for Robot Arm

loutclankedIA et Robotique

13 nov. 2013 (il y a 5 années et 2 mois)

233 vue(s)

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 4
th
, 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 27
th

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

Weekly

Meeting

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

Step3

Steps




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

45
4
40
3
2
2
0
1







s
s
s
s
Characteristics of Plant Model

Characteristics of Plant Model


Steady state error (Type

)


Step Input :


e
ss
= 0


Ramp Input : With unit ramp input,


Kv = lim sG(s) = .0694


e
ss
= A/Kv =14.4


Parabolic Input :


e
ss
=





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 = 87.8
º

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 250
T s
s s s s

   

Unity Feedback Control

Ts = 80 sec

P.O = 0 %

PM =
-
180
°

Controller Design

4 3 2
250
( )
87 1970 3600 250
Kp
T s
s s s s Kp

   
Settling time is
several times
greater than the
desired value


P Control

Ts = 4.26 sec

P.O = 20 %

PM = 79.7
°

Controller Design

5 4 3 2
250 * 250
( )
87 1970 3600 250 * 250
Kp s Ki
T s
s s s s Kp s Ki


    
Settling time
is still too
large


PI Control

Ts = 4.25 sec

P.O = 20 %

PM = 77.3
°

Controller Design

4 3 2
250 * 250
( )
87 1970 (3600 250 ) 250
Kd s Kp
T s
s s s Kd Kp


    
Settling time is better,
but still does not meet
our criteria


PD Control

Ts = 1.43 sec

P.O = 20 %

PM = 96.7
°

Controller Design

2
4 3 2
250 * 250 * 250
( )
87 (1970 ) (3600 250 ) 250
Kd s Kp s Ki
T s
s s Kd s Kp s Ki
 

     

PID Control

Settling time is better,
but still does not meet
our criteria

Ts = 1.75 sec

P.O = 20 %

PM = 69.1
°

1088 3761
( )
26.1
c
s
G s
s




Phase Lead Compensator

meet
s

our
design
criteria

Ts = .84 sec

P.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
s
T 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

Input

Selection

Scope

Selection

Controller

Selection

Controllability

& Observability

Check

Root
-
Locus

Drawing

Output

Scope

Bode

Plot

Comparison

Between 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