1. Educational Model of Control System
SYS Modern Control Engineering - Winter 2007
Educational Model of Control System
for Robot Arm
Team Members : Irena Karasik
Sylvain Ganter
Olivier Paultre
Jeong Ja Kong
TA : Wei Yang
Professor : Riadh Habash
- April 4th,

2. References
[1] Kok Kiong Tan and Han Leong Goh, “Development of a Mobile Spreadsheet-Based PID Control Simulation System”, IEEE Transaction on Education, PP , 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 , 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”

3. 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

4. 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

5. References
[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

6. 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

7. References
[5] Control of Manipulation Robots Interacting with Dynamic Environment: Implementation and Experiments

8. 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.

9. Team & Roles Start Topic Selection Role Assignment References Search
Irena Karasik (Model Analysis)
Sylvain Ganter (Controller Design)
Olivier Paultre (SIMULINK)
Jeong Ja Kong (Controller Design,
Leader)
Weekly
Meeting
Plant Modeling
Controllers Design
MATLAB Simulation
Educational Model
End

10. Steps Step3 Step1 Actuator + Process (Robot Arm) Step2 Controller GUI
Input
(Reference)
Output
(Arm Dynamics)
Controller
GUI
(Controller Gain Adjust)
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

11. Dynamic Model of Robot Arm
s(s+2)(s+40)(s+45)
G (s) =

12. Characteristics of Plant Model
State-space Model
| | | 1 |
| | | |
A = | | B = | 0 |
| | | 0 |
| | | 0 |
C = | | D = | 0 |

13. Characteristics of Plant Model
Location of Poles & Zeros

14. 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 = 

15. Characteristics of Plant Model
Controllability & Observability
det [Pc] = 3.9  10 9
 Process is controllable
det [Po] = 1
 Process is observable

16. Characteristics of Plant Model
Time Response & Frequency Response
Ts = 
P.O = 
Phase Margin = 87.8º

17. Design Criteria Settling Time, Ts  1.2 sec Maximum Overshoot,
P.O  20%
Phase Margin,
PM  45°

18. Controller Design Unity Feedback Control Ts = 80 sec P.O = 0 %
PM = -180°

19. Controller Design P Control
Settling time is several times greater than the desired value
Ts = 4.26 sec
P.O = 20 %
PM = 79.7 °

20. Controller Design PI Control Settling time is still too large
Ts = 4.25 sec
P.O = 20 %
PM = 77.3 °

21. Controller Design PD Control
Settling time is better, but still does not meet our criteria
Ts = 1.43 sec
P.O = 20 %
PM = 96.7 °

22. Controller Design PID Control
Settling time is better, but still does not meet our criteria
Ts = 1.75 sec
P.O = 20 %
PM = 69.1 °

23. Controller Design Phase Lead Compensator Ts = .84 sec P.O = 20 %
PM = 45 °
meets our design criteria

24. (Loop Transfer function)
Controller Design
Phase Lead Compensator (Continued)
Open loop
(Loop Transfer function)
Closed-loop

25. Educational GUI Design

26. Open-Loop Response

27. Closed-Loop Response Input Selection Controller Selection Output Scope
Root-Locus
Drawing
Scope
Selection
Controllability
& Observability
Check
Comparison
Between Controllers
Pole-zero
& Others
Bode
Plot

28. Closed-Loop Response

29. System Analysis (Pole-zero Map, Root-locus, Bode Plot )

30. Controller Selection & Parameter Change

31. Comparison Between 2 Controllers

32. System Output Analysis

33. 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 !

34. Challenge To Model the Robot-Arm System
To find out more interacting educational Model
To provide more Visual Learning
To add more controllers