Template for the Storyboard stage

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Mention what will be your animation medium: 2D or 3DMention the software to be used for animation development: JAVA, Flash, Blender, Shikav, Maya..etc

Animation Medium : 2D

Software : JAVA

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Title of the concept, subject. Name of the author

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ROBOT DYNAMICS & CONTROLSUBJECT : MECHANICAL ENGINEERING

NAME: PROF P S GANDHI

Definitions of the keywords used in the animation 6

1.PID Controller Simulation

2. Regulation

3. Tracking

PID Controller : Combining all three modes of control(proportional, integral and derivative) enables a controller to be produced which has no offset error and reduces the tendency for oscillations.

Regulation : User Select two point (if non interactive: point is already specified) and robot takes end effector from one point to another in two three different ways without bothering about path to go from A to BTracking : User selects two points and robot takes end effector from one point to another in a straight line (specified) fashion. Or one point is considered centre and another on the circle that the end effector draws.

PID ControllerLet us consider the Close Loop System

Where,

Plant: A system to be controlled

Controller: Provides the excitation for the plant; Designed to control the overall system behavior

Controller Plant+ -

R e u Y

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- The transfer function of the PID controller looks like the following:

Kp = Proportional gain KI = Integral gain Kd = Derivative gain

- The variable (e) represents the tracking error, the difference between the desired input value (R) and the actual output (Y). This error signal (e) will be sent to the PID controller, and the controller computes both the derivative and the integral of this error signal. The signal (u) just past the controller is now equal to the proportional gain (Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the derivative gain (Kd) times the derivative of the error.

- This signal (u) will be sent to the plant, and the new output (Y) will be obtained. This new output (Y) will be sent back to the sensor again to find the new error signal (e). The controller takes this new error signal and computes its derivative and its integral again. This process goes on and on.

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sKKsKsK

sKK IPD

DI

P

2

dtdeKedtKeKu DIP

The Close Loop System with PID Control

Where, KP : Proportional GainKD: Derivative GainKI: Integral Gain

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Describe the concept chosen and clearly illustrate how you want to explain the concept in the animation.

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1. To explain how PID Controller controls manipulator ( Slides 11 to 15) - As gain is varied animation can display how the robot links along with end effector will behave. Graph on the simulation window can be generated as the robot motion evolving in time. Interactive version: Users can change the PID gains, robot parameters interactively and observe the variation in the behavior.

2. Regulation : End effector can reach target through different paths (Slide 18) - User Select two point (if non interactive: point is already specified) and robot takes end effector from one point to another in two three different ways without bothering about path to go from A to B

3. Tracking : End Effector can follow specified path (Slide 19) - User selects two points and robot takes end effector from one point to another in a straight line (specified) fashion. Or one point is considered centre and another on the circle that the end effector draws.

Let 2DOF manipulator shown below required to move from position 1 to position 2.

In this case if we use different gains we will get different outputs, which we want to demonstrate.

1

2

X

Y

Manipulator

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For example, if we give only proportional gain, then manipulator will not reached to its desired position. It will start vibrating there as like shown below

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2

X

Y

Manipulator

X

Y

Fig: Manipulator at initial position, Position 2 => desired output

Fig: Output due to proportional gain alone 12

When the input is proportional and derivative gain, then it will stop vibrating but there will be some offset between position of end effector & desired position 2.

2

X

Y

Fig.: PD Output ( Steady State offset)

Steady State Error

time

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If we use PID controller then it will not vibrate not even there will be any offset in position. It will reached to its desired position.

2

X

Y

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-(a) => given Position of manipulator-(b) => if press P (vibration)-(c ) => if press PD (no vibration but offset)-(d) => if press PID (no vibration & offset)

Brief:

(a)

(b) (c)

(d) 15

Plots If use PD Controller, there will always be some offset. Here for different derivative gains we can show its output

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The variation with integral gain can also be plot. Here user will specified specific value.

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RegulationRegulation : User Select two point (if non interactive: point is already specified) and robot takes end effector from one point to another in two three different ways without bothering about path to go from A to B

2

1

X

Y1 2 & => User Defined Positions

A => manipulator end effector moves from 1 to 2 through path AB => same manipulator end effector moves from 1 to 2 through path B

Ie. One manipulator can take number of paths to reached desired target.

AB

=> Path B=> Path A

Note: It is single manipulator following different paths to reach same targets

Figure =>

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TrackingTracking: User selects two points and robot takes end effector from one point to another in a straight line (specified) fashion. Or one point is considered centre and another on the circle that the end effector draws.

2

1

X

Y

θ1θ1' θ2

θ2'

X

Y

θ1θ2

CASE I CASE IICase I => User Define any two points (let 1 & 2) then manipulator end effector will move from 1 to 2 through straight line by adjusting angles θ1 & θ2Case II=> manipulator end effector will move along circumference of circle by adjusting angles θ1 & θ2Note: Points and circle are within reachable workplace

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List out user interactions that will be there to enhance the understanding of the concept in the animation.

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1. User can able to see how different gains have different output.2. If we combine all gains like proportional, derivative and integral then

how the system performed?3. In slide 15, as mentioned the three press buttons indicates the

activation of required gain. User will simply press it with the mouse click and then can able to see its output through animation.

4. Regulation: case 1: manipulator is showing on desktop with given link and joint parameters. user can select any two points on desktop. If points are within reachable workspace then manipulator will work as like explained in slides. Case 2: If points are not within workspace then there should be certain option to ask for changing link parameters to bring points within workspace.

5. Tracking: user will select two points or required path. Manipulator will follow that path. As explained in slide ie either straight line or circular etc

A small questionnaire with answers based on the concept. 21

After going thru this animation, the viewer should be able to answer simple questions like:

1) What is PID controller?A) Proportional Integral Derivative (Slide 7 to 9)

2) What will be the output if only proportional controller implements?

A) Vibration (slide 12)

3) What will be the output if only proportional & Derivative controller implements?

A) Steady state offset (Slide 13)

4) What is Regulation?A) Slide No. : 18

5) What is Tracking?A) Slide No. : 19

Links for further reading/references 22

1. http://nptel.iitm.ac.in/ - link : - NPTEL courses>>Mechanical Engg.>>

Robotics(web)>>course content>> Robot Dynamics and control (Lecture 33)

1. http://decibel.ni.com/content/docs/DOC-2781

1. http://www.engin.umich.edu/group/ctm/PID/PID.html

Further User Specification23

1. Audio support required.2. Colour changes to be shown.4. Clear Demonstration of PID Controller output on manipulator5. Plots for different gains.6. Theory will come in the left panel of the animation or in response to pressing a 'Theory' button.7. Keywords should come in 'Glossary' section.8. 'Help' button should give stepwise instruction of how to operate the animation. (User Friendly Desktop)