Ada Msp Id Me 451

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PID controls in

ADAMS/ViewBy,Makarand Datar

ME 451, Spring 09

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Building the model

The model consists

of two cylindricalparts and 2 joints.The ste s for

building the modelare described in thesubsequent slides.The final modelshould like thissnapshot.

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Building the model: Parts

Turn on the Coordinate Window

(View Coordinate Window)

e ec e u cy n er oo romthe ridig body tool stack in theMainToolbox

Build the outer cylinder (OC) byselecting (0,0,0) as the start point

and (400,400,0) as the end point

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To build the inner cylinder (IC),

again select the Cylinder tool asbefore

Building the model: Parts

box is checked and put the value ofradius to be 3.0 cm

Build the IC by selecting the

center of mass (CM) of the OC asthe starting point and(1000,1000,0) as the end point.

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Apply a Revolute Joint between the

OC and ground at (0,0,0) Before applying the joint, select the

o tions for the oint as shown here

Building the model: Joints

Apply a Translational Joint betweenthe OC and IC at the location ofCM of the OC

The direction of the Translational jointshould be along the lengths of the

cylinder

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Apply a motion on thetranslational joint

Right click the motion icon andpoint to modify

Change the function value for*

Building the model: Motions

Run a trial simulation to makesure that the IC movesoutwards. If not, put a ve

sign in the function value (-12* time)

Note: Do not worry aboutwhere the motion icon ispointing.

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Parts (total 2) OC [(0,0,0)(400,400,0)

IC [CMoc (1000,1000,0)]

oints (total 2)

Building the model: Check

Revolute between OCand ground

Translational between

OC and IC Motion (total 1)

On the translational

joint

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What are we trying to achieve?

Imagine that a torque is applied at the revolute

joint between OC and the ground. As the ICextends outwards, more and more torque needs tobe a lied at this oint to kee the model in the

same orientation. Thus, a PID controlled torque is applied at the

joint.

The change in location and change in velocity of themodel is sensed and a corrective action is taken byapplying an appropriately changing the magnitude of

the torque.

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Building Measures for PID controls

2 measures will be necessary

1. Measure for the angular displacement of the model

2. Measure for the angular velocity of the model

Measure

Create the above mentioned measures by selectingappropriate options

The details of this are on the next two slides alongwith the snapshots.

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Measure for Angular

Displacement Replicate the options

as shown on right


ou can c ange t emeasure name. Becareful to change onlythe highlighted part

(see figure) in themeasure name. Theinitial part is themodel name.

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Measure for Angular

Velocity Replicate the options

as shown on right


ou can c ange t emeasure name. Becareful to change onlythe highlighted part

(see figure) in themeasure name. Theinitial part is themodel name.

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Building the PID controls

Go to Build Controls Toolkit This will launch the Create Controls

Blockwindow as shown

Create Inputs for referencemeasures and actual measures

Calculate the error in the actual

measure by comparing it withreference input

Build the PID based on this error

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Create Input-Signals Three input signals will be created

1. Reference input for theAngular DisplacementandAngular Velocity (this value will be set to zero as ourgoal is to have the model maintain its orientation and

Angular Velocity)

2. Input for the actual measured value of theAngularDisplacement(this input will use the measure for

Angular Displacement that you previously created)3. Input for the actual measured value of theAngular

Velocity (this input will use the measure for Angular

Velocity that you previously created)

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Create Reference input

Click on the Create input signal block

icon Give some suitable name by only modifying

the highlighted area

Create Input-Signals

As the reference input represents an ideal(error free) signal, in our model this value iszero. Hence enter 0.0 * timein the functionblock

Note that we will use the same reference forboth the measures (angular displacementand angular velocity) as the value of

reference is zero in both the cases.

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Create input for angular displacement

Follow the same process as before tocreate a new input

But this time, the function value is not*


. .value ofAngular Displacementmeasurewhich was previously created

Delete everything from the function area

Click on the button next to the functionexpression bar. This will launch FunctionBuilderas shown on the next slide.

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Inside the function builder, select Measures in the

Getting Object Data drop down menu Right click in the bar next to the drop down and point

to Runtime_Measure Guess and then select the


measure t at you create or t e ngu ar sp acemen Once this is done, the Insert Object Name button

under the bar will be activated. Click this button andthen select OK to close the function builder

This will take you back to the Create Controls Blockwindow. Select OK or Apply to finalize the creationof this input signal

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Follow the same procedure as before to create the

third input signal forAngular Velocity measure


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Building the error signal

The next step is to calculate the error signal by

using (Reference Measured) format Error in Angular Displacement will be

.

Error in Angular Velocity will be

Reference Input Signal Input Signal for Angular Vel.

Also note that the Error in Angular Velocity is the firsttime derivative of Error in Angular Displacement

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Creating error signal for AngularDisplacement

To build the error signal, click on the CreateSumming Block button

Give some appropriate name


Right click in the bar of Input 1 and point tocontrols_input Guesses and select thereference input that you previously created

Click the + sign under the Input 2 to toggle it

to - Right click in the bar of Input 2 and point to

controls_input Guesses and select theAngular Displacement input that you previouslycreated and then select Apply

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Follow the same procedure to create a second

error signal for the Angular Velocity


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Creating the PID block Click on the Create PID block button

Give an appropriate name Right click in the bar under the Input and

point to controls_sum Guesses and select

that you previously created

Right click in the bar under the Derivative

Input and point to controls_sum Guesses

and select the error signal for the AngularVelocity that you previously created

Use the P Gain of 200000

Use the I Gain of 1

Use the D Gain of 5000 (select Apply to finish)

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Note that the values for the gains are guessed.

The required torque depends on the configurationof the system and part inertias. If the part inertiasare chan es one will need to ad ust the ain to

Creating the PID block

scale the torque accordingly

As a thumb rule, choose a high value for the gainsto that the mechanism is quickly stabilized (andwe achieve what we want to) and then adjust itlater to make finer changes

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Applying PID Torque to the model

Select the Torque from Applied Force

tool stack Make sure that the options are selected as

Apply this torque between the ground andOC at (0,0,0). (see the snapshot)

Hint: Pay

attention to thestatus bar for cues

while building thetorque

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Once the torque is applied, we need tomodify it so that it reads values from the

PID block that we created Right click the Torque icon and select

modify to launch the modify torque


window as shown

Delete everything from the functionexpression bar

Click on the button next to thefunction expression bar to launch the

Function Builder

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Inside thefunction builder, right click the bar next to Measures

(Getting Object Data) and point to Runtime_Measure Guessesand select the name of the PID controller that you previously created

Then click Insert Object Name and select OK


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Test the model The model is ready to be simulated

Run a trial simulation of 15 seconds with 500 steps and see

the behavior If instead of maintaining the position, the torque is causing

the model to uncontrollably rotate, that means the torque is

getting applied in the opposite direction Go back to modify torque and put a -ve sign in the torque

expression {for example -(.model_1.pid_1.pid_1)}

Rerun the simulation

Simulate unexpected scenarios like an object fallingon the model (say a tree branch) and check if themodel is able to take the corrective action. See the

two attached videos

Ada Msp Id Me 451

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