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

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”

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

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

[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

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

References

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

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.

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

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

250 . s(s+2)(s+40)(s+45)

G (s) =

Dynamic Model of Robot Arm

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 |

Location of Poles & Zeros

454

403

22

01

s

s

s

s

Characteristics of Plant Model

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 =

det [Pc] = 3.9 10 9

Process is controllable

det [Po] = 1

Process is observable

Controllability & Observability

Characteristics of Plant Model

Characteristics of Plant Model Time Response & Frequency Response

Ts = P.O = Phase Margin = 87.8º

Design Criteria

Settling Time,

Ts 1.2 sec Maximum Overshoot,

P.O 20% Phase Margin,

PM 45°

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°

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 °

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 °

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 °

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 °

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

Controller Design

Open loop

(Loop Transfer function)

Closed-loop

Phase Lead Compensator (Continued)

Educational GUI Design

Open-Loop Response

Closed-Loop Response

InputSelection

ScopeSelection

Controller Selection

Controllability& Observability

Check

Root-LocusDrawing

OutputScope

BodePlot

ComparisonBetween Controllers Pole-zero

& Others

Closed-Loop Response

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

Controller Selection & Parameter Change

Comparison Between 2 Controllers

System Output Analysis

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 !

Challenge

To Model the Robot-Arm System

To find out more interacting educational Model

To provide more Visual Learning

To add more controllers