Feedback Control in Ball Beam Dynamics

- Experimenting Delay Effects

Benjamin Gertner

Framingham High School

Mike Wilson

Beverly High school

Professor Rifat SipahiNortheastern University

Young Scholars Program, Northeastern University

Background & Terminology

What is “feedback control” ?

Sensors

Stability / Instability

Cruise Control

Block Diagram Convention (Controlled)

Controller

Plant

DesiredSpeed

Comparator

Actual Speed

Feedback

Errorsignal

Controlsignal

Sensor(Encoder)

DC Motor

Block Diagram Convention (Uncontrolled)

Controller

Plant

DesiredSpeed

Comparator

Actual Speed

Feedback

Errorsignal

Controlsignal

Sensor(Encoder)

DC Motor

Block Diagram—Motor (PID Controller)

Voltage

Scope

Saturation

RPM Error

RPM

Position Error

Integrator1s

Gain 3

1

Gain 22

Gain 1

1

Gain

-0.001533980787886 *60 /2/pi

Encoder Input

National InstrumentsNIM ENC

Derivativew/ filter

50s

s+50

Derivative

du /dt

Constant

20

Analog Output

National InstrumentsNIM DAC

Sensor (encoder)

Desired Speed 20 RPM

Controller

Speed Control of the Motor-Experiments

0 0.05 0.1 0.15 0.20

2

4

6

8

10

12

14

16

18

20

RP

M

Time [sec]

Speed Control with P-Controller. Desired = 20 RPM

0 0.05 0.1 0.15 0.20

2

4

6

8

10

12

14

16

18

20

Speed Control with PI-Controller. Desired = 20 RPM

RP

M

Time [sec]

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time [sec]

Pos

ition

[rad

]

Position Tracking with P-Controller, Red = Actual, Blue = Desired

Position Control of the Motor- Experiments

0 5 10 15-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time [sec]

Pos

ition

[rad

]

Position Tracking with PID-Controller, Red = Actual, Blue = Desired

Error = ±15°!! Error = ±3°

No Delay – Ball At Start

Introduction to Ball Beam Dynamics

What is Delay and Where is it?

Time that it takes to receive a signal

Where:Remote surgery Human reaction delaysChemical processesRoboticsTele-operationMissiles and targetsLight delay (circuits, all electronics)

Delay Effects

How would you implement delay?Why does delay lead to instability?Compensation of undesirable effects

Wait before you act (observe trends)Be less aggressive when compensatingAdvanced controller development (research)

Block Diagram—Ball Beam Dynamics

SRV02 - Experiment #3BB01 - Ball & Beam

Double PV Controller : Experiment vs . SimulationRun: Setup _SRV02_Exp3

error

delay

VariableTransport Delay

To

Theta D

Theta

Step3

Step 2

Step 1

Step

SimulatedBall Position

SRV02 Closed Loop

Theta D Theta

Radiansto Degrees

R2D

Radiansto Degrees

R2D

PhysicalLimitationof Beam

Outer Loop Kp

Kp _bb

Outer Loop Kd

Kv_bb

Offset in Degrees

56

Must Opertatein LinearRegion

Derivativew/ filter

20s

s+20

Delay 1

0

Degrees toRadians

D2R

Command in

centimeters

5

Calibrate Postion to read in centimeters

(-20 to 20 )

-L*2.54 /10

Ball Positionin centimeters

Ball & Beam Simulation

x_d x

Aplha to Theta

L/r

Analog Input

National InstrumentsNIM ADC

0.2 Second Delay– Ball At Start

Delay—Graph

0 1 2 3 4 5 6 7 8 9 10-20

-15

-10

-5

0

5

10

15

Time (sec)

Posit

ion (c

m)

Delay effect from start

.2 secondsNo delay

Kv_bb=.006 Kp_bb=.01

No Delay – Ball At Equilibrium

0.1 Second Delay– Ball At Equilibrium

0.2 Second Delay– Ball Equilibrium

Max Delay for Kv_bb

Kv_bb

Del

ay

0 5 10 15-6

-4

-2

0

2

4

6

8

Time (sec)

Posit

ion (c

m)

.1 Second Delay

0 5 10 15

-6

-4

-2

0

2

4

6

8

Time (sec)

Posit

ion (c

m)

.2 Second Delay

0 5 10 15-10

-5

0

5

10

15

Time (sec)

Posit

ion (c

m)

.3 Second Delay

Getting Better

OptimizationEnergy efficientQuickest resultSafest voltage

Improving the ControllerNew degrees of freedom—P, PI, PID controllersHave the computer guess—Penalize the guess

Gain, Too Much of a good thing?Kp=1, Kp=1000

Thank you