input(Reference)
Step1
Step2
Step3
Step1 : Analysis of system characteristic (From the Dynamics of Robot Arm) Step2 : Controller Design (P, PI, PD, PID, Phase-Lead or -Lag Compensator) Step3 : Simulation (MATLAB) & User Interface Design (SIMULINK) Step4 : Evaluation of the performance of the Controlled system
Step3Steps
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250 . s(s+2)(s+40)(s+45)
G (s) =
Dynamic Model of Robot Arm
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Characteristics of Plant Model
State-space Model | -87 -1970 -3600 0 | | 1 |
| | | |A = | 1 0 0 0 | B = | 0 |
| | | | | 0 1 0 0 | | 0 |
| | | | | 0 0 1 0 | | 0 |
C = | 0 0 0 250 | D = | 0 |
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Location of Poles & Zeros
454
403
22
01
s
s
s
s
Characteristics of Plant Model
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Characteristics of Plant Model
Steady state error (Type ) Step Input :
ess= 0
Ramp Input : With unit ramp input,
Kv = lim sG(s) = .0694
ess = A/Kv =14.4
Parabolic Input :
ess =
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det [Pc] = 3.9 10 9
Process is controllable
det [Po] = 1
Process is observable
Controllability & Observability
Characteristics of Plant Model
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Characteristics of Plant Model Time Response & Frequency Response
Ts = P.O = Phase Margin = 87.8º
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Design Criteria
Settling Time,
Ts 1.2 sec Maximum Overshoot,
P.O 20% Phase Margin,
PM 45°
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Controller Design
4 3 2
250( )
87 1970 3600 250T s
s s s s
Unity Feedback Control
Ts = 80 secP.O = 0 %PM = -180°
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Controller Design
4 3 2
250( )
87 1970 3600 250
KpT s
s s s s Kp
Settling time is several times greater than the desired value
P Control
Ts = 4.26 secP.O = 20 %PM = 79.7 °
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Controller Design
5 4 3 2
250 * 250( )
87 1970 3600 250 * 250
Kp s KiT s
s s s s Kp s Ki
Settling time is still too large
PI Control
Ts = 4.25 secP.O = 20 %PM = 77.3 °
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Controller Design
4 3 2
250 * 250( )
87 1970 (3600 250 ) 250
Kd s KpT s
s s s Kd Kp
Settling time is better, but still does not meet our criteria
PD Control
Ts = 1.43 secP.O = 20 %PM = 96.7 °
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Controller Design
2
4 3 2
250 * 250 * 250( )
87 (1970 ) (3600 250 ) 250
Kd s Kp s KiT s
s s Kd s Kp s Ki
PID Control
Settling time is better, but still does not meet our criteria
Ts = 1.75 secP.O = 20 %PM = 69.1 °
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1088 3761( )
26.1c
sG s
s
Phase Lead Compensator
meets our design criteria
Ts = .84 secP.O = 20 %PM = 45 °
5 5
5 4 3 2 5 5
2.719*10 9.403*10( )
s 113.1 4241 55017 3.658*10 + 9.403*10
sT s
s s s
Controller Design
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Controller Design
Open loop
(Loop Transfer function)
Closed-loop
Phase Lead Compensator (Continued)
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Educational GUI Design
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Open-Loop Response
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Closed-Loop Response
InputSelection
ScopeSelection
Controller Selection
Controllability& Observability
Check
Root-LocusDrawing
OutputScope
BodePlot
ComparisonBetween Controllers Pole-zero
& Others
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Closed-Loop Response
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System Analysis(Pole-zero Map, Root-locus, Bode Plot )
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Controller Selection & Parameter Change
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Comparison Between 2 Controllers
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System Output Analysis
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Conclusion It is not possible to meet the design criteria with P, PI, PD, & PID
Controller of this Arm Model Controller Gain Change Effects on Both (Time, Overshoot)!
The Best Controller for this model is Phase-Lead Compensator.
Student can learn the Control theory easily: Parameter Change See the effect ! 2 Different Controllers Compare the effect !
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Challenge
To Model the Robot-Arm System
To find out more interacting educational Model
To provide more Visual Learning
To add more controllers